Citation
An Integrated Infrastructure Engineering Decision-Making Procedure: A Finance-Based Fuzzy Time-Cost-Quality Trade-Off Optimization Model over the Project Life Cycle

Material Information

Title:
An Integrated Infrastructure Engineering Decision-Making Procedure: A Finance-Based Fuzzy Time-Cost-Quality Trade-Off Optimization Model over the Project Life Cycle
Creator:
Zheng, Xi
Publisher:
University of Florida
Publication Date:
Language:
English

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Civil Engineering
Civil and Coastal Engineering
Committee Chair:
ELLIS,RALPH D,JR
Committee Co-Chair:
GLAGOLA,CHARLES ROBERT
Committee Members:
PREVATT,DAVID
ROMANO,RICHARD E

Subjects

Subjects / Keywords:
decision-making
infrastructure
madm
mcdm
modm
optimization
prioritization

Notes

General Note:
This research centers upon the study of methodology in decision making of infrastructure engineering development and management. It further proposes comprehensive finance-based time-cost-quality trade-off optimization models to help infrastructure engineering decision makers enhance their integrated decision-making procedures. After a literature review on the theory and methods of multi-criteria decision making (MCDM), two types of applications are discussed: (1) multi-attribute decision-making (MADM) optimization, and (2) multi-objective decision-making (MODM) optimization. The MADM method is proposed to be applied in the prioritization process of highway projects by constructing an index system through analysis of economic attributes, technological attributes, and environmental attributes of potential projects. The MODM method is proposed to be applied in the optimization of multiple objectives trade-off for a selected project through identification and modification of relationships among multiple objectives and through advanced optimization techniques. The former is then applied in Case Study I which aims to prioritize the Strategic Intermodal System highway projects in Florida Department of Transportation District 2, and the latter is then applied in Case Study II which provides the project sponsor with a finance-based multi-objective trade-off optimization model. An integration of analytic hierarchy process, entropy weight, and technique for order of preference by similarity to ideal solution is modeled to solve the MADM problem, while the genetic algorithm is suggested to solve the proposed MODM model. In addition, some critical success factors and key performance indicators for successful projects and successful project management are identified and incorporated in the proposed models with consideration of financial constraints over the project life cycle. Uncertainties and imprecisions that have often been encountered in the infrastructure engineering decision-making practice are modeled through the application of fuzzy sets theory. The two case studies have testified the effectiveness and the efficiency of the proposed models. Generally, this dissertation research provides infrastructure engineering decision makers (e.g., project sponsors and project managers) with a look into the existing methods and their applications to MCDM problems.

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Source Institution:
UFRGP
Rights Management:
All applicable rights reserved by the source institution and holding location.
Embargo Date:
8/31/2018

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AN INTEGRATED INFRASTRUCTURE ENGINEERING DECISION MAKING PROCEDURE: A FINANCE BASED FUZZY TIME COST QUALITY TRADE OFF OPTIMIZATION MODEL OVER THE PROJECT LIFE CYCLE By XI ZHENG A DISSERTATION PRESENTED TO THE GRADUATE SCHO OL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 201 6

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201 6 Xi Zheng

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To m y f amily

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4 ACKNOWLEDGMENTS I w ould like to gratefully and sincerely thank my supervisory committee members, Dr. Ralph Ellis, Dr. Charles Glagola, Dr. David Prevatt, and Dr. Richard Romano, for their guidance and valuable advice throughout the course of this research. Dr. Glagola was a lways there, smiling, ready for listening to my plan research work or life, and for offering me most valuable advice It was also fun to work with Dr. Glagola on a FDOT sponsored in place soil testing project. His wisdom inspired and motivated me. I wo uld have still been wasting much time a good dissertation is a done dissertation. His suggestions on research methods and processes also enlightened me a lot game theory class that encouraged me to go further into the decision making sciences. His instructions had substantial influence on my research. Dr. advice on my studies and research was always most illuminating. My deepest gratitud e go es to Dr. Ralph Ellis, my committee chair, for mentoring and putting faith in me. I cannot express my thanks adequately for his continuous support over the past f ive years. I have been amazingly fortunate to have Dr. Ellis as my advisor who g ave me the freedom to explore on my own, and whose mentorship was paramount in providing valuable guidance feedback, encouragement and experience consistent with my long term career goals. Additionally, I would like to thank Dr. Duzgun Agdas and Dr. Do n Lewis for many discussions on related topics that helped me improve my knowledge and thinking in the area. I am very thankful to my Ph.D. fellows and friends Carlos, Eileen, Jae, Kevin, Kyle, Sevcan, and Sungjin : w ithout them the whole Ph.D. life would be dull and would lack so much fun I appreciate their friendship and wish we could spend more time hanging out together. Last ly sincere thanks go to my parents, my wife, and my pretty little o ne. I love you all

