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Record for a UF thesis. Title & abstract won't display until thesis is accessible after 2010-05-31.

Permanent Link: http://ufdc.ufl.edu/UFE0022017/00001

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Title: Record for a UF thesis. Title & abstract won't display until thesis is accessible after 2010-05-31.
Physical Description: Book
Language: english
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

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Subjects / Keywords: Design, Construction, and Planning -- Dissertations, Academic -- UF
Genre: Design, Construction, and Planning thesis, Ph.D.
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theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
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Electronic Thesis or Dissertation

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Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Issa, R. Raymond.
Local: Co-adviser: Flood, Ian.
Electronic Access: INACCESSIBLE UNTIL 2010-05-31

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Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022017:00001

Permanent Link: http://ufdc.ufl.edu/UFE0022017/00001

Material Information

Title: Record for a UF thesis. Title & abstract won't display until thesis is accessible after 2010-05-31.
Physical Description: Book
Language: english
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: Design, Construction, and Planning -- Dissertations, Academic -- UF
Genre: Design, Construction, and Planning thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Issa, R. Raymond.
Local: Co-adviser: Flood, Ian.
Electronic Access: INACCESSIBLE UNTIL 2010-05-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022017:00001


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1 SYSTEMS THEORY BASED METHOD FO R CONSTRUCTION PROJECT PLANNING By WEN LIU A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2008

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2 2008 Wen Liu

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3 To my husband, Zhen Zhao; my son, Daniel Zhao; and my parents, Ying Fan and Xiqing Liu.

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4 ACKNOWLEDGMENTS I would like to gratefu lly and sincerely thank Dr. Ian Fl ood and Dr. Raymond Issa for their guidance, understanding, patie nce and encouragement during my graduate studies at Rinker School. Dr. Floods insightful comments and constr uctive suggestions at di fferent stages of my research were essential to the completion of this dissertation. He has also taught me innumerable lessons on the workings of academic research in general. Dr. Issa has spent many hours reading this work and given me a lot of editorial advi ce. His mentorship was paramount in providing a well-rounded experience consistent with my long-term career goals. My thanks also go to Dr. Robert Cox at the Purdue University, who came all the way from Indiana to attend my final defense. I am also indebted to the School of Technol ogy at Michigan Tech, for the opportunity to work in the Department of Construction Manage ment during the period of my doctoral studies. Special thanks to Dr. Scott Amos, Dean of th e School of Technology, who understood the nature of the doctoral endeavor and allowed me a lot of flexibility in the work schedule. Finally, and most importantly, I would like to thank Zhen Zhao, my husband and best friend, for his unwavering support and unconditioned love; and my parents, who had faith in me and provided continuous motivation.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........9 LIST OF FIGURES................................................................................................................ .......10 ABSTRACT....................................................................................................................... ............15 CHAPTER 1 INTRODUCTION..................................................................................................................17 1.1 Background................................................................................................................. ......17 1.2 Aim and Objectives......................................................................................................... .20 1.3 Methodology................................................................................................................ .....20 2 LITERATURE REVIEW.......................................................................................................22 2.1 Classification of Models...................................................................................................22 2.2 Bar Chart.................................................................................................................. .........24 2.3 Critical Path Method....................................................................................................... ..25 2.3.1 Deterministic Critical Path Method........................................................................25 2.3.2 Related Stochastic CPM Methods..........................................................................26 2.3 Line-of-Balance Method...................................................................................................28 2.4 Linear Scheduling Method...............................................................................................31 2.5 Simulation Methods......................................................................................................... .35 2.5.1 Discrete Simulation................................................................................................36 2.5.1.1 Three-phase approach..................................................................................37 2.5.1.2 Activity-scanning approach..........................................................................40 2.5.2 Continuous Simulation...........................................................................................44 2.6 Other Methods.............................................................................................................. ....45 3 CASE STUDIES WITH EXISTING METHODS.................................................................46 3.1 Case One: A Typical Regular Project...............................................................................48 3.1.1 The CPM Model.....................................................................................................48 3.1.1.1 Modeling of activities...................................................................................49 3.1.1.2 Modeling of dependency relationships........................................................52 3.1.1.3 Modeling of resources..................................................................................54 3.1.1.4 Modeling of other factors.............................................................................55 3.1.2 The STROBOSCOPE Simulation Model...............................................................55 3.2.1.1 Modeling of activities...................................................................................57 3.2.2.2 Modeling of dependency relationships........................................................57

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63.2.2.3 Modeling of resources..................................................................................60 3.2.2.4 Modeling of other factors.............................................................................61 3.1.3 Summary of Modeling Regular Projects................................................................62 3.2 Case Two: A Typical Linear Project................................................................................64 3.2.1 The LSM Model.....................................................................................................67 3.2.1.1 Modeling of activities...................................................................................69 3.2.1.2 Modeling of dependency relationships........................................................71 3.2.1.3 Modeling of resources..................................................................................71 3.2.1.4 Modeling of other factors.............................................................................71 3.2.2 The Continuous Simulation Model........................................................................72 3.2.2.1 Modeling of activities...................................................................................74 3.2.2.2 Modeling of dependency relationships........................................................75 3.2.2.3 Modeling of resources..................................................................................76 3.2.2.4 Modeling of other factors.............................................................................76 3.2.3 More on Linear Projects.........................................................................................76 3.2.4 Summary of Modeli ng Linear Projects..................................................................79 3.3 Case Three: A Typical Repetitive Project........................................................................79 3.3.1 The CPM Model.....................................................................................................81 3.3.1.1 Efficiency.....................................................................................................81 3.3.1.2 Resource-imposed dependency relationships...............................................82 3.3.2 The LSM Model.....................................................................................................83 3.3.3 The Simulation Model............................................................................................88 3.3.3.1 Efficiency.....................................................................................................89 3.3.3.2 Resource-imposed dependency relationships...............................................89 3.3.3.3 Hetero-relationships.....................................................................................90 3.3.4 Summary of Modeling Repetitive Projects............................................................91 3.4 Case Four: A Project of Mixed Features..........................................................................91 3.4.1 Integration of discrete and continuous activities....................................................98 3.4.2 Integration of repetitive a nd non-repetitive activities............................................99 3.4.3 Summary of Modeling Repetitive Projects..........................................................101 4 REQUIREMENT ANALYSIS.............................................................................................102 4.1 Scope of Application......................................................................................................102 4.2 Accuracy of Modeling....................................................................................................104 4.3 Form of Representation..................................................................................................107 4.4 Levels of Modeling.........................................................................................................109 5 A NEW THEORY FOR PLANNING AND SCHEDULING CONSTRUCTION PROJECTS....................................................................................................................... ....111 5.1 Theoretical Foundations.................................................................................................111 5.1.1 System Theory......................................................................................................111 5.1.2 The DEVS Formalism..........................................................................................113 5.2 The Proposed Theory......................................................................................................117 5.2.1 Atomic Activity Models.......................................................................................117 5.2.1.1 Non-resource-driven discrete models.........................................................117

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75.2.1.2 A simulation of a non-resource-driven discrete model..............................125 5.2.1.3 Resource-driven discrete models...............................................................129 5.2.1.4 Continuous models.....................................................................................132 5.2.2 Compound Activity Models.................................................................................136 5.2.2.1 Compound discrete non-re source-driven models.......................................136 5.2.2.2 Compound discrete resource-driven models..............................................138 5.2.2.3 Compound continuous models...................................................................139 5.2.3 Resource Models..................................................................................................140 5.2.4 Models for Environmental Factors.......................................................................142 6 MODELING ELEMENTS AND MODELING RULES.....................................................143 6.1 Basic Components..........................................................................................................143 6.1.1 Discrete Activities................................................................................................143 6.1.2 Continuous Activities...........................................................................................146 6.1.3 Environmental Factors..........................................................................................150 6.1.4 Resources..............................................................................................................151 6.2 Links...................................................................................................................... .........152 6.2.1 Start Links and Finish Links.................................................................................152 6.2.1.1 FS, SS, SF, FF dependency relationships...................................................152 6.2.1.2 Progress-based depe ndency relationships..................................................153 6.2.1.3 Environmental factor imposed start/finish constraints...............................154 6.2.2 Interrupt Links and Resume Links.......................................................................155 6.2.2.1 Interruptions caused by other activities......................................................156 6.2.2.2 Interruptions caused by environmental factors..........................................157 6.2.3 Adjust Links.........................................................................................................159 6.2.3.1 Adjustments caused by other activities......................................................159 6.2.3.2 Adjustments caused by environmental factors...........................................162 6.2.4 Buffers..................................................................................................................163 6.2.4.1 Minimum buffers........................................................................................164 6.2.4.2 Maximum buffers.......................................................................................166 6.2.5 Combining the links.............................................................................................167 6.2.6 Branching of the links..........................................................................................168 6.2.7 Resource Links.....................................................................................................169 6.3 Compound Activities......................................................................................................171 6.3.1 Compound Discrete Activities.............................................................................172 6.3.2 Compound Continuous Activities........................................................................175 6.4 Repetitive Activities...................................................................................................... .176 6.4.1 Defining Repetitive Activities..............................................................................176 6.4.2 Assigning Resources............................................................................................179 6.4.3 Identification and Repeating of the Links............................................................182 7 CASE STUDIES WITH THE PROPOSED METHOD.......................................................185 7.1 Case One: A Typical Regular Project.............................................................................185 7.1.1 Modeling of Activities..........................................................................................185 7.1.1.1 Duration......................................................................................................185

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87.1.1.2 Progress curve............................................................................................187 7.1.1.3 Interruption and adjustment.......................................................................187 7.1.2 Modeling of dependency relationships.................................................................188 7.1.2.1 FS, SS, FF and SF dependency relationships.............................................188 7.1.2.2 Non-time based dependency relationships.................................................188 7.1.2.3 Compound constraints................................................................................188 7.1.3 Modeling of environmental factors......................................................................189 7.2 Case Two: A Typical Linear Project..............................................................................189 7.2.1 Modeling of Activities..........................................................................................190 7.2.1.1 Productivity................................................................................................190 7.2.1.2 Slow-down and break.................................................................................191 7.2.1.3 Positions of the activities............................................................................191 7.2.2 Modeling of Buffers.............................................................................................191 7.2.3 Modeling of Resources.........................................................................................192 7.2.4 Multi-level Modeling............................................................................................192 7.2.5 Multi-dimensional layouts....................................................................................193 7.3 Case Three: A Typical Repetitive Project......................................................................195 7.3.1 Efficiency.............................................................................................................195 7.3.2 Resource-imposed Constraints.............................................................................196 7.3.3 Hetero-relationships.............................................................................................197 7.4 Case Four: A Project with Mixed Features.....................................................................197 7.4.1 Integration of Discrete and Continuous Activities...............................................199 7.4.2 Integration of Repetitive a nd Non-repetitive Activities.......................................199 8 CONCLUSIONS AND RECOMMENDATIONS...............................................................201 8.1 Conclusions................................................................................................................ .....201 8.2 Limitations and Recommenda tions for Future Research................................................206 APPENDIX A FOUNDAMENTALS OF SIMULATION TECHNOLOGY B MODELING ELEMENTS OF THE PROPOSED METHOD.............................................217 LIST OF REFERENCES.............................................................................................................219 BIOGRAPHICAL SKETCH.......................................................................................................224

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9 LIST OF TABLES Table page 2-1 General Classifications of the ex isting planning and scheduling models..........................24 2-2 Comparison of the major di screte simulation techniques..................................................42 3-1 Modeling requirements for regular projects......................................................................63 3-2 Description of the pipeline constr uction project (Shi and Abourizk 1998).......................65 3-3 Resources available to the pipeline construction project...................................................65 3-5 Modeling requirements of repetitive projects....................................................................91 3-6 Modeling requirements for pr ojects with mixed features................................................101 4-1 Summary of the basic requirements in construction project planning and scheduling....105 8-1 Comparison of the modeling accuracy of the proposed method and major existing methods........................................................................................................................ ....202 8-2 Comparison of the representation effici ency of the proposed method and the major existing methods..............................................................................................................205

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10 LIST OF FIGURES Figure page 1-1 Conceptual framework of proposed universally applicable methodology........................19 2-1 Illustration of the LOB method..........................................................................................29 2-2 Standard format of linear scheduling diagram...................................................................33 3-1 The CPM model for Case One...........................................................................................47 3-2 Discrete represen tation of an activity................................................................................50 3-3 Adjustments of Activity As duration................................................................................52 3-4 The CPM representation of a nontime-based dependency relationship...........................53 3-5 The STROBOSCOPE model for Case One.......................................................................56 3-6 Representation of an SS dependency relationship.............................................................58 3-7 Representation of an FF dependency relationship.............................................................58 3-8 Representation of the AND logic...................................................................................59 3-9 Problems of discretizing c ontinuous activities and buffers...............................................66 3-10 The LSM model for Case Two..........................................................................................67 3-11 The LSM model for Case Two with a break......................................................................68 3-12 The LSM model for Case Two with a slow-down.............................................................68 3-13 SLAM II model for Case Two...........................................................................................73 3-14 Site layout of two intersecting utility lines........................................................................77 3-15 Part of the CPM model for Case Three..............................................................................81 3-16 The LSM model for Case Three........................................................................................85 3-17 Representation of the hetero-r elationship in the LSM diagram.........................................87 3-18 The STROBOSCOPE model for Case Three....................................................................88 3-19 Representation of the hetero relationships in STROBOSCOPE.....................................90 3-20 The CPM model for Case Four..........................................................................................92

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11 3-21 The LSM model for Case Four..........................................................................................95 3-22 The STROBOSCOPE model for Case Four......................................................................97 3-23 Integration of continuous a nd discrete activities in LSM..................................................98 3-24 Representation of a continuous buffer in STROBOSCOPE..............................................99 3-25 Integration of repetitive and non -repetitive activities in STROBOSCOPE.....................100 4-1 Scope of application...................................................................................................... ...103 5-1 Basic system concepts..................................................................................................... .112 5-2 Hierarchical construction of a system..............................................................................113 5-3 Behavior of the DEVS atomic model..............................................................................115 5-4 Non-resource-driven discrete Ac tivity A with many r ealistic factors.............................118 5-5 Progress curve of Activity A............................................................................................119 5-6 Non-resource-driven disc rete model of Activity A.........................................................119 5-7 Determining the progress during the progressing phase..............................................122 5-8 Simulation of Activity As Behavior...............................................................................126 5-9 Structure of the resource-d riven discrete activity model.................................................129 5-10 Structure of the continuous activity.................................................................................132 5-11 Process of a continuous activity.......................................................................................133 5-12 Example of the compound discre te non-resource-driven activity...................................137 5-13 Example of a compound disc rete resource-dr iven activity..............................................139 5-14 Structure of the resource model.......................................................................................140 5-15 Structure of the environmental factor model...................................................................142 6-1 Discrete Activity Node....................................................................................................144 6-2 Discrete activity dialogue window...................................................................................145 6-3 Continuous Activity Node...............................................................................................146 6-4 Continuous activity dialogue window.............................................................................147

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12 6-5 Determining activity positions on a one-dimensional layout..........................................148 6-6 Determining activity positions on a two-dimensional layout..........................................149 6-7 Defining the path of a continuous activity.......................................................................149 6-8 Environmental Facor Node..............................................................................................150 6-9 Environmental f actor dialogue window...........................................................................151 6-10 Resource Node............................................................................................................ .....151 6-11 FS, FF, SS, SF Links..................................................................................................... ...152 6-12 Example of an SS link.................................................................................................... ..153 6-13 Progress-based Link...................................................................................................... ...154 6-14 Example of a progres s-percentage-based link.................................................................154 6-15 Example of a work -quantity-based link...........................................................................154 6-16 Environmental-fact or-imposed constraint.......................................................................155 6-17 Example of an environmen tal-factor-imposed constraint................................................155 6-18 Interrupt and Resume Links.............................................................................................156 6-19 Network representation of interruptions and resumptions...............................................156 6-20 Interrupt lin k dialogue window........................................................................................156 6-21 Example of an environmen tal-factor-caused interruption...............................................157 6-22 Defining breaks in the interrupt link dialogue window...................................................158 6-23 Multiple interrupt/resume links on one activity...............................................................159 6-24 Adjust Link.............................................................................................................. ........159 6-25 Example of an adjustment................................................................................................160 6-26 Adding additional adjust links.........................................................................................161 6-27 Adjust link dialogue window...........................................................................................161 6-28 Example of an environmen tal-factor-caused adjustment.................................................162 6-29 Adjust link dialogue window for envi ronmental-factor-caused adjustments..................163

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13 6-31 Example of a minimum buffer.........................................................................................164 6-32 Defining a minimum buffer with the Slowdown option..............................................165 6-33 Defining a minimum buffer with the Break for option...........................................165 6-34 Defining a minimum buffer with the Break until option..........................................166 6-35 Example of a maximum buffer........................................................................................167 6-36 Illustration of the maximum buffer..................................................................................167 6-37 Representation of AND and OR logic......................................................................168 6-38 Example of a multi-layered constraint.............................................................................168 6-39 Branching Node........................................................................................................... ....169 6-40 Example of branching..................................................................................................... .169 6-41 Resource Link............................................................................................................ ......170 6-42 Example of resource links................................................................................................170 6-43 Compound Discrete Activity Node..................................................................................172 6-44 Defining a compound discrete activity by coupling........................................................172 6-45 Adding links to a compound discrete activity..................................................................173 6-46 Defining a progress-based li nk on a compound discrete activity....................................174 6-47 Defining a compound discrete activity by decomposition...............................................175 6-48 Compound Continuous Activity Node.............................................................................175 6-49 Example of a compound continuous activity..................................................................175 6-50 Adding links to compound continuous activities.............................................................176 6-51 Repetitive Activities.................................................................................................... .....177 6-52 Defining a repetitive discrete activity..............................................................................177 6-53 Example of a repetitive disc rete activity collapsed mode.............................................178 6-54 Defining a repetitive disc rete activity expanded mode.................................................178 6-55 Assigning resources to the repetit ive activity..................................................................179

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14 6-56 Resource-imposed sequencing in the repe titive activity: two crews proceed toward each other..................................................................................................................... ....180 6-57 Resource-imposed sequencing in the repe titive activitytwo crews in alternating units.......................................................................................................................... ........181 6-58 Identification of the link in the repetitive activity...........................................................182 6-59 Repetitive link with in a repetitive activity.......................................................................183 6-60 Repetitive link between repetitive activities....................................................................184 7-1 The proposed model for Case One...................................................................................186 7-2 Customizing a step wise progress curve...........................................................................187 7-3 Representation of the AND logic in the proposed method..........................................188 7-4 The proposed model for Case Two..................................................................................189 7-5 Defining the buffer between ROW and Stringing...........................................................191 7-6 Representing resource sharing.........................................................................................192 7-7 Site layout of storm drainage Segment D97-24-25..........................................................193 7-8 Modeling a project with multi-dimensional layout..........................................................194 7-9 Defining the path of an activity in a project with multi-dimensional layouts.................194 7-10 The proposed model for Case Three: one crew...............................................................195 7-11 The proposed model for Case Three: two crews.............................................................196 7-12 The proposed model for Case Thr ee: two crews in alternating units..............................197 7-13 The proposed model for Case Four..................................................................................198 7-14 The enlarged partial model for Case Four.......................................................................199 A-1 A dependent variable in a discrete simulation model......................................................215 A-2 A state variable in a continuous simulation model..........................................................215 A-3 Approximation of a state variable in a continuous simulation model using fixed time steps.......................................................................................................................... ........215

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15 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy SYSTEMS THEORY BASED METHOD FOR CONSTRUCTION PROJECT PLANNING By Wen Liu May 2008 Chair: R. Raymond Issa Cochair: Flood Ian Major: Design, Construction, and Planning A variety of methods have already been devel oped in the past for pl anning and scheduling construction projects, includi ng the CPM method, the LSM met hod and the simulation methods. One of the biggest problems with the existing met hods is that each of them has a limited scope of application, yet most construction projects ha ve mixed features that extend beyond the boundaries of the individual tools. Second, all of the existing methods have some fundamental limitations that restricted their abilities in the modeling of many realistic situations. Thirdly, the existing methods are becoming more and mo re complicated to learn and to use. This study aims to develop a new planning and scheduling method that is simple in form, powerful in function, and universally applicable to all types of cons truction projects. The proposed method is based on the system theory a nd formalized with the DEVS (Discrete Event System Specification) specification. A set of gr aphical modeling elements have been designed so the user can easily utilize the fu ll capacity of this me thod without any specialized knowledge in the underlying theory or any computer languages. The proposed method has been applied to f our real-world projects including a typical regular project, a typical linear project, a typical repetitive project and a project of mixed features. By comparing these models with those built with the existing methods, it was

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16 demonstrated that the proposed method has advant ages in the scope of application, accuracy of modeling, form of representa tion and multi-level modeling.

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17 CHAPTER 1 INTRODUCTION 1.1 Background Construction planning and scheduling is, in a broader sense, an endeavor of modeling and optimization: real world construc tion projects are represented as abstract models so that the duration, cost or some other performance measures of a certain plan can be predicted this is modeling ; the plan can be improved to minimize or maximize the performance measures so that the project goal can be achieved this is optimization Valid modeling is always the first step to successful optimization; and optimization is the final goal of modeling. This study focuses on the modeling of construction operations. For different types of construction projects, the requirements on the modeling tool are different. Construction projects can be classified into three typical categories: regular projects, repetitive projects and linear projects. Regular projects are used to define projects in which most activities are performed only once and at one place. Construction of petroleum refineries and petrochemical plants are typical regular projects. Repetitive projects refer to projects that consist of many identical or similar discrete units, such as multi-family dwellings and high-rise buildings. Linear projects refer to projects that have a li near geometric layout, for example, highways, pipelines, and tunnels. The requirements also vary at diffe rent management levels. At the project level planning and scheduling focuses on the logic of how the proj ect will be constructed with different trades and crews and usually the objective is to minimize the overall project cost or duration; while at the operational level the focus is the collaboration among the individual resources within the crews and normally the objective is to maxi mize the utilization of the major resource.

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18 A variety of planning and schedul ing tools have been developed in the past, addressing the various needs of different types of construction projects and at di fferent management levels. The most influential ones include the Critical Path Method for regular projects; the Line-of-Balance method, for repetitive projects; the Linear Scheduling Method, fo r linear projects ; and simulation methods, primarily for operational level planning and scheduling. One of the biggest problems with the existing modeling techniques is that each of them has a limited scope of application, yet most construc tion projects have mixed features that extend beyond the boundaries of the individual tools (Flood et al. 2006). So the user must either choose one technique and sacrifice the accuracy and effi ciency of some parts of the schedule or use different techniques for diffe rent parts of the project. Moreover, as been pointed out in numerous res earch studies and field reports, each of the existing techniques has limitations that restrict their abilities in representing some realistic situations. Though these techniques have been impr oved over the years, some of their limitations cannot be overcome because the problems are ro oted in their most fundamental assumptions. Thirdly, an overall trend in the development of the existing technique s is that they are becoming more and more complicated to learn and to use which has creat ed a large barrier to their application in the constr uction industry. The majority of the industry is still using the simplest form of the traditional CPM method developed over thirty years ago, despite many of its shortcomings and limitations. A lot of the more capable but more complicated methods have only been used in the academi c field for research purposes. As todays construction projects grow in scale, variety and complexity, and under the pressure of intensified market competition, th ere is a need for a ne w type of planning and scheduling technique for construction projects.

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19 To address this need, Flood et al. (2006) has proposed a conceptual framework for a new technique that aimed to synthe size and enhance the best features of the existing ones. An example is shown in Figure 1-1.With this technique, activities can be organi zed into hierarchical structures, dependency relationshi ps can be defined between activ ities at any levels on the hierarchy and on any attributes in cluding time, progress, and distan ce. It is believed that this proposed technique is able to offer versatility in modeling all types of construction work, maintain simplicity in use, and aid visu al understanding of construction projects. Figure 1-1. Conceptual framew ork of proposed universally a pplicable methodology. [Adapted from Flood, I., Issa, R., and Liu, W. (2006) ."Rethinking the criti cal path method for construction project planning." CIB W 107 Construction in Developing Economies International Symposium, San tiago, Chile. (Page 353, Figure 1)] A research project has been launched by the Rinker School of Building Construction at the University of Florida to fully develop th is new planning and scheduling methodology. The ultimate goal is to develop a powerful, simple-to-use, applicable-to-all planning and scheduling tool that provides full modeling, optimi zation and visualization functionalities. Hierarchical Format: Task 1 Task 1.1 Task 1 Task 1 1 2 Task 1 1 3 Task 1.3 Task 1 3 Task 1 3 2 Task 1.2 Task 1 Task 1

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20 1.2 Aim and Objectives As part of the research project at the University of Florida, this study aims to establish a new modeling method that is simple in form, powerful in function, and universally applicable to all types of construction projects. It includes the following objectives: Identifying the specific needs in modeling different types of c onstruction projects; Identifying the desired characteristics of an ideal modeling tool for construction project planning and scheduling; Proposing a new modeling theory that can be applied to cons truction project planning and scheduling. Developing a new modeling tool, based on the proposed theory, to sa tisfy the identified needs and provide the identified characteristics. The scope of this study is limited to the m odeling of construction projects it proposes a new way of describing the cons truction plan and predicting the resulting performance; optimization of the plan and visu alization of the process is not involved. The performance of the project is going to be measured by time, t hough the method can be easily extended to measure cost, space or any other resources. Also, this study focuses on modeling at the project level; operational level modeling may require further cons iderations for the handling of resources. 1.3 Methodology To achieve the above aim and objectives, this study was performed in the following steps: Step one: Identify the strengths, weaknesses and fundamental limitations of the existing modeling methods throu gh literature review; Step two: Conduct case studies wi th a set of representative, real-world examples to (1) identify the specific needs for modeling each type of construction projects, and (2) examine and identify more strengths, weakne sses and limitations of the existing methods in the context of realistic, complex projects; Step three: Summarize the desired charac teristic for an ideal modeling method; Step four: Propose a new philosophy for th e modeling of construction projects;

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21 Step five: Develop a new modeling method, incl uding a complete set of modeling elements and modeling rules, based on the proposed philosophy; Step six: Apply the new method to the cases to verify whether it is able to deliver the desired characteristics and satisfy the identifi ed needs for various types of construction projects.

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22 CHAPTER 2 LITERATURE REVIEW This chapter reviews the existing modeling techniques for construction project planning and scheduling. A general classification system for models is introduced at the beginning of the chapter. Then the Gantt chart, the CPM method, the Line-or-Balance method, the Linear Scheduling Method, and the simulation method ar e examined in depth. The review not only includes the basic principles of each method, but also the major research problems and different tools that are developed around the same generic c oncept this is to ensure that the identified strengths reflect the latest development in the technique, and the identified limitations are fundamental for the generic method rather than specific for any particular tools. 2.1 Classification of Models As was mentioned at the begi nning of this dissertation, a pl an/schedule is an abstract model of a real-world project. Before we revi ew the modeling principles of each planning and scheduling technique, it would be be neficial to first introduce some basic concepts used in the general classification of models. Classification can often help to reveal the most fundamental assumptions and limitations of a modeling method. A model usually can be classified along three dimensions: Deterministic vs. stochastic : Models that have no random input are deterministic; deterministic models always give exactly the same result for a given set of initial conditions. Stochastic models, on the other hand, operate with at least some inputs being random. In stochastic models, inputs are described as probabi lity distributions rather than as unique values, and results are produced as ranges of values with specified confidence levels rather than as exact numbers. Construction projects are subjected to numerous uncertainties, such as weather occurrences, design changes, labor shortages, equipment and material delivery delays,

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23 subcontractor quality, regulatory changes. Contractors often need to know how much contingency time they should include in their bids to avoid late completion penalties, and owners often need to know how confident they can be with the predicted project delivery date and cost. Stochastic models can help answer these questions. Discrete vs. continuous : In a continuous model, the st ate of the system can change continuously over time; in a discrete model, chan ge can occur only at separated points in time. The choice between discrete and continuous modeli ng is often a matter of accuracy. For the same activity, for example, if we need to track its ac curate progress over the en tire process, continuous modeling would be necessary; but if we only need to know its start time and the finish time (the intermediate progress points could be approximate ly interpolated when needed), then discrete modeling would be sufficient and much more efficient. Static vs. dynamic : In a static model, the output at time t depends only upon the values of the inputs at time t (mathematically represented,) ,... (2 1 nx x x f Y ). By contrast, the output of a dynamic model at time t is dependent upon the history of the values of the inputs (i.e.,t ndt t x t x t x f t Y0 2 1)) ( ),... ( ), ( ( ) () the inputs could change ove r time and possibly interact with each other and with the output. Consider a model where the estimated durations of the activities are taken as the inputs. If the model can reflect the fact that the estimated durations of the activities might change as the project evolves, then it is a dynamic model. Often times, stochastic is confused with dynamic; but they are tw o distinctive concepts: a stochastic model is not necessarily a dynamic model. For example, a Monte Carlo simulation model is a stochastic model, but not a dynamic model. It is stochastic because the durations of the activities can be defined as probability distributions and the output project duration are produced as probability distributions. It is NOT dynami c, however, because once the

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24 values of the activity durations are determined by sampling, they will remain constant for that simulation run (although the values will be re-sam pled for the next simulation run). Actually, time does not play a role in the Monte Carlo Simulation. Table 2-1 shows the general classification of the major planning and scheduling techniques that are reviewed in this chapter. Table 2-1. General Classifications of th e existing planning and scheduling models Discrete Continuous Deterministic Stochastic Static Dynamic Bar chart CPM CPM-based stochastic methods LOB LSM Discrete simulation Continuous simulation 2.2 Bar Chart The bar chart is also referred to as the Gan tt chart, in deference to Henry Gantt, who developed the initial format in 1910 (Gantt 1910). A bar chart is essent ially a list of activities that are required to complete the project. These activ ities are arranged from top to bottom usually by their starting times. The start and end point of each activity are show n in a time grid and connected to form a bar. The length of the bar th erefore, represents the duration of the activity. The bar chart is a strong communication tool for scheduling information. Because its simple graphical representations can be quickly and easily unde rstood without much training, it is the most commonly used means by which the project manager reports the project status to upper management and assigns works to field forces.