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ ............... 4 LIST OF TABLES ................................ ................................ ................................ ........................... 9 LIST OF FIGURES ................................ ................................ ................................ ....................... 12 LIST OF ABBREVIATIONS ................................ ................................ ................................ ........ 14 ABSTRACT ................................ ................................ ................................ ................................ ... 16 C HAPTER 1 INTRODUCTION ................................ ................................ ................................ .................. 18 Background ................................ ................................ ................................ ............................. 18 Pr oblem Statement ................................ ................................ ................................ .................. 21 Research Questions ................................ ................................ ................................ ................. 23 Research Objectives ................................ ................................ ................................ ................ 23 Cha pter Organization ................................ ................................ ................................ .............. 24 2 BACKGROUND AND RELATED WORK ................................ ................................ .......... 26 Scope of Research on Infrastructure Engineering Projects ................................ .................... 26 The Status of Infrastructure in the United States and in Florida ................................ ............ 27 U.S. Highway System Movement ................................ ................................ .......................... 29 Overview of Project Management ................................ ................................ .......................... 29 Critical Success Factors and Key Performance Indicators ................................ ..................... 31 Time Cost Quality Tr ade off Optimization ................................ ................................ ........... 35 Measurement of Subjective Factors ................................ ................................ ........................ 40 A Possible Fourth Dimension: Sustainability ................................ ................................ ......... 41 Finance based Scheduling ................................ ................................ ................................ ...... 43 Development of a Finance Based Model ................................ ................................ ............... 45 Summary ................................ ................................ ................................ ................................ 48 3 METHODOLOGY ................................ ................................ ................................ ................. 54 Decision Making Process ................................ ................................ ................................ ....... 54 Research Framework ................................ ................................ ................................ .............. 54 Identification of CSFs and KPIs for Project Management ................................ ..................... 56 Research Methodology ................................ ................................ ................................ ........... 57 Summary ................................ ................................ ................................ ................................ 59 4 THEORY ON MULTI CRITERIA DECISION MAKING ................................ .................. 63 Single Objective Optimization Model ................................ ................................ .................... 63

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6 General Multi Criteria Optimization Model ................................ ................................ ........... 64 Multi Objective Decision Making Optimization ................................ ................................ ... 66 Gene ral Form ................................ ................................ ................................ ................... 66 The Weighted Sum Method ................................ ................................ ............................. 67 Multi Attribute Decision Making Optimization ................................ ................................ ..... 70 General Form ................................ ................................ ................................ ................... 70 Quantification and Conversion of Criteria ................................ ................................ ...... 72 Determination of Criteria Weights ................................ ................................ .................. 73 Analytical Hierarchy Process ................................ ................................ .......................... 74 Entropy Weight ................................ ................................ ................................ ............... 78 Application of Fuzzy Sets The ory ................................ ................................ .......................... 79 Fuzzy Sets ................................ ................................ ................................ ........................ 80 Triangular Fuzzy Number ................................ ................................ ............................... 81 Operations of Trian gular Fuzzy Numbers ................................ ................................ ....... 83 Measuring Fuzziness ................................ ................................ ................................ ....... 84 Fuzzy Modeling ................................ ................................ ................................ ............... 86 Fuz zy AHP ................................ ................................ ................................ ...................... 87 Fuzzy TOPSIS ................................ ................................ ................................ ................. 89 Summary ................................ ................................ ................................ ................................ 92 5 APPLICATION OF MULTI ATTRIBU TE DECISION MAKING OPTIMIZATION: PRIORITIZATION OF HIGHWAY PROJECTS IN FLORIDA ................................ .......... 99 The Needs for Project Prioritization ................................ ................................ ....................... 99 Economic Attribute Analysis ................................ ................................ ................................ 100 Project Life Cycle Costs ................................ ................................ ................................ 101 Project Economic Benefits ................................ ................................ ............................ 102 Economic Analysis ................................ ................................ ................................ ........ 104 Technological Attribute Analysis ................................ ................................ ......................... 105 Change in Network Connectivity ................................ ................................ .................. 105 Change in Accessibility ................................ ................................ ................................ 106 Environmental Attribute Analysis ................................ ................................ ........................ 106 Safety ................................ ................................ ................................ ................................ .... 109 Development of an Index System for Highway Engineering Projects Priority Ranking ..... 109 Principles ................................ ................................ ................................ ....................... 109 Construct of a Comprehensive Index System ................................ ............................... 110 Summary ................................ ................................ ................................ ............................... 116 6 APPLICATION OF MULTI OBJECTIVE DECISION MAKING O PTIMIZATION: PROJECT TIME COST QUALITY TRADE OFF ANALYSIS ................................ ........ 123 Basic Assumptions and Notations ................................ ................................ ........................ 123 Basic Problem Statement ................................ ................................ ................................ ...... 124 Further Development of Models ................................ ................................ ........................... 125 Revision to the Cost Time Linear Relationship ................................ ............................ 125 Revision to the Quality Time Linear Relationship ................................ ....................... 126 Application of Time Value of Money ................................ ................................ ........... 127