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25 However, the bar chart only has very limite d modeling capabilities. One of the primary shortcomings is that it does not represent the interdependency rela tionships among activities (Gould 2005; Hinze 2008). When the duration of one activity changes or the starting time delays, it is difficult to identify the affected activities and evaluate the impact on the projects overall completion time. This shortcoming is overcome by the linked bar chart, where bars are connected with logic links to show activity interdependencies. The linked bar chart essentially is a time-scaled activity-on-node (AON) diagram for the CPM method. A lot of software packages now allow the user to enter and edit data directly on a bar chart interface while the system inte racts with the embedded CPM module to perform the scheduling calculation; and the generated re sult would be automatically c onverted into bar charts for display. Because bar charts are primarily used as a format for presenting scheduling information and seldom as an independent modeling tool, it will not be further examined in this study. 2.3 Critical Path Method 2.3.1 Deterministic Critical Path Method The Critical Path Method (CPM) was developed in the late 1950s by DuPont in an effort to create a formalized project management tool Ever since then, it has been the most popular construction planning method among project owners, architects, engineers and contractors. A lot of owners require CPM schedules as contract submittals. Hence most commercial planning software applicati ons are CPM-based. CPM uses network diagrams to display both activities and their logic links. A network diagram can be constructed in two different graphical formats: the activity-on-node (AON) diagram or the activity-on-arrow (AOA) diagram. AON diagrams use nodes to symbolize the

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26 activities and arrows to show th eir logical links, while AOA diagra ms use arrows to represent the activities and nodes to represent events in ti me. Between the two, the AON diagram is more preferred by the construction i ndustry, and has been implemented in most scheduling software applications. The original AON diagram is limited to the Fini sh-to-Start type of relationship only. Its extension, the Precedence Diagramming Method (PDM) allows for four types of links, including Finish-to-Start, Finish-t o-Finish, Start-to-Finish and Finish-to-Start. The core of the CPM method is the forward and backward pass com putational algorithm. For a network diagram in the AOA, AON or PDM formats, through a forward pass and a backward pass, the CPM algorithm can determine th e early start time, the early finish time, the late start time, the late finish time and the floats of the activities, as well as the total duration and the critical path of the entire project. There have been some proposed modificati ons to the traditional CPM method. For example, Yi and Lee (2002) have proposed usi ng a two dimensional coordinate system, i.e., a resource coordinate and a space coordinate, to arrange CPM activities. However, the forward and backward computational algorithm has remain ed unchanged as the core of the CPM method. 2.3.2 Related Stochastic CPM Methods The CPM method has several st ochastic extensions. The Program Evaluation and Review Technique (PERT) was the first step to allow considera tion of uncertainties with the CPM. It assumes a beta probability distri bution for all activity durations, and uses the expected values (( Most Optimistic Value + 4Most Likel y value + Most Pessimistic Value)/6 ) to find the critical path. The overall project duration is determin ed by summing up the expected values along the identified critical path. PERT provides a simp lified analytical solution to calculate the probabilistic project duration. It s results are subjected to merge-event bias a systematic bias to

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27 underestimate the expected completion(David 1978) One way to eliminate the merge event bias is by using PNET (Ang et al. 1975), a method that remove paths that are hi ghly correlated with (and thus represented by) other longer (and therefore more critic al) paths in the network. The other way is by using Monte-Carlo simulation (Van Slyke 1963), a static simulation method that iteratively evaluates the CPM model usi ng sets of random numbers as inputs. It has also been realized that uncertainties not only exist in th e durations of activities, but also in the depende ncy relationships. The Graphical Evaluation and Review Technique (GERT) (Prisker 1977) can model probabilistic branches It is also able to handle the and and or logic. A GERT diagram consists of l ogical nodes and directed branches with two parameters: the probability that a given arc is ta ken and the distribution functions describing the time required by the activity. GERT uses very sophi sticated mathematical probability theory to calculate the total duration of the network. However, when EXCLUSIVE-OR or multiparameter branches are involved, conceptual and computational problems still exist. The major strengths of the CPM method (incl uding its related stochastic methods) have been well recognized: It is easy to learn, easy to understand, and simple to use. With the CPM method, it is very easy to determin e the critical path of the project and the floats of the activities, which are us eful in making management decisions. On the other hand, the CPM method has been criticized for the following limitations: The activity is represented by two discrete points (the star t and the finish point). The progress of the activity between the two point s and variations in productivity cannot be indicated (Stradel and Cacha 1982; Rahbar and Rowings 1992; Harris and Ioannou, 1998). It assumes that if an activity starts at time t it must finish at time ( t +the duration of the activity) which means that once the activity star ts, it cannot be stopped in the middle and its duration will not change no matter what happens. It does not include resources in the model. Ho wever, almost any activity can be performed with a range of different types and quantities of resources; which type of the resources is

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28 available and what quantity can be acquired when the activity starts determine the actual duration of the activity. The CPM method uses activity durations as basic input data, assuming that the preferred resources can al ways be acquired with adequate quantities (Birrell, 1980; Peers, 1974). It is not able to represent the OR logic in the constraints. In the CPM algorithm, the start/finish time of the successor activity is determined by the maximum value of the start/finish time of all its predecessors, assuming that all the constraints must be satisfied. It is cumbersome for representing repetitiv e activities (Chrzanowski and Johnston, 1986; Reda 1990; Harris and Ioannou, 1998). When applied to linear projects, the continuous activitie s have to be arbitr arily divided into many discrete segments (Mattila and Abraham, 1998). It is not able to maintain work continuit y, which is one of the major concerns in the planning and scheduling of repetitive and linea r projects (Selinger 1980; Stradel and Cacha 1982; Rahbar and Rowings 1992; Harris and Ioannou, 1998). 2.3 Line-of-Balance Method The Line-of-Balance (LOB) method was de veloped by the US NAVY in 1942 (Suhail and Neale 1994). Its methodology is based on the princi ple of the assembly line balance. It upstreams the production of each component so as to ensure that the final products can be assembled and delivered to the users on time. There are three main elements in a LOB diagra m: (1) a unit network, (2 ) an objective chart, and (3) a progress chart, as shown in Figure 2-1. When scheduling with the LOB method, the first step is to draw the objective chart (Figure 2-1 (b)) that reflect the planned delivery date of each unit. The next step is to schedule the unit network (Figure 2-1 (a)) with CPM to determine the time required for completing one unit, and obta in the time between each activitys finish and the units completion. Then the prog ress chart (Figure 2-1 (c)) of th e project for a given date can be determined. On this chart, the horizontal sc ale corresponds to the ta sks in the unit network. The vertical scale corresponds to the units to be completed. The line of ba lance shows the target progress of each task on that date. As the pr oject progresses, histograms can be drawn on the

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29 progress chart to show the actual progress of each task. By compar ing the line of balance and the actual progress represented by the histograms, late activities can be iden tified and resources can be shifted from fast ones to the delayed ones. (a) Unit Network (b) Objective Chart (c) Progress Chart Figure 2-1. Illustration of the LOB method. [Adapted from Jo hnston, D. W. (1981). "Linear scheduling method for highway construction." Journal of the C onstruction Division, ASCE, Vol. 107(No. CO2), 247-259. (Page 250, Figure 4)]. The following example illustrates the LOB method. According to the objective diagram in Figure 2-1 (b), Unit 1 to 10 are supposed to be delivered by Jan. 31st, which means that by Feb. 1st, all tasks in these units should have already be en finished. Unit 11 to 20 are expected to be delivered by the end of February, which is one month away. The unit network in Figure 2-1 (a)

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30 shows that in order for a unit to be delivered in next month, Task 1 to Task 5 for that unit should have been completed by the current time. Ther efore, as shown in Figure 2-1 (c) on Feb. 1st, in Unit 11 to 20, Task 1 to Task 5 are covered beneat h the line of balance. Th is procedure continues till the desired progress for all uni ts have been determined and shown as the line of balance. On Feb. 1st, the actual progress have been coll ected from the field and drawn on the progress chart. As indicated, Task 2 and Task 5 are ahead of the schedule, Task 1 is right on schedule, while Task 3, 4 a nd 6 are behind the schedule. Lumsden (1968) first modified the LOB meth od and applied it to building construction projects. Later, Car and Meyer (1974) used it on the scheduling of high-rise building construction. They concluded that the LO B method should only be considered as a complementary method to CPM. Suhail and Neale (1994) combined CPM and the LOB method into a new technique, which utilizes the LOB met hod to calculate the desired progress and CPM to level resources and calculate float times. Wang and Huang (1998) analyzed the inability of the original LOB method in controlling the interval ti mes between adjacent activities in a repetitive unit, and presented the multistage linear sc heduling (MLS) method as an improvement. Despite its advancement through the years, the fundamental pr inciples of the LOB method have remained unchanged: it uses an identical un it-network to represent the works required for each and every unit, and the identical unit-networks are stacked together in a fixed sequence to form the project network. By doing so, the LOB method assumes that: The project is composed of identical repetitive units; All units are processed by an identical networ k which consist of identical activities with identical durations; Only one crew is used to perform each ta sk in all units, and all crews follow a fixed sequence to work though the units.

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31 These assumptions and simplifications might be reasonable for manufacturing assembly lines, where the LOB method originated from, but th ey hardly hold true for construction projects. As a result, the LOB method only has very lim ited application in construction planning and scheduling, and it will not be exam ined further in this study. 2.4 Linear Scheduling Method For the planning and scheduling of repetitiv e projects and linear projects, the Linear Scheduling Method has been long regarded much more effective than the CPM-based methods. The fundamental concept of the Linear Sc heduling method was esta blished by Peer and Selinger (Peer 1974; Peer and Seli nger 1972), in the process of an alyzing parameters affecting construction time in repetitive hous ing project. In the Construc tion Planning Technique (CPT) they proposed, repetitive act ivities performed by one crew in different units were portrayed as one continuous line on a time-versus-units di agram, the slope of the line indicating the production rates (units per day) of the crew. Cr ews must keep certain distances from their preceding crews this constraint was satisfied by adjusting the starting points and the slopes of the lines to maintain the buffe rs between the adjacent lines. Peer and Selinger (1972) also ar gued that planning and sche duling for repetitive projects should aim to maintain work continuity and ac hieve maximum crew utilization, rather than simply calculate the project duration from an arb itrarily determined set of activity durations as the CPM method did. So they proposed that when scheduling with the CPT technique, the first step was to define what should be made critical in terms of cost consideration; and then to adjust the production rates of the non-critical activities to that of the chosen one. An optimum schedule, they pointed out, should have as many lines parallel (and thus critical) and continuous as possible. A mathematical algorithm was later developed (S elinger 1980) to support this method. This method actually could not guarantee the maximum overall cost efficiency (cost is

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32 always the ultimate measure of project performance), because it might only optimize the chosen critical activity but not the overall project, and it completely ignored the constraint on the completion date. Nonetheless, the ideas of balancing and maint aining continuity presented in the CPT technology have remained at the heart of the LSM method. A graphical format similar to that of the CPT was presented by OBrien (2000) in his Vertical Production Method for hi gh-rise building projects. He c oncluded that preparation works such as site work, foundations, and sub-structure, were better scheduled by the CPM, while repetitive works in typical floors could be more effectively scheduled usin g a floor-level versus time graph. Earlier works presenting similar graphics include the Time versus Distance diagram proposed by Gorman (1972), the Bar Chart fo r Repetitive Operations by Clough and Sears (1979), and the Trade Progress Chart by Goldhaber, Jha, and Macedo (1977). Johnston(1981) examined previous works a nd put them under one unified name the Linear Schedule Method (LSM). He summarized th e core concepts of this method and developed a detailed description of the gra phical elements that can be utilized in a LSM diagram. He applied this method to several highway constr uction and maintenance projects, included the variation of production rates, buffers, activity interruptions, calendar considerations, and resources constraints in the linear schedule. Ba sed on the case studies and a survey conducted among several highway contractors, he conclude d that for the repetitiv e portions of these projects, the LSM technology offered some adva ntages over the CPM method: it conveyed the nature of the problem easily, provided quick solutions and intuitive presentations of the result. At the same time, he also pointed out that fo r discrete activities th e CPM method was still necessary.

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33 Stradal and Cacha (1982) labeled this tec hnology the Time Space Scheduling Method (TSSM). They evaluated this method through a vari ety of projects that co nsisted of repetitive sections. Their conclusion was that this met hods major limitation was in the area of complex projects and projects where activities had different alignm ents or measuring scales. Figure 2-2. Standard format of linear scheduli ng diagram. [Adapted from Vorster, M. C., Beliveau, Y. J., and Bafna, T. (1992). "Linear scheduling and visualization." Transportation Research Record, 1351, 32-39. (Page 37, Figure 10)]. Another milestone in the development of the LSM method was made by Vorster et al. (1992), who standardized and improved the graphical format of the LSM. They suggested that an activity could always be represen ted by one of three geometrical sh apes: lines, bars and blocks (See Figure 2-2). Lines are drawn to show the continuous m ovement of a crew on a particular activity throughout the job. The slope of the line represen ts the rate of production. Blocks are used to represent activities that occupy a substa ntial portion of space for a given period of time, for example, grading. Bars are used to represent activities that require work to be performed at a given location for a long period of time, such as the construction of a bridge. They also showed that time buffers, space buffers, time constraints a nd space constraints could be easily visualized

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34 in a LSM diagram (See Figure 2-2). Harmelink and Rowings (1998) later divided the activities into seven smaller categories: continuous full-span lines, intermittent full-span lines, continuous partial-span lines, intermittent partial-span lines, full-span blocks, partia l-span blocks, and bars. Most of the early research on the LSM met hod concentrated on developing its graphical formats. The analytical ability of this tech nique, however, had been considered inadequate compared to the CPM method: it did not have a we ll-defined critical path and float times and was not as adaptable to computerization as the CPM methods. Several researchers recommended using the LSM only as a visualization tool to complement the CPM method (Chrzanowski and Johnston 1986). During the 1990s, the analyt ical capabilities of the LS M method had been greatly improved. First, Harmelink and Rowings (1998) defined the term the controlling activity path : it is analogous to the critical path in CPM scheduli ng, but it is different beca use it allows portions of an activity to be critical, whereas the CPM onl y allows the entire activity to be critical. As suggested by Harmelink and Rowings, three key features, the least time interval (LT), the coincident duration, and the least distance interval (LD), were needed to identify the controlling activity path. Harris and Ioannou (1998) found th at the controlling activity path in the LSM diagram switch from one activity to another where these activities are in the greatest proximity. They also pointed out that to maintain the reso urce continuity in repeti tive and linear projects, some non-critical activities (by CPM definition) would actually become critical although a delay in any of these activities will not delay the project, it will cause an interruption of resource usage. They termed such activities the resource critical activities Further, Ammar and Elbeltagi (2001) developed a computerized algorithm capable of identifying the controlling activity path on the LSM diagram.

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35 To summarize, the strengths of the LSM met hod mainly show in the modeling of repetitive projects and linear pr ojects, including: Its ability to maintain work continuity and achieve maximum crew utilization; Its ability to model ac tivities with either the discrete or continuous representation: the continuous representation uses a continuous line to show the changing production rates and the interruptions; the discrete representation uses blocks or bars which indicate only the start and finish points at each loca tion but hide interim progresses. Its ability to visually convey the nature of the problem, which may provide quick solutions and intuitive presentations of the result. On the other hand, the LSM method has the following fundamental limitations: It does not allow scheduling disc rete and continuous activities at the same time (El-sayegh 1998). It can be difficult to use on projects that re quire a large number of trades or operations. (Sikangwan, and Tokdemir 2002). It cannot represent projects wh ere activities have different a lignments or measuring scales. It has difficulties in representing uncertainties and dynamic factors. 2.5 Simulation Methods A simulation is an imitation of the operation of a real-world process or system over time (Banks et al. 1999). Compared to other methods, simulation has the advantages of being able to address uncertainties and dynamics in real-w orld systems (Zhang et al. 2002). Simulation modeling assumes that a system can be charac terized by a set of variables, with each combination of variable values representing a unique state or condition of the system and thereby manipulation of the variab le values simulates the movement of the system from state to state (Prisker and O'Reiley 1999). In a simula tion experiment, the systems status, i.e., the variable values, evolve dynamically according to operation rules that have been pre-designed into the model. The performance of the system can be evaluated by analyzing the statistics of the

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36 variables, or by directly obs erving the animated system co mponents, as supported by some simulation software. For a general introduction to the simulation technology, refer to Appendix A. 2.5.1 Discrete Simulation Most simulation methods developed for constr uction planning and sc heduling are discrete simulation methods, in which the va riable values change only at di screte points in simulated time referred to as event times. As introduced in Appendix A, the two main discrete simulation st rategies are activity scanning (AS) and process intera ction (PI). The third strategy, event scheduling (ES), is the underlying building block of all discrete simulati on methods, and it can be combined with either the AS or the PI strategy to increase modeling flexibility. With the AS strategy, a system is decomposed into activities whose st arts are subjected to activation conditions. For simulation advancement, AS scans the entire set of activities for eligibility, choose the one whose starting conditions are satisfied and then take appropriate actions, typically including acqui ring the requested resources, determining how long the activity will last, holding the acquired resources for the determined duration (when the activity starts), and releasing the resources (when the activity ends). Three-phase AS is a modified approach that improves ASs computing efficiency. With this strategy, the activities are se parated into Bs (activities that are bound to start at a predictable time), and Cs (activities that are not depende nt on the simulation clock but must wait until predefined conditions can be sa tisfied or until requested reso urces are available). As the simulated time advances, only the Cs will be scanned and tested, while Bs will be immediately executed once the simulation clock reaches the scheduled time.

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37 The other type of discrete-event simulation st rategy is PI. With this strategy, the modeler needs to identify the enti ties (or transactions in some cases ) that flow through the system and describes the life cycles for each class of them. Typically, the life cycles of the entities involves entering the system, undergoing some processing where they capture and release scarce resources, and then exit. During runtime, entities will be created and pushed though the life cycle, triggering the events on the path in sequence. The AS strategy, particularly the three-phase AS strate gy, has been the dominating modeling paradigm for construction simulati on, with only rare exceptions. The following discussion will thus focus on these two paradigms. 2.5.1.1 Three-phase approach The most influential simulation tool in the construction area is the CYCLONE and CYCLONE-based simulation tool s. In 1973, Halpin developed CYCLONE (Cyclic Operation Network) and it has since become the corner ston e of later simulation tools in the construction industry. CYCLONE employs the three-phase strategy, and to better suit th is strategy, it extends the ACD (Activity Cycle Diagram) by differentia ting two types of active states. The normal node in CYCLONE corresponds to the Bs in the three-phase concept, and the conditional node corresponds to the Cs. Special function nodes have also been included to duplicate and consolidate entities and to control the simula tion run length. Thereby a CYCLONE model can be readily translated into a three-phase simulation program. CYCLONE is purely graphical based the diagram is the only place where everything being specified. Consequently, it is simple to use but has several important limitations: the inability to differentiate individual resources, th e inability to access th e dynamic state of the simulated process, and the inability to make use of the resources properties and the dynamic state to define the model behavior (Martin ez 1996). There are at least four CYCLONE

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38 implementations mainframe CYCLONE, Insight, UM -CYCLONE, and Micro-CYCLONE. They have similar functions and ar e subjected to similar limitations. RESCUE (Chang 1986) is also built on CYCLONE but it makes a significant improvement on it. A Process Description Language (PDL) is provided in RESCUE to supplement the CYCLONE diagram. With the PD L, each individual resource can be assigned a unique identifier, so the resources on the same path can have different activity duration probability distributions and differe nt routing rules. Another impr ovement of RESCUE is that it can assemble and disassemble resources so that multiple resources can temporarily work as one group. Another system, COOPS (Liu 1991) greatly enhances CYCLONEs user friendliness. Developed with the obj ect-oriented programming technology, it provides an interactive interface where users can drag and drop gra phical objects to quickly build a simulation model. It can track individual resources ( but cannot characterize them) and repo rt the statistics generate and consolidate resources during the operations, and use calendars to preempt activities during work breaks. CIPROS (Tommelein et al. 1994) also uses the object-oriented technology to enhance CYCLONE. By representing resources as a hierarch ical of objects, CIPROS allows multiple real properties for resources and enables co mplex resource selection schemes. STROBOSCOPE (Martinez et al. 1994) is th e acronym for State and ResOurce Based Simulation of COnstruction ProcEsses. STROBO SCOPE is also based upon the three-phase strategy and the extended CYCL ONE ACDs, but it has eliminated many of the simplifying assumptions in CYCLONE, and its modeling ability and flexibility far exceeds other CYCLONE-based techniques. At the conceptual leve l, it represents the simulation models with

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39 an enhanced set of CYCLONE elements, which in clude four new nodes and four special purpose links. At a more detailed level, each netw ork element and resource in STROBOSCOPE has attributes and methods that can be defined, dynamically accessed, and used in expressions to define the methods and attributes of other network elements and res ources. It also gives the user the access to event-level modeling, so events can be used to tr igger all types of dynamic changes. STROBOSCOPE is able to consider uncertainty in any aspect (not just duration), such as quantities of resources produced or consumed (e.g., the volume of rock resulting from a dynamite blast.), to allow dynamic branching, to use complex resource selection schemes, to include complex startup c onditions not directly re lated to resource availa bility (e.g., do not blast rock until all crews of all trades have left the vicinity, the wiring has b een inspected, and there are lee than 10 minutes left in the curren t shift) etc (Martinez and Ioannou 1995). Though very powerful and flexible, the appli cation of STROBOSCOPE is very limited because of it complexity. The user has to have a deep understanding of the fundamental simulation principles and concep ts, and invest time to lear n STROBOSCOPE statements and comments to truly utilize its flexibility. Major features of the above CYCLONE-based discrete simulation techniques are shown in Table 2-2. Despite all the advancements in the CYCL ONE-based discrete simulation techniques methods, all of them rely on the ACD as the skeleton of modeling. As the name implies, a typical ACD (Activity Cycle Diagram) consists of circ les of activities that are linked together at common points. This structure maps directly to the operational level systems each circle can represent a type of equipment/crew that cycl es along a fixed sequence of activities; some activities require two or more equipment/crews to cooperate, t hus the circles are joined at these points.

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40 When used to model project level systems, however, the ACD is less intuitive. At the project level, activities are not threaded by resources that cycle around one resource is usually responsible for only one activity; rather, activities are linked by logical relationships. To represent the logical relationships with the ACD diagrams, a virtual entity has to be created, send through the network from the first activity to the last one, and th en terminated. Since the entity has to get out of one activity befo re it can enters the next one, it has difficulties in representing logical relationships that are not of the Finish-to-Start type, and it has to be duplicated and converged whenever there are parallel activit ies in the network. To simplify this modeling process, Martinez has developed an a dd-on for STROBOSCOPE for project level simulation(Martinez 1996). Severa l new nodes have been provided in this add-on and the resulted diagram looks very similar to a CPM network. This add-on, howev er, is only able to handle the most basic finish-tostart relationships without le ad and lag times. One way to represent the complicated logical relationships in STROBOSCOPE is by coding at the detailed level; but in that way these relationships will not show in the diagrams and is difficult to track. To use the Cyclone-based method for modeling repetitive projects, each unit in the project can be represented as one entity that travels th rough a typical unit net-wo rk. An example of such application can be found in a study by Lutz and Ha lpin (1992). In their example they assumed that: all units in the project are identical; only on e crew is working on each activity; and crews of different trades follow exactly the same sequence when working though the units. 2.5.1.2 Activity-scanning approach Shi (1999) proposed the activity-based c onstruction (ABC) modeling and simulation method with the objective to simplify the CYCLON E simulation process. In the ABC diagrams, activities (active states) are the only modeling elements, queues (idl e states) have been integrated into relevant activities as attributes, consolidating and multiplying functions are also carried out

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41 in the activities. The ABC modeling and simula tion method does not require the scheduler to differentiate between normal activities and condi tional activities or to arrange entity flows among activities or entity nodes, thereby making modeling with the ABC method very similar to constructing an AON network diagram. The si mulation algorithm developed for the ABC method is based on the pure Activity Scanning s imulation strategy rather than the three-phase strategy. It is named the three-stage simulation algorithm and involves the following three stages: (1) select an activity for execution; (2) advance simulation; and (3) release simulation entities. Shi later used the object-oriented technol ogy to implement the ABC method (Shi 2000). With the object-oriented technology, the characteristics of an activ ity can be described using six classes of attributes including the activity dur ation, logical consequence, resource requirements, etc. The major difference between the ABC method a nd the cyclone-based methods is that the ABC method has a simplified modeling interface wh ich does not require the user to define the queues and put them into proper places based on the activity scanning st rategy instead of the three-phase strategy, it does not require the user to differen tiate between the Bs (normal activities) and the Cs (conditional activities). However, its computing efficiency has been compromised, since it has to scan all activities ev ery time the simulation clock advances, rather than just the Cs. As for modeling abilities, the A BC method lacks the same level of flexibility and accuracy compared to the SCOBOSCOPE method (refer to Table 2-2).

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42Table 2-2. Comparison of the major discrete simulation techniques CYCLONE RESCUE COOPS CIPROS STROBOSCOPE ABC Activity Duration Cannot be determined by resources. Cannot be dynamically determined. Can be determined by resource type and subtype. Cannot be dynamically determined. Can be determined by resource type. Cannot be dynamically determined. Can be determined by resource type and subtype. Cannot be dynamically determined. Can be determined by any variables. Can be determined dynamically. Cannot be determined by resources. Cannot be dynamically determined. Resource selection No No No Yes Yes Yes Interruption No No Can only be triggered by resource break-time. No Can be programmed flexibly No Dependency relationships Start-up constraints Resource availability only Resource availability only Resource availability only Resource availability only Both resource availability and logical dependencies Logical dependencies only End branching Probabilistic branching Probabilistic branching Probabilistic branching Probabilistic branching and decisionbased branching Probabilistic branching, dynamic branching and decisionbased branching Probabilistic branching

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43 Table 2-2. Continued CYCLONE RESCUE COOPS CIPROS STROBOSCOPE ABC Resources Static attributes Type Type and Subtype Type Multiple attributes Multiple attributes Type Dynamic attributes No No No No Yes No Unbalanced resource involvement No Yes Yes Yes Yes No Activity Priority No On defined attributes of resource NO NO On any expressions No Probabilistic routing No No Yes No Yes No Decision-based routing No No No No Yes No Resource calendar No No No No Yes No Assembly and disassembly No No No Yes Yes No Uncertainties in resource production and consumption No No No No Yes No

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44 2.5.2 Continuous Simulation Compared to discrete simulation, the use of continuous simulation in construction planning and scheduling has been rare. Continuous simulation has been used in MUD (Carr 1979) and DYNASTRAT (MoruaPadilla 1986) in order to take account of the continuously changing factors that impact productivity and thereby activity durations in regular projects MUD(Carr 1979) suggested that these factors could be calendar-dependent (DEC AD) such as temperature, precipitation, and wind; or calendar-independent (INC AD) such as supervision. The se nsitivity of each activity to the INCAD and DECAD variables is specified by the user and used in a formula to determine a daily correction factor in MUD. The progress of an activity each day is then calculated by applying this correction factor to its estimated standard duration. For exam ple, if the correction factor for the first day of a 10 day activity is 0.7, then at the end of the day, there will be (10 1.7 =) 9.3 days of work remaining to be done. An activity is considered complete when there is no work remaining to be performed. MUD actua lly used the fixed-step continuous simulation in its computation. (See Appendix A for a br ief introduction of the continuous simulation method.) DYNASTRAT (Morua-Padilla 1986) enhan ced MUD by incorporating resource availability considerations. A vari ety of resource allocat ion strategies can be selected to specify how resources are going to be allocated among competing activities. An ongoing activity may be interrupted if its resource is requested by anot her activity with a higherpriority. The resources assigned to an activity, along with the INCAD a nd DECAD factors, will determine the daily progress. Continuous simulation has also been used to a ddress the continuity of linear projects. Shi and Abourizk (1998) simulated a gas pipe project with SLAM II, a general-purpose simulation

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45 tool widely used in the manuf acturing industry. The continuous model they developed consisted of six separate networks each representing the bi rth-to-finish process of one activity, and six subroutines written in FORTRAN each respons ible for updating the production rate and the progress status of a corresponding activity. Th e model also included a number of resource describing nodes and status detecting nodes. Th e produced results were presented in a LSM velocity format. They also built a discrete model for the same pipeline project for comparison. In this discrete model, the activities were progres sed at the completion of each operation cycle. In conclusion, they commented that even though the di screte model was easier to construct with the SLAM elements, it would require a lot more data collecting and analysis at a lower operational level. 2.6 Other Methods Models for construction planning and schedul ing can also be formulated with other techniques including linear programming (R eda 1990), dynamic programming (El-Rayes and Moselhi 2001; Senouci and Eldin 1996), integer programming (Liu et al. 1995), and optimal control theory (1986). The purposes of most of these models ar e to quickly find a satisfactory solution to improve a certain proj ect performance measure, rather than to accurately represent the project. A construction planning problem usually has to be simplified a lot to fit the assumptions of these methods, and sophisticated mathemati cal knowledge and skills are often required. So these models will not be discu ssed in detail in this study.

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46 CHAPTER 3 CASE STUDIES WITH EXISTING METHODS In Chapter 2, we have reviewed th e major existing planning and scheduling techniques. In Chapter 3, we will select proper tools from these techniques and apply them to four case studies, each representing a distinct type of construction projects, including a typical regular cons truction project, a typical repe titive construction project, a typical linear construction project, and a project of mi xed features. By doing so, two objectives can be accomplished: (1) the specific requirements for modeling each typical type of construction projects can be identif ied, and (2) the strengths and limitations of each planning and scheduling method in addressing these needs can be identified. Real-world construction projec ts are used in these case studies. The first project is the construction of a medium-rise building. Th is project has been divided into three separate case studies: the cons truction of the foundational part of the building is studied as an example of the typical regular projec t; the construction of th e upper-structure, an example of the typical repetitive project; and the whole process, an example of projects with mixed features. The second project is th e construction of a gas pipeline, which is examined as a typical linear project. The di scussion on the modeling of linear projects is further broadened with a short study on the th ird project, which i nvolves the construction of multiple utility lines. These case studies together cover the full sp ectrum of typical construction project categories. The problems presented in these case studies are very representative of the realistic, complex situations that could be encountered on the construction jobsite.

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47 Figure 3-1. The CPM model for Case One

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48 3.1 Case One: A Typical Regular Project The data used in Case One, Three and Four came from a work report on the planning and scheduling of the structural wo rk in a 14-level condominium at southern Florida (Hughes 2005). The subcontractor, he reto referred to as Company A, was responsible for the construction of the fr aming system of the foundation and the upper structure of the building. In the work report, Hughes recorded the construction process in detail, presented the CPM schedule prep ared by Company A, and reported the requirements and concerns of the mana gement members on various planning and scheduling issues from thei r individual perspectives. Case One examines the first phase of Company As work construction of the foundation for the building. This is a typical, regular construction project, which can be modeled with the CPM method and the disc rete simulation method. The LSM and the LOB method are not applicable to regular construction projects and thus will not be discussed in this case study. 3.1.1 The CPM Model The original schedule prepared by Company A used the CPM method. The schedule shown in Figure 3-1 is a revised ve rsion. The obvious errors in the original schedule have been removed, and the format has been changed for better clarity. Note that it is possible to further improve this sc hedule, but the changes would involve a lot of tricky workarounds. As the purpose of this study is to examine what the CPM method is able to do with realistic a nd moderate input, further cha nges are not going to be made. It also needs to be pointed out is that although this example was developed with the deterministic CPM method, the discussions is not limited thereby; rather, it is targeted at the most fundamental limitations and assump tions of the generic method, including both

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49 the deterministic and the stochastic CPM. Th e discussion includes four parts: modeling of activities, modeling of dependency relationshi ps, modeling of resour ces, and modeling of other factors. 3.1.1.1 Modeling of activities In the CPM method, activities are modeled as two discrete po ints with a fixed duration d in between. It assumes that an activity starting at time T will definitely end at time ( T+d) Problems with this approach have been identified as following: Durations of the activities ca nnot be dynamically determined. Durations of the activities have to be entered as real numbers or probabilist ic distributions. This means that the values of the durations cannot be dynamically determined according to real-time situations, such as what resources are availa ble when the activity st arts, the weather and the site conditions at that time, and other activities going on in adjacent areas. This often requires the scheduler to determine a value in advance with many arbitrary assumptions. The intermediate progress of the activiti es cannot be accurately represented. Every activity in the real world is a con tinuous process, progressing gradually minute by minute, day by day. With the CPM method, this continuous process has to be reduced to two discrete points a start poi nt and a finish point. When the production rate (or the expected value of the production rate) of the activity is constant, this simplification is adequate and computationally efficient. But, if the production rate varies throughout the process, such representation will lead to loss of information, which is illustrated by Figure 3-2.

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50 Figure 3-2. Discrete repres entation of an activity In Figure 3-2, the horizontal axes represent time t and the vertical axes represent progress p Suppose that the estimated duration for the activity is d and the activity starts at time T In Figure 3-2(a), the prod uction rate is constant. Gi ven a starting point (T, 0%) and an end point (T+ d, 100%), a ny intermediate progress at time (T+t) (0
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51 that production would gradually speed up and it was quite normal for the activity to progress slower at the beginni ng. Still, the project manage r would like to have some quantitative criteria to determine whether the progress was just reasonably behind or there were problems that needed immediat e correction. The CPM schedule did not help setting the intermediate goals. Interruptions during the middle of the progress cannot be represented. The CPM method assumes that once the activity star t, it will not stop until 100% finished. In reality, the activity could be interrupted in many situations. For example, whenever the temperature drops to below 40F, any activity involving concrete pl acement has to stop. When such events would occur and how l ong they would last are unpredictable. Certainly we could roughly estimate th e likelihood of such events and use a probabilistic distribution to acc ount for the impacts of possible interruptions. But this solution is not able to capture the cause-andeffect relationships between the events and the change of the durations; moreover, it might over-estimate the total amount of resources used by the activity, for it does not separate the actual time that the resources are working on the activity and the interrupti on time during which th e resources can be temporarily released. Adjustments of activity durations durin g the middle of the progress cannot be represented. Various types of events could also cau se the duration of the activity (here it refers to the actual duration excluding the in terruptions) to lengthen or shorten during the middle of its process. For instance, as show n in Figure 3-3(a), the estimated duration of Activity A was 10 days. On the third day, Activity B started, interfered with Activity A and caused its remaining duration of 7 days to extend to 11 days. With the CPM method,

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52 there is no way to model this adjustment. We cannot simply add 4 days to Activity As estimated duration to account for this possibili ty. If Activity B had started on the seventh day, for instance, Activity A would experien ce less interference and suffer less extension (as illustrated in Figure 3-3(b) ). The effect has to be determined dynamically at the point where the event occurs during the middle of the ac tivity rather than at the beginning of the project or the activity. Figure 3-3. Adjustments of Activity As duration 3.1.1.2 Modeling of dependency relationships There are four types of dependency relations hips that can be defined with the CPM method: the Finish-to-Start relationship, the Start-to-Start relati onship, the Finish-toFinish relationships and the St art-to-Finish relationship, with possible lead and lag times. These dependency relationships have to be de fined either on the star t point or the finish point of the activities, and the leads and lags have to be measured in time units, i.e., hours, days, weeks, etc. The followi ng problems have been identified: Non-time-based dependency relationships cannot be accurately represented. Non-time-based dependency relationships are ever ywhere in construction projects. In this project, it was required that the vertical lift on the first floor could not start until the foundation was at least 1/3 finished a c onstraint based on the progress of Activity (a) Activity B starts on the 3rd day (b) Activity B starts on the 7th day

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53 Foundation. Since the CPM method can only handle time-based dependency relationships, this progress-ba sed constraint had to be c onverted to a Start-to-Start relationship with a 10 days la g time (shown in Figure 3-4). The lag time (30 days 1/3 = 10 days) was calculated based on the assumpti on that Activity Foundation would take 30 days to complete and its pr oduction rate was constant. Figure 3-4. The CPM representation of a non-time-based dependency relationship This duration-based dependency relationshi p is not equivalent to the original progress-based dependency relationship. Consid er this scenario: 10 days after Activity Foundation started, only 1/5 of the foundation ha d been finished. As a matter of fact, Activity 1st Lift Vertical could not start since the progress of Activity Foundation had not reached 1/3. However, according to the CPM schedule, Activity 1st Lift Vertical would start anyway for the 10 days lag time had passed. A similar problem would occur had Activity Foundation progressed fast er than the assumed speed. For the incoming dependency relatio nships, only AND logic can be represented. In an AON network diagram, every arrow coming into an activity node represents a constraint on th e start or finish of that act ivity. The CPM method evaluates the incoming constraints by combining all of them with AND only when all of the constraints have been satisfied, the activity can start or finish. OR type logic cannot be The progress-based constraint Foundation has to be 1/3 finished was converted to a time-based lag. 10d

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54 handled. The CPM-based GERT technique is able to represent the EXCLUSIVE OR but not the INCLUSIVE OR logic. For the outgoing dependency relationshi ps, all branches will be fulfilled. The links coming out from an activity node repres ent the constraints that the activity imposes on its succeeding activities. When the activity has been finished (or started as in the SS or SF type of relationships), these constraints are satisfied and the succeeding activities may proceed. Oftentimes, however, not all of th e succeeding activities are meant to be executed. If they are exclusiv e alternatives, only one of them shall. In such cases, decisions must be made on which succeeding activity to choose. The CPM method is not able to model this situation; all outgoing br anches will be fulfilled. The GERT technique can choose one branch randomly based on the pr obabilities assigned to the branches (a feature called Probabilistic Branching ), but is not able to make the decision according to the values of user-defined variables or expressions (which is referred to as Decisionbased Branching in this study). 3.1.1.3 Modeling of resources For most construction projects, resources ar e always the critical constraints on the performance of the project. The durations of the activities are de pendent upon the type and amount of the resources available for the activity. The dependency relationships between the activities are also influenced by resource assignment: when two activities share the same resource, they cannot run in pa rallel, but have to be sequenced linearly. The CPM method does not include resources as the basic input. Durations of activities and dependency rela tionships are entered direc tly. The underlying resource constraints that determine activity durati ons and dependency relationships are not represented. Consequently, it is difficult to see and unde rstand the assumptions and

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55 limitations used in the schedule, and therefor e difficult to detect sc heduling mistakes and generate alternative schedules. 3.1.1.4 Modeling of other factors The CPM method is not able to represent fa ctors such as temperature, precipitation, wind and supervision, which may have gr eat impacts on project schedules. 3.1.2 The STROBOSCOPE Simulation Model The second model for this case study, whic h is shown in Figure 3-5, is developed with STROBOSCOPE. STROBOSCOPE was select ed because it is widely recognized as the most powerful and flexible discrete si mulation tool for construction operations and projects. The STROBOSCOPE network shown in Figur e 3-5 may look very similar to the CPM Activity-on-Node network shown in Fi gure 3-1, but there is one fundamental difference: in the CPM network, the links re present the start/finish constraints one node imposed upon another; in the STROBOSCOP E ACD diagram, the links represent the directions that the resources travel through th e activities. In Figure 3-5, a virtual resource t oken, is generated by the Queue node TokenGen at the left end of the network, a nd then sent through the nodes as directed by the links. The names of the links Ti ( i = 1 to 29) indicate that only resources of type T (Token) are allowed to flow through these links ( i in the names does not suggest any sense of sequence). The STROBOSCOPE model is al so examined in four aspects, including: modeling of activities, modeling of de pendency relationships, modeli ng of resources and modeling of other factors.

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56 Figure 3-5. The STROBOSCOPE model for Case One

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57 3.2.1.1 Modeling of activities It is able to dynamically determin e the durations of the activities. With STROBOSCOPE the duration of the activity can be defined as an expression of system variables and user-defined variables. The value of the expression is determined at the point when the activity starts, so it can reflect which type of resource has actually been acquired, the current status of weather, site conditions and impacts of any other dynamic factors. It is unable to represent the interm ediate progress of the activities. In discrete simulation, the clock advances from one ev ent to the next. With the CYCLONE-based simulation methods, each activity is essentially modeled as a pair of events: a start event at time T and a finish event at time (T + d) ( d is the duration of the activity). The state of the activity does not change between time T and time (T + d) and the intermediate progress of the activity cannot be accurately represented. It is very difficult to represent interruptions and adjustment of activity durations during the middle of activity. With STROBOSCOPE, as with any other CYCLONE-based simulation methods, the start event of an activity at time T will automatically schedule a finish event of that activity at time ( T+d ); there is no way to remove or re-schedule a finish event except with very complicated code writign at the event level. 3.2.2.2 Modeling of dependency relationships SS, SF and FF type of dependency relationships cannot be directly represented. In STROBOSCOPE, as in any othe r ACD-based simulation methods, the activities are activated by the arrival of requi red resources. The resour ces have to finish one activity before they can enter the next one. So naturally, STROBOSCOPE is most

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58 efficient with the Finish-t o-Start type of dependenc y relationships. Dependency relationships of the other t ypes cannot be directly repres ented. For example, Activity Vertical#1Lift cannot start until 10 days afte r Activity Foundation has started. The CPM method can simply represent this constraint as a Start-to-Start relationship with a 10 days lead time, as shown in Figure 3-6. W ith STROBOSCOPE, the first activity has to be divided into two nodes Activity Founda tion_1 with a duration of 10 days (the length of the lead time) and Activity Foundati on_2 of 20 days (the original duration 30 days minus the lead time 10 days) in order to allow the token to flow out during the middle of the predecessor activity to activate the successor activity. Figure 3-6. Representation of an SS dependency relationship It is even more difficult to represent SF and FF types of dependency relationships. An example of the FF dependency relations hips is shown in Figure 3-7. With the SCOBOSTROPE method, the succ essor activity needs to be represented with three different types of nodes. Figure 3-7. Representation of an FF dependency relationship Foundation_1 Foundation_2 T16 Vertical#1Lift T14 Foundation VerticalLift#1 SS 10 days StairWall#2 WaitToFi nish RetainingWall_ 1 RetainingWall_ 2 (a) CPM Model (b) STROBOSCOPE Model (a) CPM Model (b) Time Elapsed in the Current State

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59 It is able to model compound startup constraints, but not very easily and quickly. With the CYCLONE ACD diagrams, the star tup of the activity is controlled by the arrival of the required resources/tokens. An activity has to obtain resources or tokens from all of its preceding queues before it can a ttempt to start. This means that in the ACD diagram all incoming links to one activity ar e combined with AND to form the startup constraint, just as in the CPM method. However, one would find that the CYCLONE ACD diagram requires some extra n odes when used for this purpose. MEPUnderI SOG#1Pre SOG#1Pour Figure 3-8. Representation of the AND logic Figure 3-8 shows how the CPM method a nd the STROBOSCOPE method are used to describe: Activity SOG#1Pour cannot start until both Activity MEPUnderI and Activity SOG#1Pre are finished. The former only uses one type of node, whereas the latter uses three different types of nodes and ne eds to define and ini tiate the tokens that flow through the nodes. One advantage of STROBOSCOPE over the other CYCLONE-based simulation tools is that it provides a second way to repr esent the startup constr aints. The OR logic and more complicated compound logic can be defined in the Semaphore of the activity. The Semaphore is a logical expression that must return TRUE before the activity can (a) CPM Model (b) STROBOSCOPE Model

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60 attempt to start and acquire resources. A Se maphore may contain any system or userdefined variables, and may include multiple logical statements linked with AND and OR. However, one must be very fa miliar with STROBOSCOPE variables and statements in order to define the Sema phore properly. Moreover the compound startup constraints written in the Semaphore cannot be directly read from the ACD diagram. It is not able to represent non -time-based dependency relationships. As STROBOSCOPE does not model the intermed iate progress of the activity, progressbased dependency relationships have to be converted to time-based dependency relationships, which are not e quivalent conversions most of the times, as discussed in 3.1.1. It is able to represent probabilistic br anching and decision-based branching. When an activity is finished, the released reso urces/tokens can be r outed via the Fork or the Dynafork node, which is able to decide which successor activity the resource will go to next using either probabilistic br anching or decision-based branching. 3.2.2.3 Modeling of resources It is able to realistically rep resent various types of resources. In STROBOSCOPE, resources can be modeled ei ther as Generic Resources, which are simply measured by the quantity, or Charact erized Resources which have a set of properties. The properties of the characterized resources can be used to carry a lot of information and thus increase the flexibility of modeling. For example, if different dozers need different length of time to accomplish an activity Backfill, the resource Dozer should be defined as a characterized resour ce which has a property Backfill Duration. Each dozer then can be assigned different valu es for this property and spend a different length of time in the same activity Backfill. A set of resources can also be bundled

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61 together to form a Compound Resource, and the compound resource can be dissembled as required. It is able to represent acti vity priorities for shared re sources, but the activity cannot have different priorities for different res ources. When one resource is shared among multiple activities, it is necessary to specify the priorities of these activities if they are requesting the resource simultaneously. STRO BOSCOPE allows specifying the priority as one attribute of the activity; however, it assumes that the activity has the same priority for all the resources that it shares with others. It is able to model various resource sele ction schemes, but the resources have to be of the same type. When one activity could be done with several alternative resources, it is necessary to specify the pr iority of these resour ces. In STROBOSCOPE, the activity can select the res ources from its preceding queue, in which the resources are sorted according to a specified rule (e.g., first-in-fir st-out, last-in-firstout) or on the value of an evaluation expression. But the selecti on can only be performe d among resources of the same type because the sorting has to be done in a queue and one queue can only hold resources of the same type. 3.2.2.4 Modeling of other factors Temperature, precipitation, wind and othe r dynamically changing factors can be modeled with separate sub-networks in ST ROBOSCOPE. The values of these factors may be accessed by the activities and thereby im pact the attributes and behaviors of the activities. As can be seen from the analysis above, the simulation method has advantages over the CPM method in terms of modeling abilities However, there are some major obstacles in the application of the simulation method, including:

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62 It is difficult to learn and to use. As can be seen from this example, using the simulation method to model a construction pr oject requires significant amount of time, effort and skill. There is a lack of direct correspondence between the elements and rules in the simulation tools and the real constr uction project: often tim es, the user has to assemble various types of nodes and links to represent a single activity or constraint, and do fairly amount of code writing. This demands a deep understanding of the fundamental simulation theories, familiarity with the par ticular variables, functions, syntax of the specific programming language, and also cr eativity in figuring out workarounds for many situations. It does not facilitate understanding and communication. The complexity of the simulation method makes it very difficult to use it as a communication tool on the construction jobsite. A STROBOSCOPE m odel as shown in Figure 3-5 does not resemble the natural way that people would describe this project Moreover, a lot of information (such as complex startup constr aints written in the Semaphores) cannot be represented graphically in the ACD diagram, so one needs to read the code to find out the whole and accurate m eaning of the model. 3.1.3 Summary of Modeling Regular Projects Based on Case Study One, we can summarize the most important requirements for modeling typical regular projec ts. Table 3-1 shows the abi lities of the CPM method and the STROBOSCOPE method in ad dressing these requirements.

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63 Table 3-1. Modeling requireme nts for regular projects CPM STROBOSCOPE Duration Only real numbers or probabilistic distributions. Both deterministic and probabilistic. The values are dynamically determined. Can be resource driven. Progress curve No No Interruption No No Activities Duration adjustment No No FS,SS,FF, SF relationships Yes Only FS relationships can be directly represented. Non-time-based dependencies No No Compound constraints Only AND logic. Yes, but need extra nodes or coding. Dependency Relationships Branching No Support both probabilistic and decision-based branching. Direct representationNo Yes, include generic, characterized and compound resources. Activity selecting resources No Yes, but activities can only select from resources of the same type. Resources Resource selecting activities No Yes, but an activity can only be assigned one priority value for all the resources it shared with other activities. Environmental factors No Yes, but these factors need to be modeled with separate sub-networks. General Easy to learn, to use and to understand. Difficult to learn, to use and understand.

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64 3.2 Case Two: A Typical Linear Project The second case study is a typical linear project, which cont ains only continuous activities and continuous depe ndency relationships buffers. The project data came from a real-world example provided by Sh i and Abourizk ( 1998) in their study on the modeling of pipeline construction projects. The project was to in stall a 10 km long gas line in a natural bush area. As shown in Table 3-2, it consisted of six tasks: right-of-way, stringing, welding, trenching, lowering-in and backfilling. The resources available to this project are shown in Table 3-3. The Right-of-way was divided into two s ections: Section 1 of 6000m length which was in a thickly wooded area and Section 2 of the remaining 4000m length that was easier to clear. The two sections were both constructed by Crew A. Stringing used Crew B, and the productivity did not vary too much throughout the whole length. Welding was assigned to Crew C. As th ere were many uncertainties that could influence welding, the production rate of this activity followed a uniform distribution. Trenching required different equipment under different geotechnical conditions. The whole site was therefore divided into 4 sections for trench ing. The first section, 3000m long, was excavated with two backhoes; the second section, a 500m valley, only used one backhoe; the third, 4000m, used a tr encher. The fourth section, 2500m long, had similar soil conditions as the third, but once in a while (approximate ly 10% of the time) rocks were encountered and a backhoe was needed to assist the trencher. Lowering, shared Crew B with Stringing. Backfill, only used one dozer.

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65 Table 3-2. Description of the pipeline c onstruction project (Shi and Abourizk 1998) Activity Number. of sections Length of section (m) Advance rate (m/h) Crew Distance buffer (m) Right-of-way 2 Section 1: 6000 80 Crew A 100 Section 2: 4000 100 Stringing 1 10,000 400 Crew B 100 Welding 1 10,000 U(120,150)* Crew C 100 Trenching 4 Section1: 3000 T(50,70,100)* 2 backhoes 50 Section 2: 500 50 1 backhoe Section 3: 4000 100 1 trencher Section 4: 2500 U(80,100)* 1 trencher + 1backhoe Lowering-in 1 10,000 400 Crew B 20 Backfilling 1 10,000 200 1 dozer Uniform distribution. Triangle distribution. Table 3-3. Resources available to the pipeline construction project Quantity Crew A 1 Crew B 1 Crew C 1 Backhoe 2 Trencher 1 Dozer 1

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66 A distance buffer had to be maintained between any two activities. When the buffer was violated, the succeeding activity stopped or slowed down. The last column of Table 3-2 shows the required distance between an activity and its succeeding activity. Though the construction of this project is no t complex technically, it is not easy to find a proper tool to accurately model it The CPM method and the CYCLONE-based simulation methods have been excluded because they are not able to represent continuous activities and continuous depe ndency relationships (buffers ). Certainly a continuous activity could be divided into many discrete segments and a continuous buffer could be reduced to point-to-point dependency relati onships at the start and the end of the segments, this approach is complicate d, and more importantly, not accurate. Figure 3-9. Problems of discretizing continuous activities and buffers As shown in Figure 3-9, the succeeding activity might run into the preceding activity in the middle even wh en there is enough distance betw een their start points and end points. In fact, the LSM method is not adequate for this project either because it is not able to represent probabilistic production rates. Nevertheless, as it is widely considered the

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67 best scheduling tool for linear projects, we will still apply it here, ignoring all of the probabilistic factors. We will also examine a SLAM II model built for this project by Shi and Abourizk (1998), which is the only c ontinuous simulation model developed for construction projects that ha ve been published so far. 3.2.1 The LSM Model With the LSM method, the schedule can be quickly laid-out on the location-time diagram in a two-step manner: first, draw th e individual progress of each crew as if it were working independently w ithout any constraints; sec ond, arrange the progress lines from left to right, making sure that the buffers will not be violated. Figure 3-10 shows the resulting LSM schedule. The tota l project duration is 211 hours. Figure 3-10. The LSM model for Case Two If the project has a tight d eadline, the above schedule may need to be crashed. The project manager may choose to st art Stringing earlier (at the 48th hour, for example) so that all its succeeding activities can start earlier. When Stringing runs into the Right-ofWay, the stringing crew may leave the activity for a certain period of time and relocate to work on another activity. The break should be long enough to allow the crew to finish a 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 050100150200250 Total Duration = 211 h ROW String Weld Trench Lower-in Backfill

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68 fair amount of work on the other activity otherwise the time and cost involved in relocating cannot be justified. As the result of this change, the total project duration has been reduced to 190 hours, as shown in Figure 3-11. Figure 3-11. The LSM model for Case Two with a break Figure 3-12. The LSM model for Case Two with a slow-down The project manager may also choose to have the stringing crew continue its work after it has been blocked, but at a reduced pace following the Right-of-Way, as shown in Figure 3-12. Because the stringing crew is not working at its full capacity, this solution is 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 050100150200250 Stringing slows down after running into ROW Total Duration = 169 h ROW String Weld Trench Lower-in Backfill 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 050100150200250 ROW String Weld Trench Lower-in Backfill Stringing has a 44h break after running into ROW Total Duration = 190 h

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69 not very efficient cost-wise, but the projec t duration can be further reduced to 169 hours. The same strategies can be applied to other ac tivities if it is necessary to further crash the schedule. The advantages and limitations of the LSM method in the planning and scheduling of typical linear projects can be examined from the following aspects: modeling of activities, modeling of dependency relationshi ps, modeling of resour ces and modeling of other factors. 3.2.1.1 Modeling of activities It is able to show the continuous progre ss of the activities at any point in time. One major advantage of the LSM method when applied to the linear construction projects is that it is able to show the progress of th e activities at any point in time, not only at the start and the finish point as in the CPM or discrete simulation methods. It shows the positions of the activities as they progress. A big difference between the regular projects and the linear projec ts is: the activities in the regular projects usually are done at a relatively small space, such as a room or an ar ea; while the activities in the linear projects are spread along long lines thr oughout the whole project. Crews working on the regular projects change places only when they begin new activities, while crews working on linear projects are always moving. So for lin ear projects, it is necessary to show at every point in time, which por tions of the activitie s have being done, and which position is currently being worki ng at. The LSM method represents this information graphically. It is only able to represent determinis tic production rates, and only efficient for constant production rates. In this project, several act ivities had probabilistic production rates. But the LSM method can only deal with deterministic values, so the

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70 means of the distribution were used in th e models. This resulted in over-optimistic estimates of the project duration, due to th e bullwhip effect. Though it might be possible to develop a stochastic LSM method, it is doub tful whether such a method would lose the biggest advantage of the LSM method the ability to facilitate visualization. The diagram might contain too much information a nd become too complicated for the user to make sense of it. Even when there are no uncertainties in the production rates, the LSM method could become difficult to use. When all the ac tivities in the project have straight progress line all production rates are constant from the beginning to the end, scheduling with the LSM method is fast and easy. The controlling point (the point where one continuous activity touches the buffer of its predecessor activity) is either the start or the end of the progress line, which means that one can qui ckly finish the sche dule by connecting the lines head-to-head or end-to-end. However, if the activities are segmented and have different production rates in different sections (e.g., the right-of-way and th e trenching activity in the example), or the activitys progress line has a learning curve, it could be difficult to determine the controlling point. Often, knowledge in algebraic geometry is needed to calculate the accurate positions of the controlling points. It can easily represent the slow-downs a nd breaks of the continuous activity. As shown in Figure 3-11 and Figure 3-12 the LSM method shows clearly when the activity will be blocked by its preceding activ ity, whether it will slow-down to follow the pace set by the successor, or stop the work comp letely for a predefined period of time.

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71 3.2.1.2 Modeling of dependency relationships LSM can model continuous dependency relationships buffers. By maintaining the buffers between the ac tivities, the LSM method can ensure the constraints between the ac tivities at any point. LSM can model both time-based and di stance-based dependency relationships. In the LSM method, the buffers could be m easured both horizontally and vertically, which means that the imposed constraints coul d be either time-based or distance-based. 3.2.1.3 Modeling of resources LSM shows the work-path of the reso urces, but does not model resources directly. On the LSM diagram, each line represents the work path of a resource (or a crew). It could be easily read from the diagram how many crews are working on each activity, when and where each of them starts their work, where th ey are and how much work they have completed at a certain point of time, which direc tion they have been progressing in, etc. However, the LSM method does not model th e resources directly : the quantity limit of the resource, the priorities of the activ ities in requesting the shared resource, alternative resource assignme nt plans cannot be represen ted. From the LSM diagram alone, it is difficult to realiz e that Stringing and Lowering-in both used Crew B, and there was only one such crew available for the pr oject. This might result in the mistake of scheduling Lowering-in to start before Stringing was completely finished. 3.2.1.4 Modeling of other factors. LSM is not able to represent dynamic factors and their impacts. Temperature, precipitation, wind and other dynamically cha nging factors cannot be represented with the LSM method. Consequently, their imp acts on the activities cannot be modeled.

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72 3.2.2 The Continuous Simulation Model Figure 3-13 shows the continuous simulati on model for this project developed by Shi and Abourizk (1998) with the general pu rpose simulation tool Slam II. The model includes six sub-networks (Figure 3-13 (a)), ten DETECT nodes (F igure 3-13 (b)), and six RESOURCE blocks (Figure 3-13 (c )) and a user-writt en sub-routine. Each sub-network represents one continuous activity. In the first sub-network, the one represents the Right-of-w ay, two entities are generate d at the beginning of the network by the CREATE node. The two entities are then routed to the two following AWAIT nodes both waiting for the resource la beled as ROW. ROW is defined in the resource block. It has a quantity limitation of 1, and gives Activity #1 a higher priority over Activity #2. Therefore, the entity in th e upper Await node occupies the resource ROW and starts Activity #1, i.e., the first 6000m of the right-of-way. The duration of Activity #1 is defined as REL( ROW1), which means that this activity is going to be treated as a continuous proce ss, and it will be associated with a DETECT node named ROW1. The detect node ROW1 monitors the valu e of the state variable SS (1). Once the value approaches 6000m, Activity #1 will be ended, a COLLECT node will collect the statistics, and a free node will release the occupied resource ROW back to the resource pool. Then Activity #2 can start. The sub-networks of the ot her activities are constructed with a similar structure.

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73 (a) Sub-networks Figure 3-13. SLAM II model for Case Two. [Adapted from Shi, J., and Abourizk, S. (1998). "Continuous and combined event-process models for simulation pipeline construction." Construction Management and Economics 16, 489498. (Page 492, Figure 2)] (c) Resource Blocks (b) Detect Nodes

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74 In the user-written SUBROUTINE, 18 variab les are defined to represent the status of the activities. For example, SS (3) represents the progress of Activity #3 Stringing. The value of SS (3) is updated at fixed time intervals according to: SS(3) = SSL(3) + RATE(3)* DTNOW where SSL(3) is the value of S S(3) at current time TNOW DTNOW is the length of the fixed time-step, and RATE (3) is the production rate of Activity #3 for the next time interval, which is determined by: RATE (3) = 400 m (the actual production rate) when SSL (3) SSL (1) 100m and SSL (3) SSL (2) 100m; RATE (3) = 0 otherwise. where SSL (1) and SSL (2) represent the curr ent progress of the right-of-way Section 1 and Section 2. The advantages and limitations of th e continuous simulation method can be discussed in parallel to those of the LSM method as presented in 3.2.1. 3.2.2.1 Modeling of activities SLAM II is able to represent probabilistic and stochastic production rates. With Slam II, the production rate of the activity could be defined as probabilistic distributions or expressions th at contain any accessible variab les, which would lead to a much more realistic estimation of the total project duration compared to the deterministic LSM method. SLAM II is able to show the continuous progress of the activities at any point in time. At each fixed time step, the productivity of the activity is re-sampled (if probabilistic) and re-calculated, and the progres s of the activity is updated. By setting the

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75 size of the steps small enough, the resulted progr ess curve could show the progress of the activity at any point with adequate accuracy. SLAM II is able to represent slow-downs when the continuous activity is blocked, but have difficulti es in representing breaks. As demonstrated in Figure 3-11 and 3-12, whether the activity is stopped or slowed-down when it is blocked, has a big influence on the total project duration. Th e response as programmed in the SLAM II model actually imitates the slow-down option: the activity would pause for a few short intervals and proceed for a few short intervals; the resulted progress line appears like a shadow of its predecessor activity. It is very difficult to simulate the ot her option. To suspend the activity for a specified period of time would require writing codes in the subroutine to set the RATE to zero before the simulation time approaches (TNOW + specified interruption length). A more difficult task is to release the occupied resources from the interrupted activity so that they can be used elsewhere. With SL AM II, the resource is grabbed by the entity before it enters the activity a nd is not released until the ent ity leaves the activity. During the interruption, though the RATE is zero and th e activity makes no progress, the entity stays in the activity and the resource cannot be released. 3.2.2.2 Modeling of dependency relationships SLAM II is able to represent the co ntinuous dependency relationships buffers. The buffer constraints are checked at ever y fixed time step. So when the size of the steps is small enough, it could be ensu red with adequate confidence that the constraints are maintained throughout the whole process. Theoretically, SLAM II is able to rep resent buffers based on any measures. The constraints on the production rate of th e activity could be a compound expression

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76 containing any accessible variables; therefore, it is able to represent buffers measured on distance, percentage completi on or any other measures. 3.2.2.3 Modeling of resources. Resources can be realistically represented. With SLAM II, as with most of other simulation tools, resources can be represente d realistically with th eir type, quantity and other attributes. The shared resources can sel ect the next activity to execute according to the predefined priorities. 3.2.2.4 Modeling of other factors. Dynamic factors and their impacts can be represented. With SLAM II, the changes of the dynamic factors can be simulate d as continuous processes in separate subnetworks. The values of the dynamic f actors can be accessed and used in the representation of the production rates, thereby impact the progress of the activities. The continuous simulation model is even more difficult to develop and understand than the discrete simulation models. Con tinuous simulation is much less popular than discrete simulation in the area of management science. Only a few simulation packages provide continuous simulation tools as minor features, and usually those tools are not convenient to use. The user needs to build complicated networks and write codes to model even one simple continuous activity. 3.2.3 More on Linear Projects Cheng(2005) presented an interesting sche duling problem: in a site development project, there are often multiple utility lines (such as water, gas, sewage, storm water, electrical, ) that need to be constructed. Thes e utility lines usually have different layouts. The construction of each line needs its own wo rk space; when conflicts occur, the one with the lower priority has to pause to give way to the one with the higher priority. The

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77 contractor would like to predict the total proj ect duration given this requirement, so that they would be able to compare different schedules and minimize the impacts of interruptions. Figure 3-14 shows part of th e site plan Cheng presented in his study. If one tries to apply the LSM method or the continuous simulation method to this project, as in the previous example, one would quickly fail the problem poses some new challenges. If all activitie s in the project are performed along one single path (even if it is not a straight path), it is adequate to represent their positions with a one-dimensional co-ordinate, i.e., the total distance that has to be traveled from the starting point to their current position, which is often referred to as the chainage The distance between the activities therefore is the difference of their chainages. Figure 3-14. Site layout of two intersecting utility lin es. [Adapted from Cheng, B. (2005). "Limitations of Existing Scheduling Tools in Planning Utility Line Construction Projects." Un iversity of Florida, Gainesville. (Page 58, Figure 65)]

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78 Now the activities have different layouts. A two-dimensional coordinate system has to be used. The LSM method has only one axis to represent the spatial dimension, so it cannot satisfy the scheduling requirements of th is type of projects. With SLAM II, it is possible to use two variables to record the position of th e activities (e.g., use XX (i) and YY (i) to represent the horizontal and vertical coordina tes of Activity i ), and use the decomposed vector of the production rates (e. g., the horizontal component and vertical component of RATE (i) ) to update the positions; but th is would make the code-writing work in the subroutines of SLAM II even more demanding. The second problem is related with multiple levels of scheduling. The construction of one utility line includes multiple activities : just as in the previous example, the construction of the gas line in cludes 6 activities. The constr aint when the construction of Line 1 runs too close to the c onstruction of Line 2, Line 1 must yield actually means that when any activity on Line 1 runs into the bu ffer of any activity on Line 2, that activity on Line 1 must yield. Suppose that both lines consist of 6 activities to represent this constraint, 6*6/2 = 18 dependency relationships have to be defined. None of the existing scheduling methods provides an efficient way to represent these types of constraints.