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7 Introducing Multiple Attr ibute Utility Functions ................................ .......................... 129 Project Time Cost Quality Optimization ................................ ................................ ............. 130 Summary ................................ ................................ ................................ ............................... 132 7 CASE STUDY I: SIS HIGHWAY PROJECTS PRI ORITIZATION IN FDOT DISTRICT 2 ................................ ................................ ................................ ......................... 133 Case Description ................................ ................................ ................................ ................... 133 Data Sources ................................ ................................ ................................ ......................... 134 Brief Description of Selected Projects ................................ ................................ .................. 136 Demand Analysis: Trip Generation ................................ ................................ ...................... 136 Regional Travel Demand Model: Descriptive Statistics ................................ ............... 136 Discussion of the Empirical Model Results ................................ ................................ .. 139 Predictive Asse ssments ................................ ................................ ................................ 141 Discussion ................................ ................................ ................................ ...................... 142 Determination of Criteria Weights ................................ ................................ ....................... 142 Pr ioritization Based on TOPSIS ................................ ................................ ........................... 143 Summary ................................ ................................ ................................ ............................... 144 8 CASE STUDY II: MULTI OBJECTIVE OPTIMIZATION FOR PROJECT DEVELOPMENT ................................ ................................ ................................ ................. 163 Case Description and Inputs ................................ ................................ ................................ 163 Baseline Calculation ................................ ................................ ................................ ............. 163 Optimization Assumpti ons ................................ ................................ ................................ ... 163 Optimization Results ................................ ................................ ................................ ............ 164 Construction Financing and Project Development Budget ................................ .................. 164 Summary ................................ ................................ ................................ ............................... 165 9 CONCLUSIONS ................................ ................................ ................................ .................. 172 Concluding Remarks ................................ ................................ ................................ ............ 172 Suggestions ................................ ................................ ................................ ........................... 174 A PPENDIX A TRAVEL DEMAND DATA ANALYSIS ................................ ................................ ........... 177 Descriptive Statistics Details ................................ ................................ ................................ 177 District 2 Frequency Tables ................................ ................................ ........................... 177 Regression Model Details ................................ ................................ ................................ ..... 184 Model 1 ................................ ................................ ................................ .......................... 184 Model 2 ................................ ................................ ................................ .......................... 185 Model 3 ................................ ................................ ................................ .......................... 186 Model 4 ................................ ................................ ................................ .......................... 187 Model Validation Details ................................ ................................ .............................. 188 B PROJECT DATA FOR CASE STUDY I ................................ ................................ ............. 190