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79 3.2.4 Summary of Modeling Linear Projects The requirements for modeling typical li near construction projects have been summarized in Table 3-4. Table 3-4. Modeling require ments for linear projects LSM SLAM II Productivity Deterministic Pr obabilistic and stochastic Slow-down Yes Yes Break Yes No Positions Yes Difficult. Could be represented with extensive coding. Activities Layout One dimensional Difficult. Could be multidimensional with extensive coding. Buffers Yes Yes Dependency relationships Buffer types Distance-based and timebased All types, theoretically Resources Direct representation Not directly represented, but the work paths of the resources can be visualized. Yes. Resources can be defined with type, quantity, and other attributes. Environmental factors No Yes, but have to be represented with separate networks. General Easy to learn, to use and understand, and provide great visualization when the project is not complex. Difficult to learn, to use and understand. 3.3 Case Three: A Typical Repetitive Project A repetitive project consists of many similar discrete un its or continuous segments. The construction of each discrete unit can be seen as a regular project. The construction of each continuous segment can be seen as a linear project. The major problems in the modeling of repetitive projects are how to repr esent the similarities and variances of the units/segments and how to connect the units/segments.

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80 In this case study, we are going to examin e the construction of the upper-structure of the 14-level condominium, including two ga rage levels (Level 1 and Level 2) and twelve condo floors (Level 3 to Level 13). After the foundational part of the building (as presented in Case One) was done, the work developed into a rhythm repeated on each level. Each floor in this condominium was 13,000 SF and was built in two separate pours: a smaller pour of 5,500 SF, and a larger pour 7,500 SF. The larger pour carried over the center line of the building to include the area around the elevator shaft. Th e roof was also divided into two pours, 1,400 SF each. So in total there were 24 concrete pours. Each pour consists of five repeating ac tivities: Form, RMEP, Pour, Cure & Stress, and Vertical. The fi rst activity, Form, was to run aluminum beams spanning the vertical columns off the previous floor and place slab formworks. This activity experienced an apparent learning curve: th e productivity increased gradually from 1584 SF/Day, to 1703 SF/Day, to 1875 SF/day and finally stabilized at 2187 SF/day. The second activity, RMEP included the reinfo rcement of the slab, and the mechanical, electrical & plumbing prepara tion before the concrete placement. RMEP also had a learning curve: at the beginning, it took 3 days to finish a po ur; afterwards the time was reduced to 2 days. RMEP had to keep at least 1500 SF behind Form to give it enough workspace. RMEP was immediately followed by Pour, which was finished within 1 day. After the poured concrete deck hardened to 66% of its desi gned strength, the posttensioning cables were stressed. Cure and Stress took 2 days. For this case study, we are going to exam ine the CPM model, the LSM model and the STROBOSCOPE model, and focus on their weaknesses in the modeling.

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81 3.3.1 The CPM Model Figure 3-15. Part of the CPM model for Case Three Figure 3-15 shows part of the CPM sche dule developed for this case study. The following problems have been id entified in this schedule: 3.3.1.1 Efficiency Development of the CPM schedule for the repetitive project is time-consuming and error-prone. First of all, it is very time-consum ing to develop this schedule. There were 28 pours in the upper part of the stru cture, each built with the same construction method, though the duration of some activitie s varied at a few locations. The CPM schedule does not utilize this repetitive char acteristic. The sub-network of each pour has to be inputted separately. One might save some time and effort by copying the sub

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82 network of one pour and then paste it 27 times; however, the dependency relationships between these sub-networks still need to be entered one by one. The process is also error-prone. When repeatedly inputting a group of unitnetworks that have 90% similarity, one w ould tend to ignore the 10% difference. This happened with the 3rd floor, where the reinforcement plan was different from the other floors. The scheduler forgot to change the length of duration for the activity Reinforcement at this floor when copying a nd pasting the sub-networks. This mistake caused a hectic rush when the work progressed to this level. 3.3.1.2 Resource-imposed dependency relationships CPM is inflexible in re presenting resource-imposed dependency relationships. There are two types of dependency relationships in construction projects. The first type is imposed by technical requirements and norma lly cannot be altered. Most dependency relationships in regular c onstruction projects belong to this type. The dependency relationships between different activities within one unit/segment in repetitive projects also belong to this type. For example, w ithin each pour, Form must begin before RMEP, and RMEP must be finished before Pour can start. The second type of dependency relationships are imposed by resources. In regular projects, if a resource is shared among more than one activity, the activities need to be sequenced linearly. In repetitive projects, crews working on one activity need to go through the units/segments one by one, im posing predecessor/success relationships among these units/segments. Most connections between different units/segments in the schedules of repetitive projects belong to this type. The resource-imposed dependency relationships are much more flexible, and may be changed as a result of different managerial preference of cr ew utilization strategies.

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83 For example, according to the schedule shown in Figure 3-15, the Form crew was going to do Pour 1 first and Pour 2 second, but it was totally feasib le for the crew to do it the other way, i.e., Pour 2 first and Pour 1 second. The number of crews assigned to one activ ity may also change the dependency relationships among the units/segments co mpletely. Now there was only one crew working on the activity Form, so that Form in all units/segments had to be sequenced into one line with the Finish-to-Start relati onships. If the project manager decided to reduce the total duration of the project and add a second crew to work on Form, the dependency relationships would need to be changed completely. There are many different ways that the two crews could be assigned: the project manager could assign a smaller crew to work on the smaller pours, and a big cr ew to work on the larger pours; or use the same type of crews and have each of them work on the earliest available units. Each strategy would result in a different wa y of linking the units/segments. Since the CPM method cannot represent re sources, it cannot represent resourceimposed dependency relationships directly. Ev ery time the managerial preferences, the number of crews, or the cr ew utilization strategies change, their impacts on the dependency relationships need to be figured out manually, and a lot of adjustments need to be made to the schedule. 3.3.2 The LSM Model Figure 3-16 shows the LSM schedule developed for Case Three. As can be seen in this example: LSM is difficult to represent pa rallel activities on the diagram. In the example project, seve ral activities were taking place the same time in the same unit. Pour partly overl apped with Cure & Stress, which also partly overlapped

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84 with Vertical. Many color, shading and denot ation combinations had to be tried before a proper scheme could be designed to di fferentiate the parallel activities. Scheduling with the LSM method for rep etitive projects is not efficient when certain assumptions cannot be fulfilled. When used for repetitive pr ojects, the LSM method could be very effective if two assumptions are true. First, all units/segme nts are made up of the same network the activities contained in the units/segments are identical; the durations/productivities of the activities are identical; and the dependency relationships within the unit/segment are identical. Second, work continuity has to be maintained fo r all activities. Under these conditions, each repetitive continuou s activity could be represented as a straight continuous line, and each repetitive discrete activity could be represented as a straight continuous double line whose thickness is the tota l time needed to finish one unit. The schedule can be quickly developed in a similar way as presented in Section 3.2.1. However, if there are variances among the units/segments, the LSM method would be just as inefficient as the CP M method or even more cumbersome.

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85 Figure 3-16. The LSM model for Case Three Form RMEP Pour Du r P Cure & Stress Vertical V

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86 Figure 3-16. Continued Form RMEP Pour Dur. P 10d Vertical V

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87 In this project, the time needed to finish the formwork in one pour varied from 5 days to 3 days. Therefore the repetitive activity Form had to be represented unit-by-unit as a series of separated blocks (as show n in Figure 3-16). There is no easy way to determine the controlling point on this repeti tive activity, and it is very difficult to position the succeeding activities according ly. Repetitive projects consisting of continuous segments have similar problems if the productivity rates of the activit ies vary frequently from segment to segment. Scheduling with the LSM method for rep etitive projects is very difficult when there are hetero-relationships. The term hetero-relationship is borrowed from the rese arch on the LSCHEDULER algorithm (El-Rayes and Moselhi 2001). Here it is used to refer to the dependency relationships between two different units/segment s of two separate repetitive activities. Figure 3-17. Representation of the hete ro-relationship in the LSM diagram In this project, beams and deck formwork s were placed on the top of the vertical columns off the lower floor, indicatin g that the activity Form on Floor n (n = 2 to 14) Pour i (i= 1 or 2) could not start until the ac tivity Vertical on Floor n-1 (n = 2 to 14) Pour i (i= 1 or 2) was finished. To model this constrai nt, we need to add a vertical arrow at the end of each Vertical ac tivity (as illustrated in Figur e 3-17) in the LSM diagram, This arrow could be subjected to multiple interpretations. This Form activity is delayed by one day because the Vertical activity on the previous floor has not finished.

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88 and examine the related Form activity against it, If a Form activity starts before the arrow, it has to be pushed back. Because of the hetero-relationships, it is very unrealistic to maintain the work continuity in this project. RMEP, Pouring, Cu re & Stress and Vertical have to start as early as possible in every unit so as to avoi d that Form on the next level is delayed too long. As shown in Figure 3-17, in each unit, th e activities are cluste red tightly together, whereas the connections among the blocks of the same repetitive activity are frequently broken, indicating that there are a lot of interruptions along each repetitive activity. It is difficult to read from the LSM di agram what these arrows actually represent and which activities they are restraining. Th e arrow as noted in Figure 3-17 could be interpreted as a constraint on the start of For m at Floor 7 Pour 2, as it was intended to be, or be misinterpreted as a constraint on the start of Pour at Floor 7 Pour 1 or Cure & Stress at Floor 7 Pour 1. 3.3.3 The Simulation Model Figure 3-18. The STROBOSCOP E model for Case Three Figure 3-18 shows the STROBOSCOPE model developed for the Case Three. The first node Start queue holds 24 entities of t ype UN (Unit) at in itiation, each entity

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89 representing one concrete pour. Since the deck forming crew is the most critical resource for floor construction and it sets the pace of th e work, it is also included in the model. One DCrew entity is initiate d in the DCIdle queue, and it is required to start the Form1 activity. 3.3.3.1 Efficiency STROBOSCOPE is efficient at modeling repetitive activities. The construction of the 14 floors (26 concrete pours) is represented by just one cycle in the STROBOSCOPE diagram. Compared to th e CPM model in Figure 3-15 and the LSM model in Figure 3-16, it is much more concise. The variances among the units are modeled by utilizing the charac terized resources. For exampl e, the durations of activity Pour, Cure & Stress, and Vertical are identical in all units, so their values can be directly defined as an attribute of the activity. The dur ations of the activity Form and RMEP vary across the units, so their values are defined as attribute FORMDur and RMEPDur of the characterized resource Unit. As a Unit enters a Form or a RMEP activity, the value of the correspondent attribut e is assigned to the duration of the activity. Thereby, STROBOSCOPE achieves efficiency in repres enting the repetitiveness and at the same time it also provides some flexibility in representing the variances among the units. 3.3.3.2 Resource-imposed dependency relationships STROBOSCOPE is able to model resou rce-imposed dependency relationships. In front of the Combi activity Form1, there are two queues: the Start queue that holds twenty-six virtual tokens Units, and the DCIdle queue that holds one formwork crew DCrew. The activity needs to obtain one Unit and one DCrew to start. To simulate multiple crews on this activity, the project manager can simply initiate more

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90 than one DCrew in the queue. By changing ac tivity priorities and queue disciplines, many different crew utilization strategies can be represented. 3.3.3.3 Hetero-relationships STROBOSCOPE is difficult to use in representing hetero-relationships. Representing hetero-relationships with the STROBPSCOPE method usually takes many trials and errors. Figure 3-19 shows one solution. Figure 3-19. Representation of the hete ro relationships in STROBOSCOPE Two variables are defined in the model: UnitStarted which counts the total number of units that have entere d the activity Form, and UnitCompleted which counts the number of units that have finished the activ ity Vertical. A new Form activity cannot begin unless the value of the Semaphore (UnitStarted<=UnitCompleted+1) is true. Also, ONDRAW UN1 ASSIGN UnitStarted = UnitStarted + 1 ONEND Vertical ASSIGN UnitCompleted = UnitCompleted + 1 Semaphore: UnitStarted <= (UnitCompleted+1) & UnitStarted <=23 Strength: UnitCompleted== 23 Strength: UnitCompleted<23

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91 the units need to be routed back to the Sta rt queue in order to trigger the initialization of the next Form activity once they exit from the Vertical activity. But from the 23rd units, this back flow has to be stopped, otherwise the model will begin to create the th unit. A fork named Finished therefore has to be inserted to control when to stop this process. 3.3.4 Summary of Modeling Repetitive Projects The requirements for modeling typical re petitive construc tion projects are summarized in Table 3-5. Table 3-5. Modeling requirement s for repetitive projects CPM LSM STROBOSCOPE Efficiency Not efficient Efficient only when all assumptions are satisfied. Difficult to show parallel activities. Efficient Resource-imposed dependency relationships Not directly modeled. Not flexible. Show resource flows, but does not model the resources directly. Yes Hetero-relationships Have to be represented one-by-one. Very difficult Very difficult 3.4 Case Four: A Project of Mixed Features In the last case study, the whole c onstruction process of the 14-level condominiums structure system will be exam ined. This project has fixed features because: (1) it contains both non-repetitive ac tivities (as discussed in Case One) and repetitive activities (as discussed in Case Three); and (2) it cont ains both discrete activities and conti nuous activities. A CPM model, a LSM model and a STROBOSCOPE model have been developed and are presente d in Figure 3-20, 3-21 and 3-22 respectively.

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92 Figure 3-20. The CPM model for Case Four

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93 Figure 3-20. Continued

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94 Figure 3-20. Continued

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95 Figure 3-21. The LSM model for Case Four

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96 Figure 3-21. Continued

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97 TokenGen Start T0 Foundation_1 PileDelay T13 T1 ExcElevator T2 BuildPiles_1 BuildPiles_2 FormPC_1 Reinforce_PC T5 T3 T4 T17 FormPC_2 T18 PourElevPC_1 T6 T19 T7 FRPPitWall_1 WPPitWall BackfillDeepFdn T21 StairPCs_1 T8 StairPCs_2 T23 StairWall#1_1 T9 EleWallSOG#2 StairWall#1_2 T10 T30 StairWall#2 T11 RetainingWall Foundation_2 T16 Vertical#1Lift T14 FRPPitWall_2 T22 BackFillSGEnd MEPUnderI T15 T12 WaitMEPUn der T25 WaitSOG# 1 T28 SOG#1Pour T26 T29 SOG#1Pre TokenGen2 T27 T24 Start Form1 UN1 DCIdle DC1 DC4 RMEP UN2 DC2 Form2 UN3 CureAndStress UN5 UN11 Pour2 Vertical UN6 UN7 Fork U13 UN12 FF TokenGen3 MEPUnderII_2 SOG#2Pre_1 SOG#2PRe_2 SOG#2Pour T300 T302 T303 T304 T305 Delay MEPUnderII T301 TokenGen4 Masonry T401 End MasonryFini shed T402 T403 FloorFinis hed UN15 RMEPFinish UN41 Pour1 UN42(a) Substructure Phase I (b) Substructure Phase II (c) Superstructure Figure 3-22. The STROBOSCOPE model for Case Four

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This case study focuses on integration of differe nt types of activities, including integration of discrete and continuous activities, and repetitive and non-repetitive activities. 3.4.1 Integration of discrete and continuous activities Among the existing planning and scheduling tool s, the LSM method is the only one that allows easy integration of discrete and con tinuous activities. In Fi gure 3-23, Form and RMEP are represented as lin es, showing how they progress gradually over time and the continuous buffer is maintained al ong the whole process. Pour, Cure & Stress and Vertical are represented as blocks, showing only th eir start and finish times at each pour. Figure 3-23. Integration of continuou s and discrete activities in LSM The CPM method is not able to represent con tinuous activities and continuous dependency relationships. All continuous act ivities have to be divided in to discrete segments, and all continuous buffers have to be transformed in to an SS dependency and an FF dependency, which may result in mistakes as discussed in Case Two. Similarly, STROBOSCOPE can only control the st artup of the activity the value of the Semaphore and the availability of the required re sources are checked before the activity starts. No constraints can be imposed in the middle of the activity. Figure 324 shows part of the STROBOSCOPE model that is used to represent the buffer between the activity Form and the activity RMEP. This representation is more co mplex compared to the CPM representation of buffers, while it will result in the sa me mistake as the CPM method does.

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Figure 3-24. Representation of a continuous buffer in STROBOSCOPE 3.4.2 Integration of repetitive a nd non-repetitive activities. The LSM method is not able to represent nonrepetitive activities. So the schedule only contains the upper structural part. The CPM method is able to represent both non -repetitive activities and repetitive activities (but only discrete repetitive activities). However,since the CPM method represent each unit/segment of the repetitive activities separate ly, there is a large amount of repeated and redundant data in the schedule, and the inte rfaces between the repe titive part and the nonrepetitive part are often shroude d and unclear. This can be demonstrated with the CPM schedule as shown in Figure 3-20. The foundation part of this project was constr ucted in two separate phases. The second phase started from the middl e of the construction of the upper structure after the formwork of the first pour at the 5th level was done. While the link representing this dependency relationship is very im portant in project management a nd control, it is buried deeply among the entangled relationship line s among the repetitiv e activities. In the STROBOSCOPE model, the repetitive act ivities usually are linked together by the flow of a physical unit a pour in this case, while the non-repe titive activities are linked by a virtual token. Sub-networks consis ting of different types of activi ties therefore cannot be directly connected, they need to be synchronized with the use of some cont rolling variables. For example, the second phase of substructure cons truction, noted as Figure 3-22 (b), cannot start

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until 2 days after the formwork on the 1st pour of the 5th floor has been completed. To model this relationship, a variable PhaseIIStart is defined and initiate d with value 0. A semaphore PhaseIIStart==1 is added to the first activit y in Figure 3-22 (b). When Unit7 flows through Form1 in Figure 3-22 (b), it changes the value of PhaseIIStart from 0 to 1, thus satisfies the semaphore and allows Figure 3-22 (b) to start. The actually implementation is even more complicated than this, as th ere are time delays involved. Another example is Masonry cannot start until the 2nd concrete pour on the 12th floor has ended. As shown in Figure 3-25, this constraint is implemented by duplicating Unit22 when it passes through activity Pour a nd then sending the duplicate to trigger the activity node Masonry. In addition, code must be written in the Link UN6 to restrict the number of units it can draw at one time. Otherwise both the origin al and the duplicate will go to the activity Vertical. Figure 3-25. Integration of repetitive and non-repetitive activities in STROBOSCOPE BEFOREEND Pour GENERATE PRECOND Pour.Unit.ID.SumVal==22 1 Unit22; RELEASEUNTILL Vertical.Unit.Count==1

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3.4.3 Summary of Modeling Repetitive Projects The requirements for modeling co nstruction projects with mixed features are summarized in Table 3-6. Table 3-6. Modeling requirements for projects with mixed features CPM LSM STROBOSCOPE Integration of discrete and continuous activities No Yes No Integration of repetitive and nonrepetitive activities Yes, but not efficient. No Yes, but difficult.

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102 CHAPTER 4 REQUIREMENT ANALYSIS In Chapter 3, we presented four typical type s of construction projec ts and examined the models developed for them with various existi ng planning and scheduling tools. Each technique shows its strengths in the modeli ng of certain aspects and certain parts of the projects, yet each also has fundamental limitations making it inade quate for addressing a lot of requirements that arisen from real-world construction projects. So is it possible to develop a new modeling tech nique that (1) can be universally applied to any types of construction projects and (2) incorporates and enhan ces the best features of the existing techniques? If it is po ssible, what essential characteris tics should such a tool exhibit? This chapter tries to portray an ideal m odeling technique for construction planning and scheduling, while the question of whether such a technique ca n be realized and how to implement it will be left for the following chapters. The desired characteristics will be analyzed fr om four perspectives: breadth of application, form of representation, accuracy of modeling and levels of modeling. 4.1 Scope of Application Scope of application refers to the domain that the pla nning and scheduling method is designed for. Each of the existing tools has a lim ited scope of application which fits its basic assumptions: the CPM method is designed for re gular projects, the LSM method for linear projects, and the CYCLONE-based simulation method methods for cyclic operations. Although these methods can be applied to certain areas out side of their domains, such as the CPM method for repetitive projects, or the CYCLONE-based si mulation tools for regular projects, they would become very cumbersome in use. The case studies in Chapter 3 have clearly demonstrated this point.

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103 The desired planning and scheduling method s hould be able to represent all types of construction projects, namely, regul ar projects, repetitive projects, linear projects and projects that have mixed features, with sufficient efficien cy. An even more ambitious idea is for this method to incorporate the modeling of lower-level operations as well. From another perspective, the method needs to be able to integrate the discrete and continuous, repetitive and non-repetitive elements together. As shown in Figure 4-1, Regular Projects mainly consist of non-repetitive discrete activities, while Linear Projects consist of nonrepetitive continuous activities Discrete activities, when repeated many times, form the Repetitive Discrete Project; continuous activitie s, when repeated, form the Repetitive Linear Project these two types of proj ects usually are not differentiate d, both being referred to as Repetitive Projects. A project of mixed features may contain both the continuous and discrete, repetitive and non-repetitive elements. A method that is able to represen t both the discrete and continuous, repetitive and non-repetitive elements a nd integrate them together would be able to model all types of construction projects. Figure 4-1. Scope of application Regular Projects Linear Projects Repetitive (Discrete) Projects Repetitive (Linear) Projects Nonrepetitive Repetitive Discrete Continuous Projects of Mixed Features

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104 4.2 Accuracy of Modeling The concept of accuracy refers to how faithfully a model is able to represent its real-world counterpart. The more properties a nd behaviors of the real-world system the model is able to represent, the more accurate it is. In another sense, accuracy of modeling also is a measure of the scope of application. But rather than determining which type of projects can be modeled, it determines how many types of realistic situations it is able to handle. Table 4-1 summarizes the results shown in Table 3-1, 3-4 and 3-5, and provides an overview of the basi c requirements for a universally applicable planning and scheduling tool to fairly accurate ly model all types of construction projects. However, there are always trade-offs among accuracy, complexity and computing efficiency. As the accuracy of the model increas es, the complexity of the model increases too, demanding more computing resources. A very important point is that for a given objec tive, a highly accurate model may be just as valid as a less accurate one. For example, when the intermediate progress of an activity is not of concern, representing it as a contin uous activity is as valid as repr esenting it as a discrete one, but the continuous representation would require much more resources. An ideal planning and scheduling tool should allow flex ibility with regard to the le vel of accuracy, so that the complexity of the schedule could be appropriate for the objective of th e specific planning and scheduling study. Moreover, no matter how capable the modeling t ool is, it is not possible to include all properties and behaviors of its source system the properties and behaviors of a real-world system are infinite. Therefore, the desired m odeling tool should incl ude the most intrinsic properties and behaviors of cons truction projects, but it must be extensible to incorporate additional properties and behaviors when necessary.

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105Table 4-1. Summary of the key requirem ents for modeling construction projects CPM LSM STROBOSCOPE SLAM II Duration Only real numbers and probabilistic distributions. Both deterministic and probabilistic. The value can be dynamically determined. Could be resource driven. Progress curve No No Interruption No No Activities Adjustment No No FS,SS,FF, SF relationships Yes Only FS relationships can be directly represented. Non-time-based dependencies No No Compound constraints Only AND logic. Yes, but need extr a nodes or coding. Discrete Dependency Relationships Branching No Support both probabilistic and decision-based branching. Productivity Deterministic Probabilistic and probabilistic Slow-down Yes Yes Break Yes No Position Yes Could be represented with extensive coding. Activities Layout One dimensional Could be multi-dimensional with extensive coding. Buffers Yes Yes Continuous Dependency Relationships Buffer types Distance-based and timebased All types, theoretically.

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106 Table 4-1. Continued CPM LSM STROBOSCOPE SLAM II Resources Representation No Not directly represented, but the work paths of the resources can be visualized. Include generic, characterized and compound resources. Yes. Resources can be defined with type, quantity, and other attributes. Activity selecting resources No No Yes, but activities can only select resources in the same queue. Yes Resource selecting activities No No Yes, but an activity can only be assigned one priority value for all the resources it shared with other activities. Yes Environmental Factors No No Yes Yes, but these factors need to be modeled with separate subnetworks. Representation Not efficient Difficult to show parallel activities. Not efficient when certain assumptions cannot be fulfilled. Efficient Not efficient, each segment has to be represented as a separate sub-network Resource-imposed dependency relationships Not directly modeled. Not flexible. Show resource flows, but does not model the resources directly. Yes Yes Repetitive Hetero-relationships Have to be represented one-byone. Difficult Difficult Difficult Discrete and continuous No Yes No Yes Integration Non-repetitive and repetitive Yes No Yes, but difficu lt Yes, but difficult

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107 4.3 Form of Representation Form of representation refers to how the user is going to describe a project. The CPM method uses the AOA or AON network, the LSM me thod uses the time-location diagram, and most of the existing simulation method us es the ACD diagrams. Besides graphical representations, the representati on can also take the form of dialogue windows in computer programs, simulation languages, general purpos e languages, or mathematical formulations. The following characteristics are considered essential for good representations: It should be easy to learn. The popularity of the CPM method in a great de gree is owing to its advantage in this perspective. The simulation method, on the ot her hand, has not been well-accepted by the construction industry till now primarily because it takes a lot of time to learn the tricks about how to use modeling elements, modeling rules, and the program-specific simulation languages. It should be efficient in use. In planning and scheduling, efficiency is requir ed in two areas: the development of a new schedule and the editing of an existing schedule. Construction projects are characterized by th eir strict deadlines a nd dynamic natures. The project manager usually can only devote very limited time to scheduling. Under a lot of occasions he or she has to quickly develop a draft schedule within hours, and editing the schedule within minutes. As for the development of new schedules, th e CPM method is very efficient in use for typical regular projects, but not for repetitive projects. When there are n units, every repetitive activity needs to be represented n times in a CPM schedule (refer to the repetitive part of the CPM model in Case Study One). The simulation m odel is not as efficient as the CPM method for regular projects several nodes often have to be used in order to represent a simple logical

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108 relationship (refer to the non-repeti tive part of the simulation model in Case Study One). But the simulation model is very efficient for repetitive pr ojects it can use the network of one unit to represent the work of n units (refer to the repetitive part of the simulation model in Case Study One). The LSM method is most efficient for re petitive projects and lin ear projects, but only when the projects satisfy a lot of assumptions. A good planning and scheduling t ool should be efficient for all types of construction projects. As for editing, the efficiency of a planning and scheduling tool is mostly determined by how it handles repetitive activitie s and resource-imposed dependenc y relationships. As discussed in Section 3.3.1, resource-imposed dependency rela tionships are very flex ible and subject to change with different resour ce utilization strategies. It should reflect the natural way that people look at the project. One of the most important functions of a sc hedule is to facilitate communication. There are many parties involved in the planning and scheduli ng process, including the project manager, the foreman, the owner, the architect, the subcont ractors and the suppliers, who all need to understand each others needs and concerns. A modeling tool is a language that people involved in planni ng and scheduling use in their communication the modeling elements are th e words, and the modeling rules are the grammars. The modeling elements and rules should reflect the natural way th at people talk about the project. They should not requir e too much interpretation; otherw ise people will have to focus on the words and grammars rather than the meanings and ideas. Examples of unnatural representations can be found in the two simulation models in Chapter 3: a virtual token has to be generated, duplicated and routed to represent the start/finish

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109 logical dependency relationships between the ac tivities; a sub-network, a detector node and a subroutine together represent a continuous activity; etc. The time-location diagram the LSM method, on the contrary, is very na tural and intuitive. The lines, blocks, bars and buffers resemble the la yout of the activities in the real world, and thus facilitate understanding and vi sualization of the situation. 4.4 Levels of Modeling There are many different levels at which a construction project c ould be described. For example, at the top level, the construction proj ect has the constraint on when the whole project can start, the location of the project, the total resources assigned to the project, etc.; at the secondary level, the activities have the constraint on when the acti vity can start, the location of the activity, and the resources avai lable to the activity; at the th ird level, the activities can be decomposed into sub-activities, each of which has their indi vidual constraint, location, and resources. When developing a schedule, sometimes we fo llow a top-down approach we start from the top level to consider the overall situation and then focusing on the details; sometimes we follow a bottom-up approach we start from the details and then integrate them to figure out the whole. And often we need to alternate betw een these two approaches to ensure that the schedule satisfies all the re quirements at all levels. With the existing planning and scheduling tools, constraints, resources and other properties cannot be added on aggregated activities, which means that scheduling can only be performed on one level (although the scheduling results ca n be summarized to high-level views). Consequently, it is often necessary to develop multiple schedules for one project at each planning level. This results in repeated input and possible c onflicts among the many different levels of schedules.

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110 Allowing modeling on multi-levels is also re quired to improve the efficiency of representation. Constraints, reso urces and properties that are sh ared among similar activities can be defined only once at a high le vel; properties that ar e unique to individual activities can be defined separately on the low level. Actually, the way in which the SCOBOSCO PE method models repetitive activities provides an example in this aspect. Assuming that the dependency relationships among the activities (which is a type of constraints) in all units are the same, only one unit network is represented, and then the durations of the activities at each unit are separately defined through the attributes of the tokens (re fer to the repetitive part of th e simulation model in Case Study One). And this is why the STROBOSCOPE mo del is much more compact than the CPM model for the repetitive part. However, th e STROBOSCOPE method only enables modeling on two levels (one on the general activity level, one on the unit level) in a very limited way. An ideal planning and scheduling tool shoul d allow modeling on multiple levels with complete flexibility.

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111 CHAPTER 5 A NEW THEORY FOR PLANNING AND SC HEDULING CONSTRUCTION PROJECTS Chapter 4 has identified the desired characteri stic of an ideal mode ling tool universally applicable; providing adequate accuracy with enough flexibi lity and extensibility; simple, efficient and natural in representation; and s upportive of multiple-level modeling. None of the existing construction planning and scheduling tools is able to provide these characteristics. This chapter proposes a new planning and sc heduling philosophy that is aimed to deliver the desired characteristics as summarized a bove. The theoretical foundation for this new philosophy system theory and DEVS (Discr ete Event System Specification) will be introduced first, and then the proposed th eory will be explained in details. 5.1 Theoretical Foundations 5.1.1 System Theory Before we can develop a method that can be uni versally applied to model different types of projects, activities, resources etc., we need to, first of all, establish a unified concept framework that can be used to view various types of entities involved in different type of projects. System theory pr ovides such a unified view. Systems theory is a trans-disciplinary fi eld that studies the abstract organization of systems, independent of the substance, type, or spatial or te mporal scale of existence. It investigates both the principles common to all complex systems, and the models which can be used to describe them. It was founded in the 1940's by the biologist Ludwig von Bertalanffy, and furthered by Ross Ashby. It has been developed into diverse branches and has been applied in numerous areas including engineering, computing, management and ecology (Klir 1991). A system is a set of elements which interact w ith each other within the system's boundaries (form, structure, organization) to function as a whole. The central concept of system theory is

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112 that the properties of the w hole is always different from, and more than, the sum of its unassembled collection of elements. Figure 5-1. Basic system concepts. [Adapted from Zeigler, B. P., Praehofer, H., and Kim, T. G. (2000). Theory of Modeling and Simulation Harcourt India Private Limited, New Delhi, India. (Page 4, Figure 1)] As shown in Figure 5-1, a system has both internal structure and external behavior Viewed as a black box, a systems function is to transform received input time histories and generate output time histories. The relationship it imposes between the inputs and outputs is called the external behavior Inside the black box, a system has its internal structure which include three com ponents: (1) the state of the system; (2) the transition mechanism that dictates how inputs from the outside cause the current state of the system to transform into the next state; and (3) the state-to-output mapping i.e., how the current state will lead to production of outputs. Knowing the internal structure of a system allows one to simulate and analyze its external behaviors. From the system theorys point of view, the task of modeling and simulation is to develop an abstract model to mimic the intern al structure of a system for the purpose of predicting and studying the extern al behaviors of the system. As shown in Figure 5-2, a system may be broken down into component systems through decomposition, and component systems ma y be coupled together to form a resultant system SYSTEM input trajectory Time output trajectory Time state

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113 through composition. The ability to continue to compose larger and larger systems from previously constructed components leads to hierarchical construction Furthermore, if the structure and behavior of a resu ltant system can be expressed in the original formalism of its component systems, this system is considered closed-under-composition Such a system is considered to have well-defined st ructure and behavior in the system theory (Zeigler et al. 2000). Figure 5-2. Hierarchical construc tion of a system. [Adapted from Zeigler, B. P., Praehofer, H., and Kim, T. G. (2000). Theory of Mode ling and Simulation, Harcourt India Private Limited, New Delhi, India. (Page 5, Figure 2)] 5.1.2 The DEVS Formalism The structure of a system may be expressed in a mathematical language called formalism. DEVS (Discrete Event System Specification) is a fundamental, rigorous formalism for representing dynamic systems. The first versi on of DEVS was conceive d by Zeiger (1976) and referred to as TMS76. It has been improved continuously through the years and the current version is TMS99 (Zeigler et al. 2000). Now, research and development groups on DEVS are reported to be found throughout the world, incl uding the US, Canada, Korea, Japan, UK, Portugal, France, Austria, Ge rmany, Argentina and Mexico.

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114 Two concepts are at the co re of the DEVS paradigm: System specification formalisms the modeler can use different formalisms, such as continuous or discrete, to build component models, and integrate them in one system. Levels of system specification the behavior and the stru cture of a system can be described at various levels. With the DEVS formalism, at the bottom level, atomic models are developed to describe: (1) how a system makes deterministic transitions between sequential stat es autonomously; (2) how this system reacts to external input; and (3 ) how this system generates output. The structure of the atomic model is defined as M= (X, Y, S, ext, int, ta) (Equation 5-1) where X = {(p,v) | p InPorts, v Xp} is the set of input ports and values; Y = {(p, v) | p OutPorts, v Yp} is the set of output ports and values; S is the set of state variables and parameters; int: S S is the internal state transition function ; ext: QX S is the external state transition function where Q = {(s, e) | sS, 0
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115 transitory state. In the second case, the system will stay in S forever unless an external event interrupts its slumber, so S is called a passive state. When the resting time in state S expires, i.e., when the elapsed time e tas, the system outputs the value s, and changes to state int s. Note that outputs can only be generated just before internal transitions. Figure 5-3. Behavior of the DEVS atomic model. [Adapted from Zeigler, B. P., Praehofer, H., and Kim, T. G. (2000). Theory of Mode ling and Simulation, Harcourt India Private Limited, New Delhi, India. (Page 76, Figure 1)] If an external event x X occurs before this expiration time, i.e., when the system is in total state s ewith e tas, the system changes to state exts. Thus the internal transition function dictates the systems next state when no events interrupt the system since the last transition; while the external tran sition function dictates the system s next state when an external event occurs this state is determined by the input x the current state S and how long the system has been in this state when the external event occurred, e In both cases, the system is then in a certain new state S' with a new resting time tas' and the same story continues.

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116 Higher level models are constructed by coup ling component models. The components can be atomic DEVS models as well as coupled DE VS in their own right. The specification of a coupled model includes the external interface (input and output ports and values), the components (which must be DEVS m odels), and the coupling relations: N = (X, Y, D, {Md |dD}, EIC, EOC, IC, Select) (Equation 5-2) where X {(p,v ) | p IPorts v Xp} is the set of inpu t ports and values; Y {( p v ) | pOPorts vYp} is the set of output ports and values; D is the set of the component names; Components are DEVS models (i.e., for each d D), M d X d, Y d, S, ext, int, ta is a DEVS with X d {(p, v) | p IPortsd, vXp} Yd {(p, v) | p OPorts d, vYp}; External input couplings connect ex ternal inputs to component inputs: EIC {((N, ip N),(d, ipd))| ipN IPorts, d D, ipd IPortsd}; External output couplings connect co mponent outputs to external outputs: EOC {((d, opd), (N, ip N))| opN OPorts, d D, ipd OPortsd}; Internal couplings connect compone nt outputs to component inputs: IC {((a, opd), (b, ip N))| a,bD, ipa OPortsa, ipb OPortsb}; Select : 2D {} D, the tie-breaking function. Zeiger (1984) have proved that the DEVS formalism is closed-under-composition: for each pair of coupled DEVS, a resultant atomic DEVS can be constructed. As such, any DEVS model, atomic or coupled, can always be replaced by an equivalent atomic DEVS. As a coupled DEVS

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117 may have coupled DEVS as its components, hier archical modeling is supported. The constitution of the resultant atomic DEVS also makes it possible to implement a simulator capable of simulating any DEVS models. 5.2 The Proposed Theory In the proposed method, each activity, each type of resources and each group of environmental factors is regarded as an independent system, repr esented in the DEVS formalism. The state of these systems will change according to their internal transition functions if no external event intervenes, and outputs can be generated just before the occurrence of each internal transition. The internal transitions will be interrupted, however, when the system receives an input, in which case the state of the system will cha nge as dictated by the external transition function triggere d by the received input. There are three types of atomic activity mode ls in the proposed system: the non-resourcedriven discrete activity model Activityd, the resource-driven discrete activity model Activitydr, and the continuous activity model Activityc. Multiple atomic activity models can be assembled into one compound activity model, which could be a non-resource-driven discrete model Compoundd, or a resource-driven discrete model Compounddr, or a continuous model Compositec. Each compound activity model has its own input and output ports, and can be used just as an atomic activity model in the construc tion of higher-level compound activ ities. The repe titive activity model Repetitive is a special type of compound activity model. 5.2.1 Atomic Activity Models 5.2.1.1 Non-resource-driven discrete models With the non-resource-driven discrete activity model Activityd, the duration of the activity is independent of the resources, and the activ ity will progress according to the predefined progress curve (if no external event intervenes). Th is model allows the duration of the activity to

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118 be adjusted and the progress to be interrupted in the middle by external events, provided that such events are rare. If the activ ity is influenced by any environmen tal factor that is constantly changing, the activity is be tter represented with a continuous activity model Activityc. Figure 5-4. Non-resource-driven discrete Activity A with many realistic factors Figure 5-4 shows an example of a non-resource-driven discrete activity which has incorporated a number of realistic factors. In this example, Activity A-Placement Concrete cannot start until Activity B is 50% finished and Ac tivity C is completely finished, plus that the temperature has to be above 40 degrees. When Activ ity A is progressing, if the temperature falls to below 40F, it will have to pause for 1 day. The construction of a nearby Activity G will also impact Activity A, causing its productivity to decrease to .7 of the normal speed. After Activity A is 70% finished, Activity F can start. And af ter Activity A is completely finished, Activity D will be performed if the time is early enough (<30 days), otherw ise Activity E will be performed Activity Environmental Factor Interrupt Link Start/Finish Link Adjust Link Branch Node A N (10, 2) B C D E 50% F tem p >40 1d tem p <40 75% time<30 time 30 G E-Factors temp 1.4 1.0 Legend

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119 as a remedy plan. The estimated dur ation of Activity A is N (20, 4) 1, and its progress curve is depicted in Figure 5-5. Figure 5-5. Progress curve of Activity A Figure 5-6. Non-resource-driven discrete model of Activity A The structure of the non-resource-driven discre te model for Activity A is illustrated in Figure 5-6. This structur e can be described as: Ad = (X, Y, S, ext, int, ta), (Equation 5-3) in which the elements are defined as: State S. The state of the non-resource-driven discre te activity is represented with a set of parameters and state variables. The parameters include: name. This is the unique identifier of the activity. 1 N (10, 2): Sample from a normal distribution with the mean of 20 days and the standard deviation of 4 days. Ad interrupt adjust finish 75% 100% (A, 75%) (A, 100%) star t Test (S, e) (B, 50%) (C, 100%) Test (G,70%) Progress(%) d .9d Ti m 100 75

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120 work_quantity The total quantity of work involved. duration The estimated duration for completing th e activity from start to finish, without any interruptions. progress_function. The progress function progress = p (duration, time) describes the progress curve of the activity, i. e., how the activity would proceed from start to finish over time without external interruptions start_constraint. This is a compound logical expression that represents the total constraints on the start of the activity. Each start dependency relations hip is associated with one logical variable con (predecessor_name, predecessor_progress), whose initial value is set to False. The time constraints and the e nvironmental constraints on the start of the activity are represented as logical expressions. These logical variables and logical expressions are connected with the AND and OR operators in the start_constraint For example, the start_constraint for Activity A is con(B, 50%) AND con(C, 100%) AND (tem>40) whose initial value is F alse AND False AND (tem>40). finish_constraint. A compound logical expression represen ting the total constraints on the finish of the activity. interruptions. Interruptions are defined by {(interrupt_condition interrupt_length resume_condition)} where interrupt_condition represents a condition that will trigger an interruption, interrupt_length specifies the length of that interruption and resume_condition specifies the condition under which th e activity will be resumed if the length of the interruption is not provided. The interruptions for Activity A is {(tem<40, 1, ,)}. adjustments. Adjustments to the duration of the activity are defined by {(adjust_condition, adjust_factor)} where the adjust_condition represents a condition that will cause the duration of the activity to change, and the adjust_ factor specifies the adjustment factor that will be applied. The adjustments for Activ ity A is represented by {(con(G, 0%), 1.4), (con(G, 100%), 1.0)}. markers. A marker is a point on th e activitys progress where it needs to generate an output. Each dependency relations hip imposed by the activity is associated with a marker. The markers of the activity are sorted in ascending orders in a list called the markers. Activity A markers are {75%, 100%}. The state variables include: phase. A discrete activity could be in one of the four phases at any point in time: starting: the activity is waiting for th e start constraints to be satisfied. progressing: the activity is proceeding according to the specified progress curve.

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121 interrupted: the activity has been inte rrupted during the middle of its progress, waiting to be resumed again. finished : the activity has been 100% completed, and all constraints on the finish of the activity have been satisfied transition_progress. A percentage that records the progress of the activity when it enters into the current phase. a. This is the adjustment factor wh ich is going to be applied to the duration of the activity to determine the adjusted duration A non-negative real number th at records the time remaining in the current state with the absence of any external events. In other wo rds, the activity will stay in the current state for the time given by the state variable The initial state of th e activity is set to S (phase, transition_progress, a, ) = (starting, 0%, 1, ). Total State Q The total state of the activity is represented by {(s, e) | sS, 0
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122 Figure 5-7. Determining the progress during the progressing phase Inputs X As shown in Figure 5-6, each non-resour ce-driven discrete activity model has four input ports, start, i nterrupt, adjust, and finis h. The input messages could be sent from its predecessor activities in the form of (predecessor_name, predecessor_progress) or the Test signals from the influencing enviro nmental factors. InPorts = {start, interrupt, adjust, finish}, Xstart = Xinterrupt = Xadjust = Xfinish = {(predecessor_name, predecessor_progress)} Test, X= {(p,v) | p InPorts, v Xp} is the set of input ports and values. Outputs Y. The atomic non-resource driven activ ity model has one output port for every marker. Therefore, Activity A has two output por ts: % for the dependency relationship when A is 75% finished and % for when A is 100% finished. The value of the output is a message consisting of the name of the activity and the pr ogress of the activity. OutPorts = {markers(1),markers( 2),markers(i),,markers(n)} Ymarkers(i) = {(name, progress)} Y= {(p,v) | p OutPorts, v Ymarkers(i)} is the set of output ports and values. Internal Transition Functions int: S S If no external event occu rs, the activity will stay in state S for time ta(s) When the resting time in state S expires, i.e., when the elapsed time e=ta ( s) the activity outputs the value ( s ) and changes to state int (s) Under the starting a nd the finished phase, = which means that the activity will stay in a passive state until being changed by external events. During the progressing phase, the activity will proceed from one mark to the next, unless it has reached the 100% marker, in which cas e it will rest and wait for the finishing constraints to be satisfied. int(progressing, transition_progress, a, ) transition_progress progress 14.3 5.7 Time Progress(%) 100 20 7.7 35 e p (1.40, time)

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123 = (progressing, next (markers), a, (p-1(aduration, next(markers)-p-1(aduration, transition_progress)) if next(markers) 100%; = (progressing, 100%, a, ) if next(markers) = 100%. If the activity has been interrupted, when th e time specified for the interrupted phase expires, the activity will return to the p rogressing phase, and continue to proceed towards the next marker. int (interrupted, transition_progress, a, ) = (progressing, transition_progress, (p-1(aduration, next(markers)-p-1(aduration, transition_progress)). Output Function : S Y Outputs are generated just be fore the internal transitions. Activities will generate outputs only when they are under the progressing phase. (progressing, transition_progress, a, )= (next(markers), (name, next(markers)) Suppose that S = (progressing, 0%, 1, 9). When e = 9, Activity A will generate a message (A, 75%), and post it on the output port 75%. After that, Activity A will transit into the state int (progressing, 0%, 1, 9) = ( progressing, 75%, 1, 1). External state transition functions ext: QX S If an input X comes before the expiration time, i.e., when the activity is in total state s ( e ) with e= ta( s) the state of the activity will changes to state ext( s) When a message (predecessor_name, predecessor_progress) is received on one of the input ports, the value of the associated logical variable con (predecessor_name, predecessor_progress) will change to True. After that, the constraint related with that port ( start_constraint for the start port, finish_constraint for the finish port, adjustment _condition for the adjust port, interrupt_condition for the interrupt port during the progressing phase, and resume_condition for the interrupt port during the interrupted phase) wi ll be evaluated. If the input is a Test message sent by an environmental factor, th e activity will directly evaluate the value of the constraint. For example, if Activity A receives (B, 50%) on it s input port start during the starting phase, the value of con(B, 50%) will be turned to True and thereby the start_constraint con(B, 50%) AND con(C, 100%) AND (tem> 40) will become True AND con(C, 100%) AND (tem>40). Suppose that Activity A r eceives a Test message on its start input port, the start_constraint of Activity A will not change ; the value of the variable temp need to be read dynamically every time when the start_constraint is evaluated. Messages sent by the predecesso r activities and the environm ental factors are treated differently in this procedure. The progre ss of the activities cannot move backwards, therefore once the predecessor activity reache s the specified progress, the constraint it imposed on its successor activity can be perm anently removed, which means that the value

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124 of the associated variable con (predecessor_name, predecessor_progress) can be changed to True. Whereas the values of the envir onmental factors may vary in both directions: tem>40 at this moment does not guarantee it will still be true at the next moment. Therefore the constraints imposed by the envi ronmental factors need to be re-evaluated every time. If the evaluation result of the associated constr aint is False, the activity will remain in its current state, except that the time remaining, will be updated to ( -e) ; otherwise, the activity will transit into a different phase as defined in the following external transition functions: ext (phase, transition_progress, a, e, X) = (progressing, 0%, a, p-1(aduration, next(markers)) if phase = starting and InPort = start and start_condition = True; //Transit from the starting phase to the progressing phase, reaching the first marker in time p-1(aduration, next(markers). = (interrupted, progress, a, interrupt_length) if phase = progressing and InPort = interrupt and interrupt_condition(i) = True and interrupt_length(i) 0; //Transit from the progressing phase to the interrupted phase, set transition_progress to the current value of progress and rest for time interrupt_length(i). = (interrupted, progress, a, ) if phase = progressing and InPort = interrupt and interrupt_condition(i) = True and resume_condition(i) ; //Transit from the progressing phase to the interrupted phase, set transition_progress to the current value of progress and rest in a passive state. = (progressing, transition_progress, a, p-1(aduration, next(markers)p1(aduration, transition_progress) ) if phase = interrupted and InPort = interrupt and resume_condition(i) = True //Transit from the interrupted phase to the progressing phas e, without changing the value of the transition_progress continuing to proceed toward the next marker. = (phase, progress, adjust_factor(i), -e) if phase progressing and InPort = adjust and adjust_condition(i) = True // Remain in the original phase, set the value of a to the adjust factor(i) update the value of transition_progress and = (progressing, progress, adjust_factor, p-1(adjust_factorduration, next(markers))p-1(adjust_factorduration, progress))

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125 if phase = progressing and InPort = adjust and adjust_condition(i) = True // Remain in the original phase, apply the adjust_factor(i) to a update the value of transition_progress and then recalculate the time to the next marker. = (finished, 100%, a, ) if phase = progressing and InPort = finish and finish_condition = True and transition_progress = 100% // Transit into the finished phase, and rest in a passive state (or can be terminated after this point). Time Advance Function ta(s). The time remaining in current state is defined as the value of the state variable 5.2.1.2 A simulation of a non-resource-driven discrete model A simulation of Activity As behavi or is shown in Figure 5-8. (1) At initialization, Activity A is in a passive state (phase, transition_progress, a, ) = (staring, 0%, 1, ); and the values of all c onstraints associated with its input ports are set to False. Then the message (B, 50%) is received on its start input port. The external transition function ext is triggered and the value of the logical variable con (B, 50%) is changed from the initial False into True. The start_constraint con (B, 50%) AND con(C, 100%) AND temp >40 thus becomes True AND False AND temp> 40, whose value is st ill False, so the activity will continue to stay in the starting phase with = Later the temperature rises to above 40F and a Test message is received on the start input port. Again the external tr ansition function is evoked, and the start_constraint is evaluated. Since the value is still False, the state of the activity does not change. After a period of time, the message (C, 100%) is received on the start input port, the external transition func tion changes the value of the logical variable con(C, 100%) to True and thereby the value of the start_constraint becomes True AND True and (temp>40). Suppose at this point the value of the variable temp at this point is below 40F, the activity still needs to wait.

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126 Figure 5-8. Simulation of Activity As Behavior 5 (100%, (A, 100%)) (starting,0%,1, ) (progressing,0%,1, (interrupted,8%, (progressing,8%,1, (progressing,40%,1.4, 4.3) (finished,100%, 1.4, ) (progressing,75%, 1.4, Time S 01234567 89101112 0 1 2 3 4 5 6 7 8 9 10 11 12 ( %, ( A, 75% )) Y Time (start(B, 50%)) (start,Test) (start(C,100%)) ( interu p t Test ) (adjust,(G, 0%)) 0 1 2 3 4 5 6 7 8 9 10 11 12 Time X (start,Test) e 0 1 2 3 4 (a) State of Activity A Time (c) Input of Activity A (b) Time Elapsed in the Current State (d) Output of Activity A

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127 (2) At time 0, when temperature rises to a bove 40F again, another Test message is received on the Start port. This time the value of the start_constraint is True and the state of the activity changes to: ext (starting, 0%, a, e, X) = (progressing, 0%, a, p-1(aduration, next(markers) = (progressing, 0%, 1, p-1(10, 75%) = (progressing, 0%, 1, 9), and the value of e is set to 0. If no external events occur, when the resting time expires, i.e., e = 9, the state of Activity A will change according to the followi ng internal transition function: int(progressing, 0%, 1, 9) = (progressing, next (markers), a, (p-1(aduration, next (markers) p-1 (aduration, transition_progress )) = (progressing, 75%, 1, (p-1 (100%)-p-1(10, 75%)). (3) However, at time t = 3 days before this resting time expires, the temperature drops to below 40 degrees and a Test messa ge is received on the activity s Interrupt input port. The internal transition is interrupted, and the values of the interrupt_conditions are checked. As the condition temp>40 have become true, the stat e of the activity changes according to the following external transition function: ext (Progressing, transition_progress, a, e, X) = (interrupted, progress, a, interrupt_length) = (interrupted, 8%, 1, 1). Note that the progress 8% is derived from S the state of the activity, and e the time lapsed since the last transition at the point just before the occurrence of th is external transition. Now it has become the new transition_progress of the new state. The value of e is reset to 0.

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128 (4) The activity st ays in the state (interrupted, 8%, 1, 1) until e = =1, i.e., at time t = 4 days, the following internal transition takes place: int (interrupted, 8%, 1, 1) = (progressing, transition_progress, a, (p-1(aduration, next(markers)-p-1(aduration, transition_progress)) = (Progressing, 8%, 1, ( p-1(10, 75%) p-1(10, 8%)) = (Progressing, 8%, 1, 6), which means that the activity has reentered the progressing phase, and it will reach the next marker in 6 days if no external events intervenes. (5) At time t = 7 days, when e = 3, the above internal transiti on is stopped because Activity G has started and a message (G, 0%) has been re ceived on the adjust input port. The value of the logical variable con(G, 0%) is turned into True; and after that, the constraints specified in the parameter adjustment = {(con(G, 0%), 1.4), (con(G, 100 %), 1.0)} are checked. Since one of the adjustment conditions, con(G, 0%) has become true, the follo wing external transition is triggered and the value of e is reset to 0: ext (progressing, transition_progress, a, e, X) = (progressing, progress, 1/adjust_factor, p-1(aduration, next(markers))p1(aduration, progress)) = (progressing, 40%, 1.43, p-1(1.43, 75%) p-1(1.43, 40%)) = (progressing, 40%, 1.43, 4.3). (6) At time t = 11.3 days, e = 4.3 = the resting time expires a nd an internal transition is going to take place. Just before the internal tr ansition, the activity generates an output according to the following output function: (progressing, transition_progress, a, ) = (next(markers), (name, next(markers)) = (%, (A, 75%)), which means that the message (A, 75%) is posted to the output port %. Afterwards, the following internal transition occurs:

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129 int(progressing, 40%, 1.43, 4.3) = (progressing, 75%, 1.43, (p-1 (1.43,100%)-p-1(1.43, 75%)) = (progressing, 75%, 1.43, 1.43). (7) Finally, at time t = 12.73 days when the activity ap proaches the last maker 100%, another output is generated: (progressing, 75%, 1.43, 1.43)= (%, (A, 100%)), followed by the internal transition: int(progressing, 75%, 1.43, 4.3)= (progressing, 100%, 1.43, ). At this point, Activity A is completed and will rest in a passive state 5.2.1.3 Resource-driven discrete models The second type of the atomic activity model is the resource-d riven discrete activity model Activitydr With this model, the duration of the activ ity is determined dynamically according to the type and quantity of the reso urce that can be obtained. The activity will request resources after its start_contraint has been satisfied, and release resources when it has been finished. If the activity is interrupted during the middle, resource s can be returned to the resource pool and used by other activities. Figure 5-9. Structure of the resour ce-driven discrete activity model Adr interrupt adjust finish marker1 marker2 star t (S, e) rin r-request (resource_type, quantity) (resource_type, min_quantity, max_quantity) rout (resource_type, quantity)

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130 The basic structure of the resour ce-driven discrete activity model Activitydr is shown in Figure 5-9. It is similar to the structur e of the non-resource-driven activity model Activityd, with the following differences: State S. In the Activitydr model, duration is not an independent parameter; instead, it is a derived state variable whose valu e is dependent upon the parameter work_quantity and the productivity and quantity of the acquired resource. The parameter required resource = {(resource_type, min_quantity, max_quantity, productivity, priority)} represents the type, the lower lim it and upper limit of the required quantity, the productivity, and the priority of the resource if there are a number of different types of resources that can be us ed to finish this activity. The state variable resource = (resource_type, quantity) is used to represent the type and quantity of the resource that has been obtained by the activity. The state variable phase has three additional values compar ed to that of the non resourcedriven model: requesting_resource, during wh ich the activity is attempting to obtain the required resources to either start or resume the work; resource_obtained, during which the required resources have been acquired and the activity is se nding messages to clear previously submitted requests that are still waiting in resource request queues; and releasing_resource, during which the activity is releasing the e ngaged resources. The parameter interruptions in the Activitydr model is defined as { (interrupt_condition interrupt_length resume_condition, release_resource) }. The parameter release_resource is a logical variable that defines whether the engaged resources shall be released when the activity is interrupted by the specified interrupt_condition Input. The model Activitydr has an additional input port rin which is to receive resources input (resource_type, quantity) Output. The activity will post the request for resources (resource_type, min-quantity, max_type) to its output port r-request and release the disengaged resources (resource_type, quantity) through the output port rout. External Transitions, Internal Transitions and Output Functions. (1) Start-up of the activity. When the activitys start constraints have been satisfied, the activity will transit via the following external transition function: ext (starting, 0%, a, e, X) = (requesting-resources, 0%, a, 0). From this state the activity will take the following internal transition:

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131 int (requesting-resources, 0%, a, 0) = (requesting-resources, 0%, a, ) i.e., the activity will put itself into a passive state, waiting for the arrival of the required resources. But right before the internal transition, an output will be produced: (requesting-resources, 0%, a, 0) = (r-request, (activity_name, res ource_type, min_quantity, max_quantity)). The activity posts the message (activity_name, resource_type, min_quantity, max_quantity) to its r-request output. This massage contains the name of the activity that is sending the request, the type of the resource with the highest priority in its parameter required-resource and the range of the quantity required. This message will be send to the re source, which will return a message (activity_name, resource_type, quantity) to the "rin" port of th e activity in response. A request that cannot be satis fied outright will be saved in the waiting queue of the resource, and the quantity in the returned message will be set to 0. Upon receiving such a message, the activity will check if there ar e any alternative resources listed in its requiredresource If not, it will stay in the passive state, waiting for the requests in the waiting queues to be handled and fulfilled; otherwise, the passive state of the activity will be ended, as will be changed from to 0 as in the following external transition function: ext (requesting-resources, 0%, a, e, X) = (requesting-resources, 0%, a, 0). Under this state, the activity can send a new request to the re source with the second highest priority in its required-resour ce. The above processes will be repeated until the activity receives a message with a non-zero quantity on its "rin" port, upon which, the activity will be changed into a temporary r esource_obtained phase via: ext (requesting-resources, 0%, a, e, X) = (resource_obtained, 0%, a, 0). From this state, the activity will start pr ogressing toward the next immediate marker: int (resources-obtained, 0%, a, 0) = (progressing, 0%, a, p-1(aduration, next(markers))p-1(aduration, progress) in which the duration is calculated as: duration = work_quantity/(productivityquantity). Right before the above internal transition, the ac tivity produces an output to clear all of its previous requests stored in the wa iting queues of re lated resources: (resource-obtained, transition_progress, a, 0) = (r-request, (activity_name, resource_type, 0, 0)). (2) Finishing of the activity.