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8 Project # 208001 1 ................................ ................................ ................................ ................ 190 Project Summary ................................ ................................ ................................ ........... 190 Project Map ................................ ................................ ................................ ................... 190 Crash Data ................................ ................................ ................................ ..................... 191 Environmental Impact ................................ ................................ ................................ ... 191 Other Information ................................ ................................ ................................ .......... 192 Project # 209301 3 ................................ ................................ ................................ ................ 193 Project Summary ................................ ................................ ................................ ........... 193 Project Map ................................ ................................ ................................ ................... 194 Crash Data ................................ ................................ ................................ ..................... 194 Other Information ................................ ................................ ................................ .......... 195 Project # 209537 4 ................................ ................................ ................................ ................ 196 Project Summary ................................ ................................ ................................ ........... 196 Project Map ................................ ................................ ................................ ................... 196 Crash Data ................................ ................................ ................................ ..................... 197 Environmental Impact ................................ ................................ ................................ ... 197 Project # 209658 4 ................................ ................................ ................................ ................ 198 Project Summary ................................ ................................ ................................ ........... 198 Project Map ................................ ................................ ................................ ................... 198 Crash Data ................................ ................................ ................................ ..................... 199 Project # 209659 3 ................................ ................................ ................................ ................ 200 Project Summary ................................ ................................ ................................ ........... 200 Project Map ................................ ................................ ................................ ................... 201 Crash Data ................................ ................................ ................................ ..................... 201 Project # 210711 2 ................................ ................................ ................................ ................ 202 Project Summary ................................ ................................ ................................ ........... 202 Project Map ................................ ................................ ................................ ................... 202 Crash Data ................................ ................................ ................................ ..................... 203 Project # 213323 1 ................................ ................................ ................................ ................ 204 Project Summary ................................ ................................ ................................ ........... 204 Project Map ................................ ................................ ................................ ................... 204 Crash Data ................................ ................................ ................................ ..................... 205 Project # 213345 7 ................................ ................................ ................................ ................ 206 Project Summary ................................ ................................ ................................ ........... 206 Project Map ................................ ................................ ................................ ................... 207 Crash Data ................................ ................................ ................................ ..................... 208 Environmental Impact ................................ ................................ ................................ ... 208 Project # 428865 1 ................................ ................................ ................................ ................ 209 Project Summary ................................ ................................ ................................ ........... 209 Project Map ................................ ................................ ................................ ................... 209 Crash Data ................................ ................................ ................................ ..................... 210 Environmental Impact ................................ ................................ ................................ ... 210 LIST OF REFERENCES ................................ ................................ ................................ ............. 211 BIOGRAPHICAL SKETCH ................................ ................................ ................................ ....... 221

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9 LIST OF TABLES Table page 2 1 ................................ ................ 49 2 2 U.S. Highway System Development Phases ................................ ................................ ...... 49 2 3 Definition of Project Management ................................ ................................ ..................... 50 2 4 Distinctions Among Some Concepts ................................ ................................ ................. 51 2 5 PMI Knowledge Areas of Project Management ................................ ................................ 51 2 6 Literature on TCT or TCQT Trade off Analyses ................................ .............................. 52 4 1 Benefit Cost Analysis Worksh eet ................................ ................................ ...................... 93 4 2 Summary of Widely Used BCA Tools ................................ ................................ .............. 93 4 3 Pairwise Comparisons ................................ ................................ ................................ ........ 95 4 4 RCI values for different values of n ................................ ................................ ................... 95 4 5 Aggregation of Ranking ................................ ................................ ................................ ..... 95 4 6 Triangular Fuzzy Numbers for Pairwise Compar ison ................................ ....................... 95 4 7 Application of Fuzzy Methods ................................ ................................ ........................... 96 5 1 Importance of Transportation Infrastructure ................................ ................................ .... 117 5 2 Components of Benefit Cost Analysis ................................ ................................ ............. 117 5 3 Benefits and Costs Associated with Transportation Projects ................................ .......... 117 5 4 Key Highway Financials in the United States ................................ ................................ 117 5 5 DelDOT Project Prioritization Process ................................ ................................ ............ 118 5 6 NCDOT Project Prio ritization Process ................................ ................................ ............ 119 7 1 NCDOT Project Prioritization Criteria ................................ ................................ ............ 145 7 2 National Highway and Transportation Data Sources ................................ ....................... 145 7 3 List of New Variables for Travel Demand Analysis ................................ ....................... 146 7 4 List of Interaction Variables ................................ ................................ ............................ 146