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132 When the activity is finished, i.e., after th e activitys progress has approached 100% and the finish constraints have all been satisfied, the activity will transit into a temporary state releasing-resource, during which it will releas e the engaged resources, and then continue to transit into the finished state: int(releasing-resource, 100%, a, 0) = (finished, 100%, a, ), (releasing-resource, 100%, a, )= (rout, (resource_type, quantity)). (3) Interruptions and resumptions. If the activity is interrupted with the option release resources se tting to be true, the activity will first enter into the releasing-re source state and produ ce an output to export the resources before it enters into the interrupted state: int(progressing, transition_progress, a, ) = (releasing-resource, progress, a, 0); (releasing-resource, transition_progress, a, ) = (rout, (resource_type, quantity)); int(releasing-resource, transition_progress, a, ) = (interrupted, transition_progress, a, interrupt_length (or )). When the condition for resumption is satisfied, the activity will first enter the requestingresource phase and then the resource-obtained phase befo re it can proceed, similar to the procedure at the st art up of the activity. 5.2.1.4 Continuous models As shown in Figure 5-10, the struct ure of the continuous activity model Activityc has a lot of similarities with that of th e resource-driven discrete model Activitydr. They have the same input and output ports, and under most phases their external transition and in ternal transitions are essentially the same. The major difference betw een the two lies in the progressing phase. Figure 5-10. Structure of the continuous activity Ac interrupt adjust finish marker1 marker2 star t (S, e) rin r-request rout

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133 As shown in Figure 5-11, the continuous activity does not transit directly from one marker to the next during the progressing phase, but ad vances gradually at fixed time steps. At every step, the value of the productivity will be re-sampled, and the modifiers (modification factors determined by the values of dynamically changing variables) will be reapplied. Figure 5-11. Process of a continuous activity If the activity steps across a marker, it will ge nerate an output at the end of that step. The activity in Figure 5-11 reaches 70% between ti me 9.75 and 10.75. The output is produced at time 10.75. If the activity is going to violat e the buffer constraint after ta king a step, it could pause for that interval (approximating the slow-down option) or stop co mpletely (modeling the break option). Figure 5-10 shows a pause at time 4. Note that the activ ity is still under the progressing phase, for it will c ontinue to attempt to advance at the next step. If the option

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134 break is selected instead of slow-down, the activity will be put into the interrupted phase for a specified length of time or until being resumed by an external input. External inputs could also cause the continuous activity to stop or to adjust the productivity rate. The external inputs are pr ocessed immediately upon their arri val. In Figure 5-11, during the middle of a step at time 5.25, the activity receives a message on its interrupt input port and is stopped, with its progress increased by (.25 lengt h of the interval productivity). When it is resumed at time 8.75, it continues to advance one interval a time. Listed below are the state parameters and variables specific to the continuous activity model, together with its internal tansitions a nd output functions during the progressing phase. Since its external transition functi ons are essentially the same as t hose of the discrete model, they are not presented here. State. The continuous activity has three unique parameters buffer and modifiers The definition of the parameter start_constraint is also different from the discrete activity models. This parameter interval specifies the length of the fixe d time step at which the state of the activity is going to be update d under the pro gressing phase. buffer The parameter buffer consists of {(buffer_constraint, pause, pause_period, release_ resource)} The buffer_constraint is a logical expression that may contain any variables and the AND and OR operators. When the value of the buffer_constraint becomes True, the activity will pause fo r the current interval and attempt to continue at the next step (to approximate the slow-down option), provided that the value of pause is 0; if the value of pause is 1, it will stop for the length specified by pause_period (to represent the break option). The value of release_resource specifies whether the engaged resources will be released during the break. modifier. The modifier is a function f (mi) ( i=1 to n) that are dependent upon dynamically changing factors mi. The modified productivity ( f(m1,m2 mn) productivity) is denoted as m_productivity start_constraint The buffer_constraint will be combined with th e constraints explicitly defined as the start constraint s to control the star t of the continuous act ivity. If there are more than one buffer constraints, all of th em will be connected with "AND" into the start_constraint

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135 Internal Transitions. The internal transition under th e progressing phase for the continuous activity model is completely different from that of other two types of activity models, and it is described as below: int (progressing, progress, a, ) =(releasing-resource, 100%, a, 0) If ( progress + a m_productivity ) 100%; // The progress of the activity is going to exceed 100% after taking a full step. The activity transits into the releasing-res ource phase, which will be followed by the finished phased. = (progressing, progress + am_ productivity a, ) If buffer_constraint = False and ( progress + a m_productivity ) <100% ; //Buffer not violated, the ac tivitys progress advances by (a m_productivity ), and will remain at this level during the next time interval = (progressing, progress, a, ) If buffer_constraint = True and pause = 0 and ( progress + am_productivity ) <100% ; //Buffer violated. The option slow-down is selected. The activity will hold the current step, but it will remain in the progr essing phase and continue to attempt to proceed at the next step. = (interrupted, progress, a, pause_period) If buffer_constraint= True and pause=1 and release_ resource=0 and ( progress + a m_productivity ) <100% ; //Buffer violated. The break option is selected and the parameter release_resource is set to The activitys progress will not increase, and it will be put into the interrupted phase for the specified pause_period When the pause_period expires, the activity will re-enter the progressing phase via the internal transition function int (interrupted, progress, a, pause_period) = (progressing, progress, a, ). =(release-resource, progress, a, pause_period) If buffer_constraint= True and pause=1 and release_ resource=1 and ( progress + a productivity ) <100% ; //Buffer violated. The break optio n is selected and the parameter release_resource is set to The progress will not change. The ac tivity will enter into the releasing-resource state and releases the engaged resources via (releasing-resource, progress, a, 0) = (rout, (resource_type, quantity)) Then it will rest in the interrupted state for the specified pause_period When the pause_period expires, it has to go through the requesting-resource and the resourceobtained phases befo re re-entering the progressing state. Output function. At the end of every step, the out put function will check whether the activity has crossed a marker a nd produce the outputs accordingly. (progressing, progress, a, )

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136 = (marker1, (activity_name, marker1)) if progress < marker1 and (progress + am_ productivity ) > marker 1 ; (marker2, (activity_name, marker2)) if progress < marker2 and (progress + a m_productivity )> marker 2 ; .... (markerN, (activity_name, markerN)) if progress < markerN and (progress + a m_productivity )> marker N To summarize, the progress of the conti nuous model are controlled by two types of constraints: the constraints th at comes through the input ports, which may trigger a one-time response; and the constraints defined as the bu ffer constraints, which will be evaluated every time the continuous activity advances. By contrast the discrete models only allow the first type of control. 5.2.2 Compound Activity Models A group of atomic activity models can be coupl ed to construct a compound activity model. The compound model could be discrete and non-resource-driven, denoted as Activitycd; or discrete and resource-driven, Activitycdr; or continuous, Activitycc. The compound activity models have the same sets of ports and external behavior s as their atomic counterpa rts. They can be used just as the atomic models in the construction of hi gher-level models, thus providing a closedunder-composition hierarchical structure. 5.2.2.1 Compound discrete non-resource-driven models The structure of the compound discrete nonresource-driven model is defined as: Acd = (X, Y, D, EIC, EOC, IC), (Equation 5-4) in which: X is the set of input ports and values. The input ports and the acceptable values on these ports are the same as those of the atomic model Ad Y is the set of output ports and values. The out put ports and generated values are the same as those of the atomic model Ad

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137 D is the set of the component names. In th e example shown in Figure 5-12, D = {A1, A2}. The components could be of any type of atomic activity models, including Ad, Adr and Ac, as well as any type of compound activity models Figure 5-12. Example of the compound di screte non-resource-driven activity IC i.e., Internal Couplings, connect component outputs to component inputs. In Figure 511, IC = {(A1, %), (A2, start)}. EIC i.e., External Input Coupli ngs, connect external inputs to component inputs. The EIC connections are established according to th e following rules in the proposed theory: External input on the start port will be dupli cated and routed to th e start ports of all components that do not have any start constraints; External input on the interrupt, resume or adjust port will be duplicated and routed to the interrupt, resume or adjust ports of all components; External input on the finish port will be duplicat ed and routed to the finish ports of all components that do not have su ccessors in th e components. Therefore, for the exampl e shown in Figure 5-12, A interrupt adjust finish star t 90% 20% A.1 interru pt ad j us t finish 100% star t 100% 50%A.2 interru pt ad j us t finish 100% star t 75% EIC EOC IC

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138 EIC = {((A, start), (A1, start)), ((A interrupt), (A1, interrupt)), ((A, finish), (A2, finish))} EOC i.e., External Output Couplings, connect component outputs to external outputs. Only one EOC connection is established by default in the proposed theory the connection between the % output ports of the components that do not have any successors within the compound activity and th e % external output port. Other EOC connections have to be specified by the user In the above example, the compound activity A needs to generate outputs when it is 20% and 90% completed. The user specifies, based on his or her judgment, that 20% completion of A is best signaled by 50% completion of its component A1, and 90% completion of A by 75% completion of A2. So the EOC for A is: EOC = {((A1, %), (A, %)), ((A2, %), (A, %)), ((A2, %), (A, %))}. If the progress of the compound activity needs to be defined with the progresses of more than one component, a virtual activity, whose duration is zer o, needs to be created to implement the EOC connection. The outputs from the components will be sent to the virtual activity, which will send a message to th e external output ports when all component outputs have been received. 5.2.2.2 Compound discrete resource-driven models Compared to the non-resource-driven model Acd, the resource driven model Acdr has three extra ports: r-request, r-request and rout. The structures of the two models are similar, except for the EIC and EOC couplings rules invo lving the three extra ports. Figure 5-13 shows the resource-related couplings in a co mpound discrete resource-driven activity. When a component posts a message to its r-r equest port, the message will be forwarded to the external r-request por t. The message returned by the resource, upon arriving at the external rin port, will be routed to the rin port of the component according to the name of the activity it contained. After a component is finish ed, the released resour ce on the rout port will be sent to the external rout port.

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139 Figure 5-13. Example of a compound discrete resourcedriven activity 5.2.2.3 Compound continuous models As discussed in 5.2.1.4, the behaviors of the atom ic continuous models can be impacted in two ways: one is through the extern al inputs, as with the discrete models; the other is through the variables in its buffer constrai nts. This is also true for the compound continuous model. The inputs and outputs of the compound contin uous model are routed according to the same rules as with the compound discrete model. Buffers constraints in the compound continuous models are handled according to the following rules: Buffer constraints on a compound continuous activity will be imposed on all of its continuous components i.e., all of its continuous components will have to maintain the external buffer constraints when they attempt to start and advance; Buffer constraints imposed by a compound continuous activity will be compiled to multiple buffer constraints, each imposed by one of its continuous components i.e., the A interrupt adjust finish star t rin rout r-request marker2 marker1 A1 interru pt ad j us t finish marker1 marker2 start rin r-request rout A2 interru pt ad j us t finish marker1 marker2 start rin r-request rout (A1, resource_type, min_quantity, max_quantity) (resource_type, quantity) (A2, resource_type, min_quantity, max_quantity) (resource_type, quantity) (A1, quantity) (A2, quantity) EIC EOC

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140 successor activity has to maintain the buffer between all the continuous components of the compound activity that has st arted but not finished. 5.2.3 Resource Models In the proposed theory, each type of resour ces is represented as a DEVS model. The structure of the resource model R is illustrated in Figure 5-14. Figure 5-14. Structure of the resource model R= (X, Y, S, ext, int, ta) (Equation 5-5) Inputs X As shown in Figure 5-14, each resource model has two input ports: one is to receive the request sent by the activities; the other is to receive the released resources. InPorts = {request, rin}, Xrequest = {(activity_name, resource ty pe, min_quantity, max_quantity)}, Xrin = {(resource type, quantity)}. Outputs Y The resource model only has one output port that is to export its responses to the requests from the activities. OutPorts = {rout}, Yout = {(activity_name, resource type, quantity)}. State S The state of the resource model is re presented by the following parameters and variables: type. Resource type. total. The total amount that has be en assigned to the project. available. The amount that is in the resource pool a nd can be used to satisfy the activities requests. phase. The resource could be in one of th e two phases: passive and active R rin request (S, e) rout (activity_name, resource type, min_quantity, max_quantity) (resource_type, quantity) (activity_name, resource_type, quantity)

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141 activity_ priority. This parameter consists of {(activ ity_name, priority)}. It stores the names of all the activities that might use th e resource, and their respective priorities. waiting_queue. This queue stores all th e requests that have been received but cannot be fulfilled at the moment. It consists of {{( activity_name, resource type, min_quantity, max_quantity) }, }. +1indicates that these requests are going to be sorted in the ascending order on their priorities, and -1 in dicates the opposite. For activities with equal priorities, they are going to be sorted on a first-come-first-serve basis. External Transitions, Internal Transitions and Output Functions. At initiation, the resource is resting in the passive phase with ( = ). It will not make any internal transitions a nd outputs under this state. When the resource receives a request (activity_name, resour ce type, min_quantity, max_quantity) on its request port: If the maximum requirement can be fulfilled (available max_quantity) the variable available will be reduced by the required maximu m amount, and the resource will transit into the active phase, which is temporary ( = 0). During this phase, the resource outputs (activity_name, resource_type, max_quantity) through the rout port, and then returns to the passive state via the internal transition int (active, ) = (passive, ). If the available quantity ca nnot fulfill the maximum requirement, but exceeds the minimum requirements (available min_quantity and availabl e < max_quantity), the available quantity will decrease to 0 and th e resource will transit into the temporary active state. After the output (activity_name, resource_type, av ailable) is generated and sent to the rout port, it re turns to the passive state. If the available quantity cannot meet the minimum requirement, the request will be inserted into the waiting_queue The resource remains in the passive state. When the resource receives the message (resource_type, quantity) on its rin port: If the message is a clean-up message ( quantity = 0), the corresponding request will be removed from the waiting_queue The resource remains in its passive state. Otherwise, the value of the variable available will be increased by the released quantity, and the resource will be put into the checkin g phase by the external transition. During the checking phase, the following internal tran sitions take place: the resource finds the first request in its waiting queue (the requests are sorted on the specified priority in either the ascending order or the descending order) whose requirement can now be fulfilled, it then deduct the output amount from the available amount, se lf-transit into the active phase, generate the output, and come back into the checking phase to search for the next request that it can fulfill. When the search has reached the end of the queue, the resource will return to the passive phase and rest.

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142 5.2.4 Models for Environmental Factors Factors that change dynamically, such as te mperature, precipitation and wind can be modeled with the environmental model E An environmental model may be used to simulate more than one factor, provided that these fact ors can be updated with the same frequency. Figure 5-15. Structure of the environmental factor model As shown in Figure 5-15, the environmental model has no input port, only output ports. The state of the model consists of the parameter interval variable list { (variable_name, value)} and threshold_list {(variable_nam e, threshhold, direction)} The values of all variables are resampled and re-calculated at every time step. If the value of a variable exceeds a threshold (when direction = +1), or falls below a threshold (when direction = -1), a message Test will be generated and posted to the corres ponding output port, and then sent to the connected activities. Generating outputs at the threshol ds is just one way that th e environmental models could influence the activities. The values of the factors in the environmental models could also be read dynamically and thereby affect the duration, productiv ity and other properties or behaviors of the activities. Besides the activities, resources and envi ronmental models, there are a few accessory models in the proposed theory. One of them is th e Delay model, which can take in any types of input messages, hold them for a specified length of time, and then pass th em on to the designated destination. Another is the Branch model, which can route an input to one of its output ports depending on probabilistic selections or the value of a decision variable. E (S, e) Threshold 1 Test Threshold 2 Threshold 3 Test Test

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143 CHAPTER 6 MODELING ELEMENTS AND MODELING RULES Chapter 5 introduced the fundamental theory proposed in this study how each type of the models is structured, how they behave and how they interact. This chapter presents a new planning and scheduling method that was developed based on this theory. We will introduce the graphical modeling elemen ts and the modeling rules in this method and show how they can be used to represent various situations in real-world complex construction projects. The graphical representation of the proposed method is similar to the Activity-OnNode diagrams, but with many enhanced f eatures. The nodes can represent different types of activities, resources and environmenta l factors; and the links can represent both logical constraints and resource flows. In the following sections, we will first in troduce the modeling of atomic activities, resources and environmental factors, then the links that connecting these basic components, and finally the construction of compound activities and re petitive activities. 6.1 Basic Components 6.1.1 Discrete Activities As shown in Figure 6-1, in the network, discrete activities are represented as rectangles, with the name and the duration of the activity indicated in the middle. An activity should be modeled as a discrete activity if all of the following assumptions are true: The duration of the activity can be pred icted fairly accurately at the time it starts. Should the duration change because of interr uptions or adjustments, such changes should be rare.

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144 Figure 6-1. Discrete Activity Node Only the start and the finish time of the activity are of importance, the intermediate progress is either not of concern or can be satisfactorily approximated with a pre-defined progress curve. Except at the start and the finish poi nt, the activity interacts with other activities only sparsely during the progress. The activity is not very sensitive to continuously changing factors such as temperature, wind, precipitation, etc. The activity is performed at a fixed pos ition or its movement does not need to be tracked. Resources engaged in the activity do not need to be closely monitored. Otherwise, it is more proper to mode l the activity as a continuous activity. A discrete activity can be defined thr ough the window-based us er interface, as shown in Figure 6-2. The items need to be entered include: Name The name of each activity must be unique. Work Quantity and Unit The total quantity of work involved in the activity and the unit of measurement. The progr ess of the activity will be measured with the same unit herein provided. Th e default value is %, in which case, the progress of the activity will be measured in percentage completed. Duration (for non-resource driven activities). The duration can be defined as a constant number, a probabilistic dist ribution, or an expr ession containing any accessible functions and variables. The value of the duration will be determined at the point when the activ ity starts, and will not change unless being adjusted by external inputs. Resource Type, Minimum/Maximum Quantity, Priority and Productivity (for resource-driven activ ities). If the activity is resource-driven, the user needs to specify the type, minimum qua ntity, maximum quantity and priority of the resources that can be used to finish the work. The productivities of the resources on the activity could be obtai ned from a pre-established database, and may be a constant number, a probab ilistic distribution, or an expression containing any accessible functions and vari ables. The duration of the activity Name Duration

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145 is dependent upon which type of the resources and what quantity can be actually acquired, and it will be determin ed dynamically at the point when the activity starts with the following formula: source Aquired the of Quantity source Aquired the of oductivity Quantity Work Duration Re Re Pr (Equation 6-1) Progress Curve The progress curve descri bes how the activity would proceed from start to finish with th e passage of time without any external inputs. Three types of progress curves are predefined to be selected from: Type I assumes a constant speed; Type II considers the learning curve effect; Types III reflects a slow-fast-slow pattern (see Figure 6-2). The progress curve can also be customized by defining the progress function Progress = p (duration, time). Figure 6-2. Discrete ac tivity dialogue window

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146 A discrete activity node will be compiled in to an atomic discrete activity model, either the resource-driven Ad or the non-resource-driven Adr, in accordance with the selected option. 6.1.2 Continuous Activities Continuous activities are repr esented as shown in Figure 6-2 as rectangles with a double left border line, with the name and the productivity of the activ ity indicated in the middle. A continuous activity needs to be defined with: Figure 6-3. Continuous Activity Node Name Work Quantity Interval The state of the continuous activ ity will be updated at fixed time intervals during the progre ssing phase. The interval must be defined as a constant number. Depending on the re quired level of accuracy, different continuous activities in one project can be defined with different lengths of intervals. Resource Type, Min/Max Quantity, and Priority. Productivity The productivity of the continuous activity can be defined as a constant number, a probabilistic distribut ion, or an expressi on. Different from the discrete activity, the value is re-sam pled (if probabilistic ) and recalculated every time the activity advances. Productivity Modification Factor. This factor is used to take account of the effects of dynamically changing variab les on the continuous activity. Every time the activity advances, this fact or is going to be applied to the productivity to calculate the Modified Productivity which determines the increase of the progress for the next interval. Name Productivity

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147 Figure 6-4 shows the dialog window used to define the continuous activity Form. The productivity is defined as a unifo rm distribution U (240, 260) sf/hour. The modification function indicates that the producti vity of the activity Form is affected by two continuously changing variables: temper ature and weather. Suppose that at time t the temperature is 90F, then the value of the step func tion which is dependent upon temperature is .85; the weathe r is Cloudy, then the valu e of the conditional function which is dependent upon weather is 1.0. So th e modified productivity of Activity Form at time t is: (.85 1.0) U (240, 260) = .85 248 = 210.8 sf/day. Figure 6-4. Continuous ac tivity dialogue window Often times it is necessary to track the move ment of the crew that is working on the continuous activity. If all con tinuous activities in the project have the same layout, only two parameters need to be provided:

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148 Start Position. The distance between the point where the activity begins and the designated point. The default valu e is 0, i.e., it is assumed that the activity start from the designated point. Direction. In the one-layout situation, th ere are only two directions any activity can take: position or nega tive, with positive as the default value. With these two parameters, the positions of the crews can be derived from the progress of the activity at any time. From example, in Figure 6-5, the start position of both Activity A and Activity B is +150m, A is proceeding toward the positive direction, and B toward the negative direction. If it is known that at time t A has progressed 400m, and B has progressed 600m, it can be determined that A is at +550m, B is at -450m, and the distance between the two is 1000m. Figure 6-5. Determining activity pos itions on a one-dimensional layout If the layouts of the activities are differe nt, a two-dimensional coordinate system needs to be established, and the following parameters need to be provided for each continuous activity: Layout Function. The user needs to specify the shape of the layout with a function y=f(x) Start Position. The (x, y) coordinate s of the start point. End Position. The (x, y) coordinates of the finish point. 0 + 150 m A B 400 m 600 m

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149 Figure 6-6. Determining activity pos itions on a two-dimensional layout In the example shown in Figure 6-6, the layout functions, start positions and end positions of Activity A and B can be specified. If their progress at time t is known, their positions at time t,) (t A t Ay x and ) (t B t By x, can be determined, and the distance between the two activities at time t, t ABd, can be calculated with: 2 2) ( ) (t B t A t B t A t ABy y x x d (Equation 6-2) Figure 6-7. Defining the path of a continuous activity 0 X Y ) (0 0 A Ay x ) (' A Ay x ) (0 0 B By x ) (' B By x) (t A t Ay x) (t B t By x ) (A Ax f y ) (B Bx f y t ABd

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150 Figure 6-7 shows the dialogue window used to define the path of continuous activities. 6.1.3 Environmental Factors Environmental factors are used to represen t dynamically changing variables such as temperature, precipitation and wind speed. The environmental f actor is represented as a hexagon, with the name of the factor and th e names of the variab les indicated inside. Figure 6-8. Environmental Facor Node Attributes of the environmental object include: Name A unique identifier of the environmental factor. Variable Name and Value. The name of the variab les and the expressions that determine their values. Interval The interval at which the values of the variables are going to be updated. The interval can be a constant number, a probabilistic variable or an expression. Variables that require different updating inte rvals need to be generated by different environmental factors. Therefore one projec t may include more than one environmental object. Figure 6-9 displays the di alogue window that defines the environmental object Clock. Two variables, temperature and w eather are updated every tw o hours. The value of temperature is assumed to have a Poisson distri bution Poisson (65, 12). The value of weather is assumed to follow the distribution ((clear, 0.5), (Cloudy, 0.3), (Rainy, 0.1), (Snow, 0.1)). Name Variable 1 Variable 2

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151 Figure 6-9. Environmental factor dialogue window 6.1.4 Resources Resources are represented as ovals in th e network. The type and the total quantity are indicated in the middle of the oval. A re source has to be defined with the following attributes: Figure 6-10. Resource Node Type The type should be a standardized name or code for the resource. Total Quantity This should be the total quant ity of the resource available to the project. Type Total Quan.

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152 6.2 Links Links are used to show how the behaviors of an activity are controlled and affected by other activities, resources and environmen tal factors. The links are divided into start/finish links, interrupt links, adjust li nks, buffers, and resource links, based on which behavior is being c ontrolled and affected. 6.2.1 Start Links and Finish Links Start/finish links are repres ented as arrows. The head of the arrow is connected to the activity being controlled and constraine d, which could be either continuous or discrete, resource-driven or not resource-driven; the tail of the arrow is connected to the influencer which could be an activity of any type or an environmental factor. 6.2.1.1 FS, SS, SF, FF dependency relationships Figure 6-11. FS, FF, SS, SF Links Using the arrows, the Finish-to-Start, Start-to-Start, Start-to-Finish, Finish-toFinish dependency relationships method are represented just the same as in the AON A B lag A B lag A B lag A B lag (b) Finish-to-Finish (c) Start-to-Start (d) Start-to-Start Note: the predecessor and successor activities can be either discrete or continuous activities. (c) Resource Blocks (a) Start-to-Start

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153 network of the CPM method (shown in Figure 6-11). However, they are interoperated differently by the proposed method. Figure 6-12. Example of an SS link In Figure 6-12, there is an SS dependenc y relationship between the activity Foundation and the activity Vertical Lift #1 w ith a lag of two days This link will add a marker % in the marker_list of the activity model Foundationd, and insert a logical variable con(Foundation, 0%) into the start_constraint of the activity model Vertical_Lift_#1d. When Foundationd reaches the state (phase = progressing, progress = 0%), it will generate a message (Foundati on, 0%) and post it to its % output port. After a delay of 10 days, this message is ro uted to the start input port of activity Vertical Lift #1, which causes the value of the logical variable con(Foundation, 0%) turn from False to True. 6.2.1.2 Progress-based dependency relationships The arrows can also represent progre ss-based dependency relationships as illustrated in Figure 6-13. As discusse d in Section 3.1.1, the duration-based SS relationship in the above example is not an accurate description of the real relationship between the two activit ies. With the proposed method, we can represent when Activity Foundation is 1/3 completed, Activity 1st Lift Vertical can start accurately as shown in Vertical Lift #1 25 days Foundation 30 days

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154 Figure 6-14. Note that this start link is conne cted to the bottom of the predecessor at the position of about 33% length. Figure 6-13. Progress-based Link Figure 6-14. Example of a progress-percentage-based link If the work quantity of the activity F oundation is defined as 3000 CY, then the progress of the activity will be measured in CY instead of the percentage completed, and the above link should be specifi ed as shown in Figure 6-15. Figure 6-15. Example of a work-quantity-based link 6.2.1.3 Environmental factor impose d start/finish constraints When the start/finish constr aint is imposed by the envir onmental factor, constraint condition should be indicated on the arrow as shown in Figure 6-16. The example in Figure 6-17 shows that the activity Foundation cannot start if the temperature is below 40F. Lag Progress

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155 Figure 6-16. Environmental-f actor-imposed constraint Figure 6-17. Example of an environm ental-factor-imposed constraint The condition temp>40 will be inserted into the start_constraint of the activity model Foundationd, and the (temp, 40, +1) will be added into the threshold_list of the environmental model Clocke. When the value of the variable temp rises above 40 degrees, a Test message will be generated by Clocke and sent to the s tart input port of Foundationd. 6.2.2 Interrupt Links and Resume Links The interrupt links shown in Figure 6-18 ar e used to model interruptions caused by sudden events during the middle of the progres s of an activity. Th e interrupt link is represented as an arrow with a solid diamond hea d. It is often used in pairs with a resume link, which is represented as an arrow w ith a hollow diamond head. Similar to the start/finish links, they can be used to contro l both the discrete and continuous activities, and the influencer can be either an activity or an environmental factor. temp> 40 Foundation 30 days Clock temp condition

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156 Figure 6-18. Interrupt and Resume Links 6.2.2.1 Interruptions caused by other activities An example of interruption caused by a nother activity is: when Activity Blasting, starts, Activity B has to stop; after Activity A is finished, Activity B can resume. Figure 6-19 shows the network representation of this example. Figure 6-19. Network representation of interruptions and resumptions Figure 6-20. Interrupt link dialogue window Details about the inte rrupt link need to be further specified in the dialogue window, as shown in Figure 6-20. By default, during the interruption, the res ources engaged in the B A (Blasting) The tail is connected to the left end of A to indicate when A starts The tail is connected to the right end of A to indicate when A finishes The head of the interrupt/resume link should be connected to the top or the bottomofB If the stop for value is not specified, a resume link must be added to the successor activity. (Progress) (Progress)

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157 activity will be retained, so that the activity does not need to re-acquire the resources when it resumes. But the retained resources wi ll be idled during the interruption. To fully utilize the resources, the user should unc heck the Retain Resource option in the Interrupt Link dialogue window. The interrupt and resume links could al so be progress-based, i.e., the receiver activity can stop/resume after the sender ac tivity has achieved a certain progress. The value of the progress should be indicated ne ar the connecting point of the sender activity and the link. Lags can also be represented. If a lag is indicated above the link, the receiver activity will not stop/resume i mmediately when it receives the message from the sender, but hold for the specified length of time. 6.2.2.2 Interruptions caused by environmental factors Figure 6-21 shows an example where the interruption is caused by the environmental factor. The activity Foundation will stop whenever a storm comes. It usually requires a period of Poisson (2, 0.5) hours for the storm to pass and for the crew to clear-up the site before the work can resume. Figure 6-21. Example of an enviro nmental-factor-caused interruption Foundation 30 days weather = Storm Clock Temperature Weather

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158 In this example, the interrupt link is no t used in pairs with the resume link. The activity will resume by itself after it has b een paused for Poisson (2, 0.5) hours, as specified in the Interrupt Link dialog window in Figure 6-22. Figure 6-22. Defining breaks in the interrupt link dialogue window An activity might be under the control of multiple interrupt/resume links, as shown in Figure 6-23. To avoid errors in the simu lation process, the interrupt link and the resume link that work in pairs will be assi gned with the same number identification in their ID if the interrupt link that represen ts when the temperature is lower than 40F, the activity Foundation must st op has the ID Interrupt (n) the resume link that represent Activity Foundati on will resume when the temp erature rises to above 40F will be identified as Resume (n)

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159 Figure 6-23. Multiple interrupt/resume links on one activity 6.2.3 Adjust Links Adjust links are used to model duration/productivity changes caused by sudden events during the middle of the activitys prog ress. The head of the adjustment link is a circle, with the value of the ad justment factor indicated insi de, as shown in Figure 6-24. Figure 6-24. Adjust Link Every activity, either discrete or cont inuous, has three predefined adjustment factors a1, a2 and a3, whose original values are 1. They are so named to be differentiated from the productivity modification factors of the continuous activities. The productivity modification factors will be updated and applied every time when the continuous activity advances, whereas the adjustment factors will only be applied when the activity receives inputs on its adjust input port. 6.2.3.1 Adjustments caused by other activities Consider the example used in Figure 614, which specifies that Activity Lift #1 cannot start until the acti vity Foundation is 33% finished. We can add an interrupt link to weather = Storm Foundation 30 days Clock temp weathe r (Progress) a i

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160 further describe that when the activity Ver tical Lift #1 starts, Ac tivity Foundation will be interfered and its duration will be extended to 1.4 times as long as estimated normal length, as shown in Figure 6-25. Figure 6-25. Example of an adjustment The specified value .4 will be assigned, by default, to the first adjustment factor a1. According to the original progress curv e of the activity Founda tion, it takes 13 days (actual working time) to finish the first 33% of the work, and the remaining 67% will take 17 (= 30 -13) days. The activity Ver tical Lift #1 only impacts the remaining 67% work and extends the remaining duration to: Adjusted Remaining Duration = Remaining Duration 1a2a3a = 17 1.4 = 24 days. Therefore, Activity Foundation takes 37 (=13+ 24) days in total to complete. If Activity Vertical Lift #1 starts at a later point (which is very possible as its start is controlled by other activities), the time to complete Activity Foundation will not be extended as much. 17 1.4 17 Progress 30 100% 13 33% 33% Foundation 30 days Vertical Lift #1 25 days 1.4 37 Day

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161 Figure 6-26. Adding additional adjust links Furthermore, to represent the fact that wh en Activity Vertical Lift #1 finishes its impacts on Activity Foundation will also end, an other adjust link need s to be added as shown in Figure 6-26. Note that it must be ensured that in the di alog window it is the value of the adjustment factor a1 that will be changed, as shown in Figure 6-27. If the value 1 is given to a2 or three, the product of a1 a2 a3 will remain as 1.4 1 1=1.4. Figure 6-27. Adjust link dialogue window In the above example, the activity is a di screte activity, and the remaining duration of the activity has been changed by multiplying with the specified adjustment factor. If 1 33% Foundation 30 days Vertical Lift #1 25 days 1.4

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162 the activity is a continuous activity, what will be adjusted is the modified productivity of the continuous activity, and th e formula is as follows: Adjusted Productivity =M odified Productivity a1a2a3. (Equation 6-3) 6.2.3.2 Adjustments caused by environmental factors Adjustment can also be caused by environm ental factors. For example, the activity Foundation involves a lot of concrete placemen t. When the temperature drops to below 40F, special construction methods must be ta ken to avoid concrete cracking. In Figure 628, it has been specified that when constructi on enters the winter season and temperature is below 40F, the duration of the activity would be extended to 1.7 times. In Figure 6-29, the dialogue window for Link Adjust02, the adjust ment factor to be changed is set to a2. So under the combined impacts of temper ature and Activity Vertical Lift #1, the remaining duration of Activity Foundation will be extended by (1.4 .7) times. If the adjustment factor is left as the default a1, the duration will be extended by either 1.4 or 1.7 times, depending on which link ha s been activated the latest. Figure 6-28. Example of an enviro nmental-factor-caused adjustment Clock temp weather 1.7 temp<40 1 33% Foundation 30 days Vertical Lift #1 25 da y s 1.4

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163 Figure 6-29. Adjust link dialogue window for environmental-factor-caused adjustments A final caution with the use of the adjust li nks is: if the activity is very sensitive to environmental variables that are constantly changing, it would be much more efficient to model the activity as a continuous activity and the impacts of the environmental variables should be specified using the productivity m odification factors (refer to the example illustrated in Figure 6-4). 6.2.4 Buffers Buffers can only be defined between two continuous activities. The buffer is represented as a wavy arrow, w ith the size of the buffer indi cated on the top, as shown in Figure 6-30. Figure 6-30. Buffer Link The buffer link will be compiled into a logical condition: Progress of the predecessor Progress of the successor Buffer Size. (Equation 6-4) Buffer Size

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164 This logical condition will be inserted into the buffer_constraint of the successor activity. The buffer_constraint will be checked when the successor activity attempts to start and every time when it attempts to advance (refer to Section 5.2.1.4). If the buffer_constraint is not violated, the successor activ ity will make one step with the adjusted productivity ; otherwise, it will slow down to follow the progress of the predecessor activity or stop for a specified peri od of time, depending on the users option. The proposed method also allows the buffe rs to be measured on the distance between the two activities, pr ovided that the movements of both activities have been defined (refer to Section 6.1.2). The buffer links can be used flexibly to represent many realistic situations, which will be introduced below. 6.2.4.1 Minimum buffers The most common type of buffers is mi nimum buffers two activities have to maintain a minimum distance from each othe r. Figure 6-31 shows an example in which the activity RMEP has to maintain a minimu m buffer of 2000 SF from the activity Form. When being blocked, RMEP will slow down to follow Form. The buffer dialogue window is displayed in Figure 6-32. During th e progressing phase, at every time interval, if (the progress of Activity Form the progress of Activity REMP) 2000sf, Activity REMP will slowdown to follow th e pace of Activity Form. Figure 6-31. Example of a minimum buffer

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165 Figure 6-32. Defining a minimum buffer with the Slowdown option We can also change the option in the di alog window as shown in Figure 6-33 to specify that Activity RMEP will have a break of 2 hours when the buffer is violated. Another possible situation is when Activity RMEP runs into the 2000sf buffer, it will stop until Activity Form is 3000sf ahead of it. This situation can be represented as in Figure 6-34. Whether the resource working on the follower activity would be retained during the period of interruption can be controlled through the Retain Resource checkbox. Figure 6-33. Defining a minimum buffer with the Break for option Time Progress 2 hours Time Progress

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166 Figure 6-34. Defining a minimum buffer with the Break until option 6.2.4.2 Maximum buffers Instead of keeping away from each other, sometimes activities need to follow each other closely. When the distance of the tw o activities exceeds a specified maximum buffer size, the activity that takes the lead has to stop to wait for the activity that follows behind. To represent this type of situation, the head of the buffer link should be connected to the leadi ng activity and the tail of the buffer link should be connected to the follower activity (in this case, the leading act ivity is the successor in the buffer link, and the follower activity is the predecessor). Th e size of the buffer must be entered as a negative value. In the example shown in Figure 6-35, Activity A has a faster pace than Activity B, so the distance between the two activities will increase with time. Every time when Activity A attempts to advance, it will check the value of (the progress of Activity B the progress of Activity A). If Activity B la gs behind by 2100sf, then the value of the difference would be (-2100), which is smalle r than the specified buffer size (-2000 sf). Time Progress 3000 sf

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167 Activity A therefore will slowdown or pause to wait for Activity B to catch up. Figure 636 illustrates the situation where A would pause for 2.5 hours every time when it runs out of the 2000sf buffer. Figure 6-35. Example of a maximum buffer Progress Figure 6-36. Illustration of the maximum buffer 6.2.5 Combining the links A lot of times, the behaviors of the activ ity are controlled by joint conditions. For example, when Activity A is finished AND Activity B is 50% complete, Activity C can start; or when Activity A is finished OR Activity B is 50% complete, Activity C can start. In the proposed method, AND logic are represented by simply merging the head of the links, as shown in Figure 6-37(a); O R logic are represented by joining the links with a node, as shown in Figure 6-37(b).

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168 Figure 6-37. Representation of AND and OR logic Multi-layered constraints can also be quickly constructe d with the proposed method. The constraint (A fini shed OR B 50% complete) AND temp>40 is represented in Figure 6-38. Figure 6-38. Example of a multi-layered constraint 6.2.6 Branching of the links Branching of the link is represented w ith a diamond node as shown in Figure 6-39. If the selection is random, th e probabilities of taking the bran ches need to be indicated, and they must sum up to 1. In the example shown in Figure 6-40 (a), the likelihood of executing Activity B is .6 and the likelihood of executing Activity B is .4. temp>40 50% A B C Clock temp weather 50% 50% A B C A B C Note: the representation of the AND a nd OR logic applies to all type of links, including the start link, finish link, interrupt link, resume link, adjust link and buffer. (a) AND logic (b) OR logic

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169 prob (criterion) prob(criterion) Figure 6-39. Branching Node Figure 6-40. Example of branching If the selection is decision-based, the crit eria of choosing the branches need to be indicated and they must be mutually excl usive. In Figure 6-40(b), when Activity A finishes, if the time is still early enough (time<30), Activity B will be executed; otherwise Activity C, which might be an e xpensive remedy plan, will be executed. The branch node will be compiled to a branch model. It can route the received input from the predecessor activity, to one of its output ports according to the value of a random variable or the decision condition, fr om where the message can be passed on to the selected successor activity. 6.2.7 Resource Links The resource link is used to represent the activitys requirement fo r a certain type of resource. As shown in Figure 6-41, it is draw n as a straight line, with the required B C .6 .4 A B C time<30 time 30 A (a) Random Selection (b) Decision-based Selection

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170 quantity indicated on the top. The quantity coul d be a single positive number or a range expressed as (min, max) showing the uppe r and lower limit of the requirement. Figure 6-41. Resource Link The notation *p at the activ itys end indicates the pr iority of the connected resource; if the resource is the only type that the activity is ab le to use or the first choice among all the alternatives, the notation *1 can be omitted. At the other end, near the resource, the notation *p' indicates the prior ity of the activity to the resource. If the resource is not shared by any other activities, or if the activity has the highest priority for the use of that resource, the notation can be omitted. Figure 6-42 shows an example on the use of the resource link. In this example, Activity A could be finished either with tw o units of Resource S, or with one unit of Resource P. As Resource S has the higher priority (*1 has been omitted) between the two, Activity As requests for resources wi ll be sent to Resource S first. Figure 6-42. Example of resource links Suppose that by the time Activity As request arrives, Resource S has also received another request from Activity B. As Activ ity B has a higher priority over Activity A for A Resource S 4 units Resource P 2 units B *2 *2 ( 3 ) 2 1 Quantity *P *P'

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171 Resource S, Activity Bs request will be processed first. A ll remaining units of Resource S will be assigned to Activity B, whose lower limit is 3, upper limited is omitted, which means the more the better. Activity As re quest cannot be fulfilled, and thus will be stored in the request queue of Resource S. Resource S will generate and send a waiting notice to Activity A. Upon receiving the waiting notice, Activity A will submit another request to Resource P. If this request could be fulfilled by Resource P, Activity A will send a message to remove its previous request stored in the request queue of Resource R. If the request fails again, Activity A will be hol d in the Requesting_Resource phase until either of the requests is satisfied. 6.3 Compound Activities One of the most important features of the proposed method is multi-level modeling. With the bottom-up approach, multiple activities (could be of different types) can be coupled together to form a compound activ ity; the compound activity can be further coupled with other activities either atom ic or compound in the construction of higher-level compound activities. With the top-down approach, an atomic activity can be decomposed into a compound activity containing component activities, each of which could be further broken down into lower-level component activities. A compound activity could be defined as di screte or continuous and the discrete compound activity could be either res ource-driven or non-resource-driven. Seeing as a black box, the compound activity is used just as its at omic counterparts: any links that can be applied to an atom ic continuous activity can be applied to a compound continuous activity; any rules that ha ve to be followed when linking an atomic

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172 continuous activity have to be followed wh en linking a compound continuous activity. So does the discrete ones. 6.3.1 Compound Discrete Activities A Compound Discrete Activity may contain both discrete and continuous components. It is represented as a box w ith a + sign in the upper right corner to differentiate it from the atomic discrete activity. The name of the compound activity is indicated in the upper left corner. Figure 6-43. Compound Disc rete Activity Node Figure 6-44. Defining a compound discrete activity by coupling C B D A E Couple into a Discrete Activity Continuous Activity + N ame

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173 In Figure 6-44, Activity B, C and D are selected and coupled into a compound discrete activity named BCD. We can add star t, finish, interrupt, resume, and resource links to the compound activity BCD just as to an y discrete atomic discrete activities. An example is shown in Figure 6-45. (For the rules governing the rout ings of the links between the compound discrete activity and its components, refer to Section 5.2.2.1 and 5.2.2.2.) Figure 6-45. Adding links to a compound discrete activity The only difference when linking a compound activity is: if the link is based upon the partial completion of the compound activ ity, the user needs to define with the progresses of its components when such a state is considered achieved. For example, when adding a link to represent that Activ ity S cannot start until Activity BCD is 50% completed, a dialogue window will pop up as shown in Figure 6-46. The user may specify that, according to his or her best j udgment, Activity BCD can be considered 50% completed when its components Activity C an d Activity D both have completed 50%. + C B D A E B C D Clock Blasting P Q + Blasting = on Blasting = off

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174 Figure 6-46. Defining a progress-base d link on a compound discrete activity We can also break-down an atomic di screte activity to a compound discrete activity. In Figure 6-47, the at omic discrete Activity D has been decomposed into three components including D1, D2 and D3, each of wh ich needs to be defined separately as an atomic discrete activity or an atomic continuous activity. The Activity D becomes a compound activity and loses its originally defined attributes including the duration, progress curve and resource requirements. + C B D A E BCD Q 50%

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175 Figure 6-47. Defining a compound discrete activity by decomposition 6.3.2 Compound Continuous Activities The Compound Continuous Activity shown in Figure 6-48 has a + sign in the right upper corner to differentiate it from the atomic continuous activity. The compound continuous activity could also be formed through coupling or decomposition. However, there must be at least one continuous co mponent in the defined compound continuous activity. Figure 6-48. Compound Con tinuous Activity Node As shown in Figure 6-49, one discrete act ivity and three conti nuous activities have been coupled into one compound continuous activity, Activity Li ne1. In Figure 6-50, Line1 is connected with another two com pound continuous activities Line 2 and Line 3, and a compound discrete activity Mobilization. Figure 6-49. Example of a compound continuous activity A B C D +Lin e 1 D C B A E + D2 D1 D3 + N ame

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176 Figure 6-50. Adding links to co mpound continuous activities The start, finish, interrupt, resume and adjust links between the compound continuous activity and its components are rout ed in the same way as with the compound discrete activity (refer to Section 5.2.2.1 and 5.2.2.2 for the routing rules). So the start-up constraints from Mobilization will be imposed on Activity A, the component that does not have any predecessors in Line1. The rules governing the routi ngs of the buffer constraint s have been presented in Section 5.2.2.3. According to these rules, when the component Activity B, C or D attempts to start or advance, they are re strained by the buffer constraints imposed on Activity Line 1. And since this buffer constrai nt is imposed by Line 2, which is also a compound continuous activity, the buffer distance has to be maintained between all the continuous components in Activ ity Line 2 that have st arted but not finished. 6.4 Repetitive Activities 6.4.1 Defining Repetitive Activities The repetitive activity is a special type of the compound activity. It is divided into the Repetitive Discrete Activity (shown in Figure 6-51(a)) and the Repetitive Continuous Activity (shown in Figure 6-51(b)). Instead of th e plus sign, the repetit ive activity has the number of the repetitive units/segments indicat ed in the upper right co rner of the activity box. 100ft 100ft Line1 + Line2 + Line3 + Mobilization +

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177 (a) Repetitive Discrete Activ ity (b) Repetitive Continuous Activity Figure 6-51. Repetitive Activities Figure 6-52 illustrates how to define a repe titive discrete activity. The selected components are duplicated 10 times to form the repetitive discrete activity Phase II shown in Figure 6-53. Figure 6-52. Defining a repetitive discrete activity In the newly formed repetitive activity, all units have the same set of activities, and all activities have the same durations, wo rk quantities, and resource requirements. Therefore, Activity A in all units of Phase II will be assigned a duration of 4 days. Click C 5d B 3d D 7d A 4d E 10d Repeat and couple into a Repetitive Discrete Activity Repetitive Continuous Activity n N ame n N ame

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178 on the number in the upper right corn er, the repetitive act ivity will expand, as shown in Figure 6-54, and the at tributes of the individual activities could be changed. Activities can also be added to or delete d from each individual unit network in the expanded mode. Click on the units again, the repetitive activity will collapse and the range of the durations for each activity will be displayed. Figure 6-53. Example of a repetitive di screte activity collapsed mode Figure 6-54. Defining a repetitive di screte activity expanded mode C 5 d B U (2, 4) d D 7d A 4 d E 10 d Phase II 10 units C(1) 5d B(1) U ( 2 4 ) d D (1) 7d A(1) 4 d E (1) 10d Phase II 10 units C(2) 5d B(2) U ( 2 4 ) d D (2) 7d A(2) 5d E (2) 10d C(10) 5d B(10) U ( 2 4 ) d D (10) 7d A(10) 5d E (10) 10d

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179 As can be seen in the expanded mode in Figure 6-54, a variable i ( i=1 to 10 ) has been assigned to the activities in the repetitive Unit (i) So, for example, Activity C (5) refers to Activity C in Unit 5. This variable i is very important when adding links and assigning resources to repetitive activiti es, as will be discussed below. Repetitive continuous activities are define d in a similar way, except that a key component (which must be continuous) needs to be designated. Note that all activities duplicated from that designated key component will become key components and thereby be controlled by the buffer constraint imposed on the repetitive activity. 6.4.2 Assigning Resources Notice that in Figure 6-40, no links have been added among the units, this means that activities of the same t ype have not been sequenced. When the start constraints on the repetitive activity is satisfied, all A(i) (i = 1 to 10) can start at once. With the proposed method, sequencing of activities amon g the units is modeled through resource assignments. By changing the available numbe r of resources and the priority settings, various resource utilizati on strategies could be easily represented. Figure 6-55. Assigning resources to the repetitive activity i C 5 d B U (2, 4) d D 7d A 4~5 d E 10 d Phase II 10 units Crew A 1

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180 Figure 6-56. Resource-imposed sequencing in the repetitive activity: two crews proceed toward each other *(i) C 5 d B U (2, 4) d D 7d E 10 d Phase II 10 units Crew A 1 i Crew B 1 A 4~5 d C ( 1 ) B ( 1 ) D ( 1 ) A(1) E ( 1 ) Phase II 10 units C ( 2 ) B ( 2 ) D ( 2 ) A(2) E ( 2 ) C ( 9 ) B ( 9 ) D ( 9 ) A(9) E ( 9 ) C ( 10 ) B ( 10 ) D ( 10 ) A(10) E ( 10 ) Crew A Crew B (a) Collapsed Mode (b) Expanded Mode

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181 Figure 6-57. Resource-imposed sequencing in the repetitive activitytwo crews in alternating units i C 5 d B U (2, 4) d D 7d E 10 d Phase II 10 units Crew A 1 i Crew B 1 A 4~5 d i=1,3,5,7,9 i=2,4,6,8,10 Phase II 10 units C(1) B ( 1 ) D(1) A(1) E(1) C(3) B(3) D (3) A(3) E (3) C( 4 ) B ( 4 ) D( 4 ) A(4) E( 4 ) C(2) B(2) D(2) A(2) E(2) (a) Collapsed Mode Crew A Crew B (b) Expanded Mode

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182 In Figure 6-55, one Crew A is assigned to Activity A, so only one A( i ) could be worked on at any time. As the priority of the activities are set as their unit number i Crew A is going to work in the order of A(1), A(2) A(10). If the prior ity is defined as *(i) Crew A is going to start fr om A(10) and finish at A(1). In Figure 6-56(a), Crew B has been added to work on Activity A with the priority set as *(i ). So Crew A and Crew B will be working towards opposite directions as illustrated in Figure 6-56(b). Figure 6-57 shows another example where Crew A and Crew B work in alternate un its in the same direction. 6.4.3 Identification and Repeating of the Links As a special type of compound activity, the repetitive activities follow all the rules governing the linking of compound activities, but there are tw o additional usages about the links that are designed to a ddress their unique repetitiveness. Figure 6-58. Identification of th e link in the repetitive activity One is identification of the link In the example shown in Figure 6-58, Phase III will start after Unit 5 in Phas e II has finished. One FS dependency relationship has been added between Activity E in Phase II and th e compound activity Phas e III. To indicate C 5 d B U (2, 4) d D 7d E 10 d Phase II 10 units A 4~5 d Phase III + i=5

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183 that this link is only connected with Activity E(5), i=5 is annotated at the end of the link near Activity E. Note that the identificati on can be used at either the tail end or the head end of the links. The other is repeating of the link All links, including the start/finish links, interrupt/resume links, adjust links, and buffers can be used to show repetitive relationships simply by changing their tails from a single line to a double line. Figure 659 shows an example of usi ng the repetitive link. In th e construction of high-rise buildings, to protect the drywa lls from weather, it is ofte n required that dry wall should not be put on until the building envelope on upper floors have been finished. As illustrated below, we can specify that Exterior Wall on the 6th floor has to be finished before Dry Wall on the 1st floor can start, Exterior Wall on the 7th floor has to be finished before Dry Wall on the 2nd floor can start,, Exterior Wall on the 100th floor has to be finished before Dry wall on the 95th floor can start, with just one repetitive link. Figure 6-59. Repetitive link w ithin a repetitive activity The repetitive links can also be used betw een two repetitive activities. Suppose that Building 1 has 100 floors, and Building 2 has 50 floors. Since these two buildings are connected, Activity P in Building 2 on each floo r cannot start until Activity D in building Dry Wall Building 100 floors i (i=6 to 100) i-5 Exterior Wall

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184 1 on the same floor has completed. This relationship can be modeled by a simple repetitive link as shown in Fi gure 6-60. Because this is an ith to ith relationship, the i identification at both ends have been omitted and only the applicable scope of i has been noted. Figure 6-60. Repetitive link be tween repetitive activities C D E Building 1 100floors A B Q S T Buildin g 2 50floors P (i=1 to 50)

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185 CHAPTER 7 CASE STUDIES WITH THE PROPOSED METHOD In Chapter 3, four case studies are presen ted, each representing a typical class of construction project. In this ch apter, the proposed method is app lied to those four cases, and the new models are compared with those developed with the existing methods. 7.1 Case One: A Typical Regular Project The project examined in the first case study has been descri bed in Section 3.1. Figure 7-1 shows the model developed with the proposed method for this case study. This model will be compared with the CPM model (in Figure 3-1) and the STROBOSCOPE model (in Figure 3-5) on the modeling of activities, dependency re lationships and environmental factors. 7.1.1 Modeling of Activities 7.1.1.1 Duration Similar to the STROBOSCOPE method, the pro posed method is able to represent both deterministic and probabilistic durations, and de termine the values dynamically. In Figure 7-1, the duration of the activ ity Foundation is defined as a proba bility distribution of U (25, 35) days. We can also specify that if the foundati on is poured in winter, it would take much longer to get the job done. Defined as IIF (M arch< time. month < Nov, U(25,35), U(35,45)) ( time is a system variable that record when the activity attempts to st art), the duration of the Activity Foundation would be U(25,35) if the activity star ts between March and November; and U(35,45) otherwise. U( ): Uniform Distribution

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186 Figure 7-1. The proposed model for Case One

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187 7.1.1.2 Progress curve The CPM model and the STROBO SCOPE model are not able to represent the progress curves of the activities. In the proposed method, by default, a ll discrete activi ties proceed at a constant rate from start to finish, i.e., have a Type I straight progress curve. The Activity Foundation is defined to have a Type II curve, which takes account of th e learning curve effect. The progress curve can also be customized. For example, to show that the foundation is poured in five separate parts and each part is not cons idered done until completely finished, we could define that the progres s function is STEP (0 t<.2, 0%, .2 t<.4, 20%, .4 t<.6, 40%, .6 t<.8, 60%, .8 t<100, 80%, t=1.0, 100%), as il lustrated in Figure 7-2. Figure 7-2. Customizing a stepwise progress curve 7.1.1.3 Interruption and adjustment Different from the other two models, the define d durations of the disc rete activities could be changed by interruptions and adjustments in the proposed new model. In Figure 7-1, the Activity Foundation would stop when the temperat ure drops to below 40 degrees and resume .2 .4 .6 .8 1.0 Duration 60% 40% 20% Progress 80% 100%

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188 when the temperature exceeds 45 degrees; and its remaining duration would be extended to 1.4 times as the construction of the Vertical Lifts starts. 7.1.2 Modeling of dependency relationships 7.1.2.1 FS, SS, FF and SF dependency relationships The representation of the FS, SS, FF and SF re lationships and lag times in the new model are exactly the same as in the CPM method. The us er does not need to generate virtual tokens, divide activities, or add extra node s as in the STROBOSCOPE model. 7.1.2.2 Non-time based dependency relationships Except for the time-based dependency relationshi ps, the proposed method is also able to represent progress-based dependenc y relationships. So, the requireme nt that the vertical lift on the first floor cannot start until th e foundation is at least 1/3 finish ed can be directly represented as in Figure 7-1, and does not need to be converted into an SS re lationship with a 10 days lag. If Activity Foundations duration changes, or its pr ogress curve is non-linear, or the activity has been interrupted or elongated, this progress-based relationship will still be accurate. 7.1.2.3 Compound constraints The representation of the AND logic in the proposed method is as easy as in the CPM method, as can be demonstrated with the ac tivity SOG #1 Pour (enl arged in Figure 7-3). Figure 7-3. Representation of the AND logic in the proposed method

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189 7.1.3 Modeling of environmental factors The environmental factor temperature is represented as variable temp = p (50, 15) in the environmental factor Clock 1, whose interval is 2 hours. The impacts of weather and wind speed can be included in similar ways. 7.2 Case Two: A Typical Linear Project In Section 3.2, the constructi on of a gas line has been disc ussed as the example for the linear projects. A model has been developed with the proposed method for this project. Figure 74 (a) shows this model with th e compound activities collapsed; in Figure 7-4 (b), the compound activities have been expanded. Figure 7-4. The proposed model for Case Two In this project, the buffers need to be measur ed on distance, and the paths of the activities need to be tracked. The point where the project star ts is designate as Point and the direction P ( ): Poisson distribution. (a) Collapsed Mode (b) Expanded Mode

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190 toward which all activities are progressing is ta ken as the positive direction. The paths of the activities are defined as shown in Table 7-1. Sinc e the default values (0 for the Start Position, positive for the Direction) apply to most of the activities, only a few activities need to be defined specifically. Table 7-1. Defining the path of the activities for Case Two Compared with the LSM model in Figure 3-10 and the SLAM II model in Figure 3-13, the proposed model has the fo llowing characteristics: 7.2.1 Modeling of Activities 7.2.1.1 Productivity As SLAM II, the proposed method allows both deterministic and probabilistic productivities. But the proposed method is also able to represent the impacts of dynamically changing factors on the productivi ties. For example, the produc tivity of Activity Welding is sensitive to temperature. This can be modele d by defining the Productivity Modification Factor as a function on the variable temperature Activity Start position Direction ROW-1 0 Positive ROW-2 6000 Positive Stringing 0 Positive Welding 0 Positive Trenching-1 0 Positive Trenching-2 3000 Positive Trenching-3 3500 Positive Trenching-4 7500 Positive Lowering-in 0 Positive Backfilling 0 Positive

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191 7.2.1.2 Slow-down and break With the proposed method, it can be easily modeled whether an activity will slow-down or break when being blocked by its preceding activity. Figure 7-5 shows the dialogue window defining the buffer between the activity ROW an d Stringing. With the LSM method, if these options changes, the whole di agram needs to be redrawn. Figure 7-5. Defining the buffer between ROW and Stringing 7.2.1.3 Position of activities With the defined paths and directions of th e activities, the proposed method can determine positions of the activities at any time based on the simulated progress values. For example, if at time t the progress of Activity Trenching-3 is 1000 m, it can be determined that it is (3500 + 1000 =) 4000m away from the project start point. Should the activity goes toward the negative direction, it would be at the (3500 -1000 =) 2500m position at this point. The result can be plotted as a LSM diagram (if the layout is one -dimensional) for further graphical analysis. 7.2.2 Modeling of Buffers The proposed method can maintain the buffer between two activities measured on progress or distance. The buffers are represented as links similar to the discre te type of dependency

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192 relationships. Though this represen tation is not as gra phically intuitive as the actual buffers shown on a LSM diagram, it is much easier to draw and change. Compared to the SLAM II simulation method, where the buffer c onstraint has to be coded in subroutines, the advantages of the proposed method in this area are even more obvious. 7.2.3 Modeling of Resources The proposed model can represent resources directly when necessa ry. In this project, Crew B is shared between Stringing a nd Lowering-in, which can be represented as in Figure 7-6. The priority of Activity Stringing to Crew B is (o mitted), and the priority of Lowering-in is So Lowering-in cannot go on in parallel with Activ ity Stringing and has to wait until Stringing has been totally completed. Figure 7-6. Representing resource sharing 7.2.4 Multi-level Modeling This model can be viewed on two different leve ls: the expanded model shows all activities at the detailed level, the collapsed model empha sizes the big picture and the overall arrangement. The multi-level modeling ability of the pr oposed method enables both the top-down and bottomup approach. At the initial planning stag e, the project manager may create an activity Trenching as an atomic continuous activity and specify its external relationships with other activities; and later on as more information become available, break it down into smaller, more controllable activities and focus on the internal re lationships within the activity. Or in the other way, the project manager may first have the forema n of trenching work out the details of this

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193 activity: how it is going to be divided into sectio ns, which crews are going to be assigned to each section, etc; then he can coupl e these activities into one comp ound activity and look at it from a higher point of view to coordinate it with Activity Welding and Lowering-in. 7.2.5 Multi-dimensional Layouts Following this single utility line project, we can further examine the site development project discussed in Section 3.2.3, which consists of two intersecting uti lity lines. This example can demonstrate the ability of the proposed method for modeling linear projects with multidimensional layouts. Figure 7-7. Site layout of storm drainage Segment D97-24-25 For convenience, the site plan of this projec t is again presented in Figure 7-7. Suppose that there are 200 segments in the storm line and 220 segments in the sewer line, the two activities can be represented as in Figure 78. As the two activities have diffe rent layouts, the paths of their Segment D97-24-25

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194 segments need to be defined in a two-dimens ional coordination system. Figure 7-9 shows the dialogue window defining the path of Segment D97-24-25 in the storm line. Figure 7-8. Modeling a project with multi-dimensional layout Figure 7-9. Defining the path of an activity in a project with multi-dimensional layouts With the defined paths, at any time t the current positions of the crews working on the segments can be determined from the activitys progress value. When any segment in Activity Sewer Line (denoted as Seweri) attempts to start or advance, it will be restrained by the 10ft external buffer constraint. Suppose that there ar e two crews working on th e Activity Storm Line and currently two segments are und er construction (denoted as Stormp and Stormq), the following constraints will be checked for each Seweri: Distance between Seweri and Stormp 10 ft and Distance between Seweri and Stormq 10 ft ;

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195 in which the distance is measured between th e current positions de rived from the progress values. 7.3 Case Three: A Typical Repetitive Project The third example has been described in Section 3.3. The CPM model, LSM model and STROBOSCOPE model for this example are pres ented in Figure 3-15, Figure 3-16 and Figure 319 respectively. Figure 7-10 shows the m odel developed with the proposed method. Figure 7-10. The proposed model for Case Three: one crew The whole project is represente d as a repetitive activity c ontaining 24 repeating units, each unit for one pour. This model has the following characteristics compared with the other models: 7.3.1 Efficiency Compared to the CPM model and the LSM mode l which occupies more than two pages, this model is obviously more efficient in repr esentation. It is also much simpler than the STROBOSCOPE model it contains only abou t half as many nodes as the STROBOSCOPE model does. Certainly, the expanded model c ontains many more nodes, but it is seldom Pour 1 day Cure&Stress 1 day Vertical 0 to 2 days i (I=1 to22) i+2 Form 3~5 days RMEP 2~3 days Crew A 1 24 units i 1 day 1 day Floors