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10 7 5 District 2 Model ................................ ................................ ................................ ............... 146 7 6 District 2 Validation Sample (316 Cases) ................................ ................................ ........ 147 7 7 Values Assigned for Facility Type ................................ ................................ .................. 147 7 8 Values Assigned for Area Type ................................ ................................ ....................... 147 7 9 Values Assigned for Level of Service ................................ ................................ ............. 147 7 10 Values Assigned for Linguistic Terms ................................ ................................ ............ 147 7 11 Pairwise Comparison Assumed ................................ ................................ ....................... 14 8 7 12 Raw Data about P roject Information ................................ ................................ ............... 149 7 13 Numerical Values for Critical Project Information ................................ ......................... 150 7 14 Original AHP Calculation ................................ ................................ ................................ 150 7 15 Fuzzy AHP Calculation I ................................ ................................ ................................ 151 7 16 Fuzzy AHP Calculation II ................................ ................................ ................................ 152 7 17 Fuzzy AHP Calculation III ................................ ................................ .............................. 153 7 18 Normalization of Fuzzy AHP Weights ................................ ................................ ............ 153 7 19 Final Weight from AHP Calculations ................................ ................................ .............. 154 7 20 Data Used for Entropy Weights Calculation ................................ ................................ ... 154 7 21 Entropy Weights Calculation I ................................ ................................ ......................... 155 7 22 Entropy Weights Calculation II ................................ ................................ ....................... 155 7 23 Entropy Weights Calculation III ................................ ................................ ...................... 155 7 24 Entropy Weights Calculation IV ................................ ................................ ...................... 156 7 25 Entropy Weights Calculation V ................................ ................................ ....................... 156 7 26 Determination of Final Weights ................................ ................................ ....................... 156 7 27 TOPSIS Input Data ................................ ................................ ................................ .......... 157 7 28 TOPSIS Normalized Criterion Matrix ................................ ................................ ............. 157 7 29 Weighted Criterion Matrix ................................ ................................ ............................... 158

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11 7 30 Final Ranking from TOPSIS ................................ ................................ ............................ 158 8 1 Example Project ................................ ................................ ................................ ............... 166 8 2 Project Schedule ................................ ................................ ................................ ............... 166 8 3 Project Optimization ................................ ................................ ................................ ........ 167 8 4 Project Development Budget ................................ ................................ ........................... 168 9 1 K nowledge Gap between the Existing Research and the Proposed Research ................. 176

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12 LIST OF FIGURES Figure page 1 1 Change of Project Features with Time ................................ ................................ ............... 25 1 2 Organization of Dissertation Chapters ................................ ................................ ............... 25 2 1 The Iron Triangle ................................ ................................ ................................ ............... 53 3 1 Decision Making Process ................................ ................................ ................................ .. 60 3 2 Positive Feedback in an AEC Firm ................................ ................................ .................... 60 3 3 Research Framework ................................ ................................ ................................ ......... 61 3 4 Guidelines of M eta Analyses ................................ ................................ ............................. 62 4 1 Cover Sheet of California Life Cycle Benefit/Cost Analysis Model ................................ 96 4 2 Cover Sheet of FHWA Tool for Operation s Benefit/Cost ................................ ................. 97 4 3 Cover Sheet of FDOT Benefit Cost Analysis Template ................................ .................... 97 4 4 Example of Order of Scale Values ................................ ................................ ..................... 98 4 5 AHP Hierarchy Structure ................................ ................................ ................................ ... 98 5 1 FDOT Highway Analysis Approach ................................ ................................ ................ 120 5 2 Scoring System Developed by Utah Department of Transportation ............................... 121 5 3 EIA Process ................................ ................................ ................................ ...................... 122 5 4 Sufficiency rating system for roads on Florida State Highway System .......................... 122 6 1 Linear Relationship Between Time and Cost ................................ ................................ .. 132 6 2 Linear Relationship Between Time and Quality ................................ .............................. 132 7 1 An Example of a FDOT SIS Project Listed in the 1 st Five Year Plan ............................ 159 7 2 FDOT Strategic Investment Tool Highway and Connector M easures ............................ 160 7 3 Decision Making process of FDOT for funding SIS investments ................................ ... 161 7 4 Map of FDOT Districts ................................ ................................ ................................ .... 161 7 5 Map of Major Projects Being Planned in District 2 ................................ ......................... 162