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196 necessary to expand it except when we need to find out detailed information in a specific unit for Activity Form or Activity RMEP, which have variations among different units. 7.3.2 Resource-imposed Constraints Among the existing models, only the STROBOSC OPE model is able to represent the resource-imposed constraints. In the proposed method, the resource-imposed constraints can be represented easily and flexibly. Figure 7-10 shows that one Crew A is going to work on Activity Form, and the units will be processed from Unit 1 to Unit 24 (the priority is defined on the unit identification variable i ). If there are two Crew As that can work on this activity, we can simply change the available number of the resource to 2. If the two crews are of different types, and Cr ew A is preferred over Crew B, the model can be quickly changed to Figure 7-11, in which *2 is noted on the resource link connected with Cr ew B to indicate its priority. Figure 7-11. The proposed model for Case Three: two crews Suppose that one Crew A is going to work on the odd-numbered units, and one Crew B is going to work on the even-numbered units, the situ ation can be represented as shown in Figure 7-12. Pour 1 day Cure&Stress 1 day Vertical 0 to 2 days i+2 Form 3~5 days RMEP 2~3 days Crew A 1 24 units *i Crew B 1 *i *2 i (i=1 to 22)

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197 Figure 7-12. The proposed model for Case Three: two crews in alternating units 7.3.3 Hetero-relationships As discussed in Section 7.3, the representation of the hetero-r elationships is one of the biggest challenges in the mode ling of repetitive activitie s for the LSM method and the STROBOSCOPE method. In the proposed method, he tero-relationships ca n be easily modeled by repeating and identifying the links. For example, as shown in Figure 7-10 to 7-12, a repetitive link is drawn between Activity Form and Activity Vertical. It show s that Vertical 1 is connected to Form 3(=1+2), Vertical 2 is connected to Form 4 (=2+2), and Vertical 22 is connected to Form 24(=22+2), with the simple notations on the re petitive link Vertical ( i ) (i=1 to 22) connected to Form ( i +2). No coding is required as in the STROBOSCOPE method. 7.4 Case Four: A Project with Mixed Features The project examined in Case Four include s both the foundation a nd the upper-structural parts of the 14-level Condo, as de scribed in Section 3.4. The comple te model developed with the proposed method is shown in Figure 7-13. It demons trates the ability of the proposed method in the integration of differe nt features, including: Pour 1 day Cure&Stress 1 day Vertical 0 to 2 days i+2 Form 3~5 days RMEP 2~3 days Crew A 1 24 units *i Crew B 1 *i i (i=1 to 22) i=1,3,,23 i=2,4,,24

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198 Figure 7-13. The proposed model for Case Four Foundation U(25,35) days Pile Delay 7 days Excavate & Dewater 2 days As-built & Chip Down Piles 3 days Form Elevator & Column PCs 2 days Reinforce Elevator & Column PCs 2 day SS 67% SS 50% Pour Elevator & Column PCs 1 day Waterproof Elevator Walls 1 day Backfill Deep Foundation 3 days F, R, P Elevator Walls & Column 4 days Stair PCs 4 days SS 75% Stair Wall #1 3 days Elevator Walls SOG-2nd 4 days Stair Wall #2 4 days SS 50% Retaining Wall 10 days MEP Underground 1 5 days FF 2 days FF 1 days Vertical Lift #1 25 days Backfill to Subgrade 15 days FF 2 days SOG #1 Pour 1 day SOG #1 Pour Prep 2 days Pour 1 day Cure&Stress 1 day Vertical 0 to 2 days Unit i (i=1 to 22) Unit (i+2) Form 1584~2187 sf/day RMEP 6500 sf/day Retaining Wall 10 days Unit 1 FF 2days Masonary Unit 22 SS 67% Crew One 1 24 units *i Floors 1500 sf

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199 7.4.1 Integration of Discrete a nd Continuous Activities In Figure 7-13, Activity Form and Activity RMEP are represented as continuous activities, for it is required to ensure the 1500 SF buffer between them. These two continuous activities are integrated seamlessly in the project where the majo rity of the activities are discrete activities: they can be connected with the di screte activities with discrete types of links, and can be coupled with the discrete activitie s to form compound activities and repetitive activities. 7.4.2 Integration of Repetitive and Non-repetitive Activities As shown in Figure 7-14, the enlarged upper struct ural part of the model, Form in Unit 1 in the repetitive activity Floor cannot be finished until 2 days after the non-repetitive activity Retaining Wall (the border of the box is dotted as this activity is duplicated in this model for easy of display) is finished, and Ac tivity Masonry (a non-repetitive activity) cannot start until Activity Pour in Unit 22 in the repetitive activity is finished. Figure 7-14. The enlarged pa rtial model for Case Four Pour 1 day Cure&Stress 1 day Vertical 0 to 2 days Unit (i+2) Form 1584~2187 sf/day RMEP 6500 sf/day Retaining Wall 10 days Unit 1 FF 2days Masonary Unit 22 Crew One 1 24 units *i Floors 1500 sf

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200 Unlike the STROBOSCOPE method where the re petitive and non-repe titive activities are modeled with different concepts and have to be synchronized with extensive coding work, the proposed method connects the repetitive and non -repetitive activities di rectly with links. Moreover, by collapsing the repeti tive activities and identifying the links with the variable i, the relationships between the two types of activi ties are emphasized and clear, not obscured by a large number of links like in the CPM model.

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201 CHAPTER 8 CONCLUSIONS AND RECOMMENDATIONS 8.1 Conclusions Existing construction planning and scheduling methods all have a specific scope of application and some fundamental limitations th at restrict their ability in the modeling of complex, realistic construction projects. In or der to develop a method that is universally applicable, powerful and simple-to-use, a new theory needs to be established. The method proposed in this research is base d on the system-theory and it is formalized with the DEVS specification, which enables it to integrate any modeling formalisms and model a system at different levels. A set of graphical mo deling elements have been designed so the user can easily utilize the full capaci ty of this method without a ny specialized knowledge in the system theory or computer languages. According to the requirements for planni ng and scheduling construction projects as summarized in Chapter 4, the pe rformance of the proposed method can be examined from the following four perspectives: scope of applicatio n, accuracy of modeling, form of representation and level of modeling. Scope of application. The proposed method was applied to four case studies in Chapter 7 including a typical regular project a typical linear project, a typical repetitive project and a project of mixed features. It was demonstrated that the proposed me thod is able to represent both the discrete and continuous, repetitive and nonrepetitive elements and integrate them all together.

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202Table 8-1. Comparison of the modeling accuracy of the proposed method and major existing methods CPM LSM STROBOSCOPE The proposed method Duration Only real numbers or probabilistic distributions. Both deterministic and probabilistic. The values are dynamically determined. Can be resource driven. Both deterministic and probabilistic. The values are dynamically determined. Can be resource driven. Progress curve No No Yes Interruption No No Yes Activities Adjustment No No Yes FS,SS,FF, SF relationships Yes Only FS relationships can be directly represented. Yes Non-time-based dependencies No No Can be based on progress or work quantity Compound logic constraints Only AND logic. AND logic can be graphically represented. OR logic requires code writing. AND, OR and multi-layered logic all can be graphically represented. Does not need code writing. Discrete Dependency Relationships Branching No Support both probabilistic and decision-based branching. Support both probabilistic and decisionbased branching. Productivity Deterministic Dete rministic and probabilistic. Accounts for impacts of dynamically changing variables. Slow-down Yes Yes Break Yes Yes Activities Layout Only one-dimensional Bo th one-dimensional and multidimensional. Buffers Yes Yes Continuous Dependency Relationships Types Distance-based and timebased Progress-based

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203Table 8-1. Continued CPM LSM STROBOSCOPE The Proposed Method Resources Representation No Not directly represented, but the work paths of the resources can be visualized. Include generic, characterized and compound resources. Resources can be defined with type, minimum/maximum quantity, and other attributes. Activity selecting resources No No Yes, but activities can only select resources from the same queue. Priorities of the resources can be defined on any variables. Resource selecting activities No No Yes, but one activity can only be assigned one priority value for all the shared resources. One activity can have different priority values to different resources. Environmental factors No No Yes, but these factors need to be modeled with separate subnetworks. Modeled with a single node. One node can include multiple variables. Representation Not efficient Not efficient when certain assumptions cannot be fulfilled. Difficult to show parallel activities. Efficient Efficient. Resource-imposed dependency relationships Not directly modeled. Not flexible. Show resource flows, but does not model the resources directly. Yes Flexible in modeling multiple crew strategies. Repetitive Hetero-relationships Must be represented one-byone. Difficult. Difficult. Require extensive code writing. Does not require code writing. Discrete and continuous No Yes No Yes Integration Non-repetitive and repetitive Yes No Yes, but difficult. Yes

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204 Accuracy of modeling. Table 4-1 summarizes the major pr operties and behaviors that a universally applicable planning and scheduli ng method needs to inco rporate in order to accurately represent the projects described in th e case studies. Table 8-1 compares the proposed method and the major existing methods on their ab ilities to represent thes e factors based on the cased studies conducted in Chapter 3 and Chapte r 7. It was demonstrated that the proposed method has overcome many of the limitations of the existing methods. Moreover, this method is highly expandable. Theoretically, there is no limit on what properties and behaviors it is able to represent. Properties such as cost, material consumption and physical dimensions can be added as additional parameters to the activity models, and their changes can be linked to the progress of the activity and simulated dynamically. The resource model can also have additional parameters su ch as calendars, maintenance schedules and required working conditions to make it more accurate. Form of representation. The proposed method is built with a black-box approach the users can fully utilize the functions of the modeling elements without knowing their inside structures and the underlying theo ry. As a result, the representa tion of the proposed method is easy to learn and understand It uses a representation sim ilar to the CPM AON diagram. As shown in Case One, for typical regular projects, the proposed model could be just the same as the CPM model. In other words, if the user just wa nts the same level of accuracy in the modeling of regular projects, there is no difference between the models built with these two methods. But the proposed method is able to extend the same style of simple representation to other types of projects and much more complex situations. It can be just as effective as or even more powerful than the existing simulation methods incl uding STROBOSOCOPE and SLAM II for the

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205 modeling of construction projec ts, without the need of using the Combis, Queues and any simulation languages. It is also very efficient in modeling and editing. Table 8-2 compares the number of nodes, links and lines of codes used by different met hods for the four case studies. As it shows, the proposed method uses the least number of nodes and links for all of the f our cases, and does not require the user to write computer codes as the STROBOSOCOPE and SLAM II simulation methods often do. What is more, unlike the LSM models, which require a whole model to be redrawn every time an activity or dependency rela tionship needs to be a dded, deleted or changed, the editing of the proposed models are quick and easy. Compared to the CPM, STROBOSOPE and SLAM models, the advantage of the proposed models on the efficiency of editing is also obvious if the compound activitie s, repetitive activities and re source-imposed dependency relationships could be fully utilized. Table 8-2. Comparison of the representation effi ciency of the proposed method and the major existing methods Case One (regular) Case Two (linear) Case Three (repetitive) Case Four (mixed features) N* L* C* N L C N L C N L C CPM 20 18 0 1521900 177 212 0 STROBOSCOPE 31 29 0 13 14 5 55 53 9 SLAM II 65 75 27 Proposed Method 20 18 0 17 11 0 7 7 0 28 26 0 *N: number of nodes *L: number of links *C: lines of codes Moreover, it is natural and intuitive Existing simulation methods for construction planning and scheduling all rely on the ACD diagrams, which are shaped by the underlying

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206 three-phase simulation strategies. They require all activity nodes to be linked by the traveling of the resources. Many abstract nodes, such as the Generate node, Combi node, Queue node, have to be used to manipulate the flow of the resources. Logical dependency relationships often cannot be directly represented and have to be implemented by manipulat ing the virtual tokens through many tricks. The proposed models have smaller gaps with realistic construction projects. All of the modeling elements maps directly to real-world objects or concep ts and own the same attributes and behaviors as their real-wor ld counterparts. Both the logical constraints and the resourceimposed constraints can be directly represente d. So the user can think and communicate with terms used in construction, rather than term s used in simulation or any program-specific languages. Multi-level modeling. One of the biggest advantages of the proposed method is that it establishes a hierarchical construction for the ac tivities and thereby enables modeling at different levels. This feature can signifi cantly improve efficiency in m odel building and editing, provide insight for complex projects, and support both the bottom-up and top-down scheduling approach. 8.2 Limitations and Recommendations for Future Research This study is just the first step in introducing the system th eory into construction planning and scheduling. Although the system theory and the DEVS Formalism contain no fundamental limitations for modeling complex dynamic cons truction projects, the proposed method has several major aspects that need to be improved: Currently, the method only measures the time performance of the project. To measure the project performance in other aspect, such as cost and material consumption, additional parameters and transitional functions n eed to be added to the activity models. A hierarchical structure needs to be established for the res ources. In a construction project, crews are formed with one or more types of labors and equipment. Individual resources often need to be assembled and dissembled into different crews. A hierarchical

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207 construction will be able to represent the assembling of resources, and simplify model constructions under many situations. For repetitive activities, an option needs to be provided to ensure resource continuity. Maintaining resource continuity can reduce th e idle time and maximize the learning curve effect for the repetitive activities. To mainta in resource continuity, the starting time of the first unit in the repetitive activity needs to be strategically delayed. An algorithm needs to be developed to search for the st arting point to en able this option. Besides enhancing the above areas, th e proposed method also need to be: Implemented on computer. Chapter 5 has desc ribed the DEVS specifications for the major models in the proposed method. These models can be implemented with the DEVSJAVA or the DEVS/C++ packages provided by the Ar izona Center for Integrative Modeling & Simulation(available on http://www.acims.arizona.edu/SOFTWARE/software.shtml last accessed on March 28, 2008). Also, an interface needs to be developed to compile the graphical models to DEVS languages. Field tested. In this study, the proposed me thod is verified with case studies. A future research should be conducted to evaluate it s effectiveness and efficiency with empirical experiments. The major data need to be coll ected include: the averag e learning time a user needs before he or she can use this method to represent a fairly complex construction project, the average time a us er spends on modeling a certain project with this method compared with other methods, the number of errors in the models developed with this methods compared with that in other models, etc. The users can also be surveyed on their opinions regarding the ease-ofuse, modeling ability and li mitations of this proposed method.

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208 APPENDIX A FOUNDAMENTALS OF SIMULATION TECHNOLOGY Overview of Simulation A (dynamic) simulation is an imitation of the operation of a real-world process or system over time (Banks et al. 1999). Compared to analytical methods, simulation has the advantages of being able to address randomness and dynamics in real-world systems (Zhang et al. 2002). Simulation modeling assumes that a system can be characterized by a set of variables, with each combination of variable values representing a unique state or condition of the system and thereby manipulation of the variable values si mulates movement of the system from state to state(Prisker and O'Reiley 1999). In a simulatio n experiment, the systems status, i.e., the variable values, evolve dynamically according to operation rules that have been pre-designed into the model. The performance of the system can be evaluated by analyzing the statistics of the variables, or by directly obs erving the animated system co mponents, as supported by some simulation software. Discrete vs. Continuous Simulation In (dynamic) simulations, time is the most im portant independent variable. Other variables are functions of time and are the dependent variables. According to the behaviors of the dependent va riables, simulation models can be classified into two basic categories. In discrete simulation models the dependent variables changes only at discrete points in simulated time referred to as event times as shown in Figure A-1. In continuous simulation models the dependent variables may ch ange continuously over simulated time (Prisker and O'Reiley 1999), as shown in Figure A-2. Note that continuous and discrete are modi fiers to the simulation model, not to the actual system that the model aims to represents. A real-world system often can be modeled either

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209 as a discrete model or a con tinuous model, depending on the obj ectives of the study (Pidd 1998; Prisker and O'Reiley 1999) As described by Pi dd (1998) in an example where an underground railway is being considered, if th e analyst only concerns about th e time it takes for a passenger to travel between stations, then the system should be simulated with a discrete model; but if the speed of the train as it travels be tween stations is of interest, th en the system has to be viewed from a continuous prospective. It has also been realized that discretely changing and continuously changing variables can co-exist in one system model. But it was until recently that a few simulation software systems allow users to program such combined discre te-continuous models, incl uding SlamII (Prisker and O'Reiley 1999) and Extend (Krahl 1996). Continuous Simulation Technology In a continuous simulation mode l, the state of the system is represented by dependent variables which change c ontinuously over time. These variables ar e referred to as state variables to be distinguished from disc retely changing variables. To construct a continuous simulation model, the modeler needs to define the derivative dt ds for every state variable s, over time t, together with s(0) the initial value of s at time 0. Theoretically, this allows the values of the state variables to be computed at any poi nt of time by integrating Equation A-1: st tdt dt ds t S t S1) ( ) (1 2 (Equation A-1) However, analytical solutions to differential equations are not always attainable. Hence, integration of the differential equations is us ually performed using num erical methods which divide time into small slices referred to as st eps, and calculate state variables by employing an

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210 approximation to the derivatives of the variable s over the time step. The accuracy of these methods depends on the order of the selected appr oximation algorithm and the size of the step. An efficient algorithm can adjust the size of the step by increasi ng it when the change is smooth, and decrease it when the change is abrupt. For some continuous systems, the derivatives dt ds do not change very fast and can be regarded as constant during short time periods. These continuous systems can be modeled using Equation A-2: t r S Sk k 1, (A-2) where Sk+1, the value of a state variable S at step k+1, is derived from its previous value Sk at time k, by adding the increment (r t) between the two steps. Time ha s been disretized into fixed steps of length t, and the rate of change r is assumed constant for any t. Figure A-3 shows approximation of a state variab le in a continuous simulation model using fixed time steps Discrete Simulation Technology In management science, discrete simulation is much more commonly used than continuous simulation. The technology of discrete simulation can be discussed from four perspectives: time advancement techniques, simulation strategi es, graphical modeling representations, and simulation languages. Time Advancement Techniques Time advancement techniques deal with how to advance the simulated time in the simulated system. The fixed time-step method can be used in the time handling of discrete simulation models as well as in the continuous simulation models as discussed above. Actually, it is the simplest way that mimics the natural flow of time. However, for discrete simulation

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211 models, dependent variables change only at discrete event times, in other words, they change much more sparsely than the state variables do in continuous simulation models. It would be unnecessary to examine and update the models at each time step; rather, time can be advanced from one event to the next wit hout any lost of information. This timing mechanism is referred to as the next-event technique, and simulations em ployed this technique are called discrete-event simulations. The next-event time advancement technique is the corner stone of the discrete simulation technology. Simulation Strategies Simulation strategies generally guild how the re al-world system is going to be decomposed into entities and mimicked. Different simulation strategies employ different control mechanisms to select the next-event and manage the si mulation time during a experimentation. There are three most common discrete-event simulation strategies: event sc heduling (ES), act ivity scanning (AS) and process in teraction (PI). The relationship between the con cepts of events, activities and processes are illustrated in Figure A-4. An activity consists of one start event and one end even t, and a process consists of a sequence of events and/or a number of activities. With ES, the modeler needs to identify the even ts that can change the state of the systems and then determine all possible consequences as sociated with each event type. A simulation of the system is produced by executing the events in a time-ordered seque nce(Banks et al. 1999; Pidd 1998). ES is at the lowest level of simulation programming (modeling elements in AS and PI based models will eventually be translated in to events and get simula ted, but this process is hided from the user). It has complete flexibility and computation is fast The problem with this strategy is that, it is very difficult to ensure that all possible consequences are accounted for

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212 within the developed event routine, especially fo r complicated systems. Therefore, ES is seldom used alone, but often in combination with AS and PI to enhance their flexibility. With AS, the modeler decompose the system to constituting activities and describe the conditions which cause an activity to start. During the simulation, every time the simulation clock advances, the entire set of activities will be scanned. If the conditions for starting an activity are satisfied, the appropriate action is ta ken (Pidd 1998). These actions typically include acquiring the requested resources, determining how long the activity wi ll last, holding the acquired resources for the determined duration (when the activity starts), and release the resources (when the activity ends). Because all activities need to be scanned every time the simulation clock advances, the simulation runs much slower than its ES-oriented counterparts. Three-phase AS is a modified approach that improves ASs computing efficiency. With this strategy, the activities are se parated into Bs (activities that are bound to start at a predictable time), and Cs (activities that are not depende nt on the simulation clock but must wait until predefined conditions can be sa tisfied or until requested reso urces are available). As the simulated time advances, only Cs will be sca nned and tested, while Bs will be immediately executed once the simulation clock reaches the scheduled time. AS is particularly well suited to situations where activities have ve ry complex startup or ending conditions, or where resources with dis tinct properties must collaborate according to highly dynamic rules (Hooper 1986). Most AS-based simulation languages were developed in the 1960s, including GSP, CSL, and HOCUS. The third type of discrete-event simulation st rategy is PI. With this strategy, the modeler needs to identify the enti ties (or transactions in some cases ) that flow through the system and describes the life cycles for each class of them. Typically, the life cycles of the entities involves

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213 entering the system, undergoing some processing where they capture and release scarce resources, and then exit (Martinez and Ioannou 1999). These describe life cycle processes will be translated into a sequence of events by the simu lation executive. During runtime, entities will be created and pushed though the life cycle, trigge ring the events on the path in sequence. This strategy is particularly suited to systems wh ere the moving entities are differentiated by many attributes while the machines or resources that se rve these entities have few attributes, and do not interact too much (Hooper 1986). As most manufacturing and service systems are of this type, a lot of commercial simulation systems are based on PI, including GPSS, SIMAN, SLAM, ModSim, etc. Graphical Modeling Representation. The simulation strategies provide a guide on how to abstract a real-world system into a conceptual model. The conceptual model can be represented, to some extent, by graphical diagrams, which can then be translated to simu lation languages that the computer can recognize. A major graphical modeling tool used for disc rete-event simulation is the activity cycle diagram (ACD). ACDs evolved from wheel char ts which was developed for the GSP simulation language(Tocher 1964), and was later popularized by Hill in his HOCUS simulation system (Hill 1971). An activity cycle diagram is a map that s hows the life cycle of each class of flowing entities and displays graphically their interactio ns. There are only two types of symbols in the original activity cycle diagram: circles called queues that representing the dead state of the entities, and squares called activities that repr esenting the active state. The path of a moving entity usually consists of altern ating circles and rectangles conn ected together with links. Paths of different types of entities cross where collabo rations take place. A common approach to draw an activity cycle diagram is to dr aw the activity cycles of each type of entities first and then

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214 combine those cycles into one network by join ing the activities that they have in common (Senior and Halpin 1998). ACDs are a natural means for representing AS or three-phase simulation models, and have been proved usable for ES and PI models (Mathewson 1974). They are often used as the blueprint at the conceptual level too much detail will obscure the diagram. As commented by Pidd (1998), though activity cycle diagrams are seldom able to include the full complexity of the system being simulated, they do provide a clear skel eton that can be enriched and enhanced later. Simulation Languages A simulation model can be built with ge neral-purpose languag es, special-purpose simulation languages or simulators (Kelton et al. 2004). Simulation w ith general-purpose languages like FORTURN, PASCAL and C++ is very customizable and flexible, but timeconsuming and error prone, even with the help of support packages and pre-written libraries. Special purpose simulation langua ges like GPSS, Simscript, SLAM and SIMAN, provide a much better framework that meet the needs of most types of simulations. Nevertheless, users still need to invest considerable time to learn their synt ax and how to use them effectively. By contrast, high-level simulators are very easy to use. They provide graphical interfaces, menus and dialogue boxes so users can construct a mode l without any programming. However, high-level simulators usually are limited to a certain appl ication domain or even a certain kind of problem. As a rule, as ease-of-use increases, flexibility compromises.

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215 Figure A-1. A dependent variable in a discrete simulation model Figure A-2. A state variable in a continuous simulation model Figure A-3. Approximation of a stat e variable in a continuous si mulation model using fixed time steps Time State Variable Time State Variable EventTimes State Variable Time

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216 Figure A-4. Relationships among events, activities a nd processes. [Adapted after Prisker, A. A. B., and O'Reiley, J. J. (1999). Simulation with Visual SLAM and AweSim, John Wiley & Sons, Inc, New York. (Page 395, Figure 12-2)] Process Event StartEvent EndEvent Activity

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217 Name Duration Name Variable 1 Variable 2 APPENDIX B MODELING ELEMENTS IN THE PROPOSED METHOD Symbol Name Notes Examples Discrete Activity Figure 6-2 Continuous Activity Figure 6-3 to 6-6 Compound Discrete Activity Figure 6-32 to 6-35 Compound Continuous Activity Figure 6-36, 6-37 Repetitive Discrete Activity n: number of repetitive units Figure 6-38 to 6-43 Repetitive Continuous Activity n: number of repetitive segments Figure 7-8 Environmental Factor Figure 6-7 Resource Figure 6-41 to 6-43 Start/Finish Link Figure 6-8 to 6-13 Name Productivity Type Total Quantity Lag (Progress) + N ame + N ame n Name n Name

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218 Q uantit y *P *P' Symbol Name Notes Examples Resume Link Figure 6-13, 6-17 Adjust Link ai: adjustment factor Figure 6-18 to 6-20 Buffer Link Figure 6-23 to 6-26 Resource Link *p: priority of alternative resources *p: priority of activities for shared resources Figure 6-31, 6-41 OR Node Figure 6-28, 6-29 Branching Node Figure 6-30 Doubling the link line Repetitive Link Figure 6-45 to 6-46I Unit Identification Variable Figure 6-41 to 6-46 prob (criterion) prob(criterion) Lag (Progress) (Progress) ai Buffer Size

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219 LIST OF REFERENCES AbouRizk, S. M., and Hajjar, D. (1998). "A fram ework for applying simulation in construction." Canadian Journal of Civil Engineering, 25(3), 604-617. Ammar, M. A., and Elbeltagi, E. (2001). "A lgorithm for determin ing controlling path considering resource continuity." Journal of Computing in Civil Engineering, 15(4). Ang, A. H., Abdelnoor, J., and Chaker, A. A. (1975). "Analysis of ac tivity networks under uncertainty." ASCE Journal of the engi neering Mechanics Division, 101(4), 373-386. Ashley, D. B. (1980). "Simulation of repetitive-unit Construction." Journal of Construction Division, 106(2), 185-194. Banks, J., Carson, J. S., Nelson, L. N., and Nico l, D. M. (2000). Discrete-Event System Simulation, Prentice Hall. Carr, R. I. (1979). "Simulation of construction project duration." Journal of Construction Division, ASCE, 105(CO2), 117-128. Carr, R. I., and Meyer, W. L. (1974). "Plann ing construction of repetitive building units." Journal of Construction Division, ASCE, 100(3), 403-412. Ceric, V. "Hierarchical abilities of diagrammatic representations of di screte event simulation models." Proc. of the 1994 Winter Simulation Conference, 589-584. Chang, D. Y. (1986). "RESCUE: A Resource Base d Simulation System for Construction Process Planning," Ph.D. Dissertation, Univer sity of Michigan, Ann Arbor, MI. Cheng, B. (2005). "Limitations of Existing Sc heduling Tools in Planning Utility Line Construction Projects," Universi ty of Florida, Gainesville. Chrzanowski, E. N., and Johnston, D. W. (1986). "Application of linear scheduling." Journal of Construction Engineering and Management, 112(4), 476-491. Clough, R. H., and Sears, G. A. (1979). Construc tion Project Management, John Wiley and Sons, Inc., New York, N.Y. David, E. D. "Pert and simulation." Proceedings of the 10th conference on Winter simulation, Miami, FL. El-Rayes, K., and Moselhi, O. (2001). "Optim izing resource utiliz ation for repetitive construction projects." Journal of Construction Engineering and Management, 117(3), 1827.

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220 El-sayegh, S. M. (1998). "Linear Constructi on Planning Model (LCPM): A New Model for Planning and Scheduling Linear Construction Projects," Texas A & M, College Station, Texas. Fan, S. L., and Tserng, H. P. (2006). "Object-oriente d scheduling for repetitive projects with soft logic." Journal of Construction Engineering and Management, 132(1), 35-58. Fan, S. L., Tserng, H. P., and Wang, M. T. ( 2003). "Development of an object-oriented scheduling model for c onstruction projects." Automation in Construction, 12(3), 283-302. Fischer, M. A., and Aalami, F. (1996). "Sche duling with computer-interpretable construction method models." Journal of Construction E ngineering and Management-Asce, 122(4), 337-347. Flood, I., Issa, R., and Liu, W. (2006)."Rethinking the critical path method for construction project planning." CIB W107 Construction in Developing Economies International Symposium, Santiago, Chile. Gantt, H. L. (1910). "Work, Wages and Profit." The Engineering Magazine, NY. Goldhaber, S., Jha, C. K., and Macebo, M. C. (1977). Construction Management, John Wiley and Sons, Inc., New York, N.Y. Gorman, J. E. (1972). "How to get visual impact on planning diagrams." Roads and Streets, Vol. 115(No. 8), 74-75. Gould, F. E. (2005). Managing the Construction Process, Pearson Pretice Hall, Upper Saddle River, New Jersey. Handa, V. K., and Barcia, R. M. (1986). "Linea r scheduling using optimal control theory." Journal of Construction Engineering and Management, 112(3), 387-393. Harmelink, D. J., and Rowings, J. E. (1998). "Development of contro lling activity path." Journal of Construction Engineering and Management, ASCE, 124(4), 263-268. Harris, R. B., and Ioannou, P. G. (1998). "Sch eduling projects with repeating ac tivities." Journal of Construction Engineering and Management, ASCE, 124(4), 269-278. Hill, P. R. (1971). HOCUS, P.E. Group, Egham, Surrey. Hinze, J. W. (2008). Construction Planning and Scheduling, Pearson Pretice Hall, Upper Saddle River, New Jersey. Hooper, J. W. (1986). "Strategy related character istics of discrte-even t languages and models." Simulation, 46(4), 153-159.

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BIOGRAPHICAL SKETCH Wen Liu earned her bachelors and masters de grees in construction pr oject management at the Tianjin University in China. She attende d the M. E. Rinker, Sr. School of Building Construction at the University of Florida to obtain her Doctor of Philosophy in the field of building construction, which will be awarded in May 2008. She also holds a master degree in decision and information sciences from the Wa rrington College of Business Administration at the University of Florida.