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13 8 1 Project Schedule ................................ ................................ ................................ ............... 169 8 2 Construction Costs S Curve Distribution (Cumulative) ................................ .................. 170 8 3 Construction Costs S Curve Distribution (Monthly) ................................ ....................... 170 8 4 Funds Draw Schedule ................................ ................................ ................................ ...... 171

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14 LIST OF ABBREVIATION S AEC Architecture, Engineering, and Construction AHP Analytical Hierarchy Process BCA Benefit Cost Analysis CPM Critical Path Method CSF Critical Success Factor EF Early Finish ES Early Start FF Free Float GA Genetic Algorithm GAO Government Accountability Office IMS Integrated Master Schedule IRR Internal Rate of Return KPI Key Performance Indicator LF L ate Finish LOB Line of Balance LS Late Start MADM Multi Attribute Decision Making MCDA Multi Criteria Decision Analysis MCDM Multi Criteria Decision Making MODM Multi Objective Decision Making NGO Non Government Organization NPV Net Present Value PRISMA Preferred Reporting Items for Systematic reviews and Meta Analyses

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15 SIS Strategic Intermodal System TBL Triple Bottom Line TCQT Time Cost Quality Trade off TCT Time Cost Trade off TF Total Float TOPSIS Technique for Order of Preference by Simil arity to Ideal Solution TTS Travel Time Savings

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16 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy AN INTEGRATED INFR ASTRUCTURE ENGINEERING DECISION MAKING PROCEDURE: A FINANCE BASED FUZZY TIME COST QUALITY TRADE OFF OPTIMIZATION MODEL OVER THE PROJECT LIFE CYCLE By Xi Zheng August 201 6 Chair: Ralph Ellis Major: Civil Engineering This research centers upon the s tudy of methodology in decision making of infrastructure engineering development and management. It further proposes comprehensive finance based time cost quality trade off optimization model s to help infrastructure engineering decision makers enhance th eir integrated decision making procedures. After a literature review on the theory and methods of multi criteria decision making (MCDM) two types of applications are discussed : (1) multi attribute decision making (MADM) optimizat ion and (2) multi objective decision making (MODM) optimization The MADM method is proposed to be applied in the prioritization process of highway projects by constructing an index system through analysis of economic attributes, technologic al attributes, and environmental attributes of potential projects. The MODM method is proposed to be applied in the optimization of multiple objectives trade off for a selected project through identification and modification of relationships among multiple objectives and through advanced optimization techniques. The former is then applied in Case Study I which aims to prioritize the S trategic Intermodal System highway projects in Florida Department of Transportation District 2, and the latter is then applied in Case Study II which provides the project sponsor with a finance based multi objective trade off optimization model.

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17 An integration of analytic hierarchy process, entropy weight, and technique for order of preference by similarity to ideal solut ion is modeled to solve the MADM problem, while the genetic algorithm is suggested to solve the proposed MODM model. In addition, s ome critical success factors and key performance indicators for successful projects and successful project management are id entified and incorporated in the proposed model s with consideration of financial constraints over the project life cycle. Uncertainties and imprecisions that have often been encountered in the infrastructure engineering decision making practice are modeled through the application of fuzzy sets theory. The two c ase studies have testif ied the effectiveness and the efficiency of the proposed model s Generally, t his dissertation res earch provides infrastructure engineering decision makers (e.g., project sponsors and project managers) with a look into the existing methods and their applications to MCDM problems.

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18 CHAPTER 1 INTRODUCTION Background Governments and other infrastructur e administration agencies must make decisions among a great many potential projects, on which project s to fund, when to fund, and how much to fund. This is especially the case in the United States where maintenance and replacement costs of aging infrastru cture facilities are high and where budgets are constrained. This requires the decision maker rational planning and programming to accommodate the needs for budgeting and scheduling the acquisition and development of infrastr ucture engineering projects. Therefore, prioritization of potential projects becomes one of a decision maker Once an infrastructure engineering project is selected and bids published, a rchitecture, engineering, and construction (AEC) fir ms are then faced with decisions about project selection project management, and corporate development. The management and project managers of such organizations (i.e., project owners or sponsors such as government agencies as well as AEC firms) wo nder as to which decision would be best. While project owners must have a comprehensive view on overall project risk and return, m any AEC firms are struggling with promoting their competitiveness by taking successful projects through best project managemen t competitiveness are positively interrelated, while project management practice serves as a been indicated by several studies. For example, Cooke Davies ( 2002 ) discussed the importance of project management and operations management working together to deliver beneficial change from projects, and further depicted the corporate context for project success.

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19 With limited budgets and expedited schedules in the infrastructure engineering industry in these days, planners, engineers, contractors, along with other decision makers, must be equipped with speedy decision making tools and techniques in select ion of optimal solutions to cope with project capital constraints and rapidly changing environment. On the first hand, s election of appropriate projects requires prioritization of potential projects at the very beginning of the planning phase. The prioriti zation and selection process has considerable impacts on project risks and costs over the project life cycle. As indicated in Figure 1 1 PMBOK (Fifth Edition, 2013, pp.40) cost of changes is lowest at the start of the project, when risk and uncertainty a re usually greatest. Specifically, c ost of changes tends to increase fast with the progress of the project although the project uncertainty decreases with time In other words, construction time can be reduced if we spend more time in planning and designi ng, and thus proje ct prioritization and selection are critical to project success. Accordingly, project owners or sponsors usually play a critical role in influencing costs of project construction as the decisions they make at the very beginning of a proje ct cycle will have much greater influence than later. Again, this makes adequate planning and feasibility studies necessary and important. On the other hand, t raditionally, a project is viewed as a successful project if it is delivered on time, within bu conflicts exist among these multiple objectives. This calls for research on time cost quality trade off (TCQT) optimization analysis. Most existing studies are conducted based on some constrai nts with certainties. In real engineering practice, however, the existence of uncertainties spatial variability on the job site, weather conditions, management qualities, material supplies, equipment operation status, and so on. These uncertain factors have extensive impacts on project

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20 time, cost, and quality and thus make project objectives fuzzy. In order to take such risky or uncertain project conditions into account, probability theory and fuzzy sets theory are often applied into TCQT analysis. Besides time, cost, and quality objectives that are commonly considered in the process of project management decision making, other significant objectives, for example, project safety and sustainability (with regard to project environment), have gradually been added to the key control objectives. Correspondingly, with the rapi d development of computing techniques and computer engineering, more critical factors (e.g., construction safety, health, sustainability indicators, etc.) are also suggested to be incorporated in the optimization models. A recent trend in the literature ha s been emphasized that project life cycle performance should also be included in the trade off analysis. Usually, TCQT problems are analyzed at the project level. It should be noted that techniques above the project level are also critical to project succe ss as well as to corporate success. A key to best project management decision making above the project level requires the integration of engineering skills with finance sciences. However, there seems a big gap between the practice of engineering and the un derstanding of finance. In the real world, project owners and AEC firms can make better financial decisions with the understanding of project engineering, and vice versa. In fact, i ntegrating the scheduling and financing functions of construction project m interest (Elazouni 2009). property development, design, construction and facility management, has often been provided by m any of the most successful construction companies. Such an approach helps in a way that multiple project objectives are under control by one single team.

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21 This dissertation aims to improve the infrastructure engineering decision making procedures by develop ing practical finance based model s for an extensive TCQT optimization over the whole project life cycle. A framework, which integrates the positive feedback from is also de veloped. Building on existing asset management strategies, t h is research provides a methodology to help infrastructure development stakeholders make suitable and sustainable decisions to support project life cycle economic activity, and is intended to offe r tools to help the project financing and prioritization processes. Problem Statement In the real world where resources are limited, decisions have to be made on whether a project proposal should be accepted and then whether the project should be executed within a specific timeline. The goal of the project selection process is to approve or reject project proposals by analyzing project feasibility and prioritizing a group of potential projects based on established criteria that usually include time, cost, a nd quality requirements. Therefore, the selection process serves as the starting point of project planning. This is important, as i nitiation of a project without proper planning by a state highway agency (SHA) has been identified as one of the root cause s of time delays in highway construction projects (Thomas and Ellis, 2001). During project execution, o continuous attention since the creation of Critical Path Method (CPM) in the 1950s. Concer ned with the optimal allocation of scarce resources to activities over time (Karger et al., 1997), the practice of scheduling theory makes it necessary for research on multi objective trade off analysis during the project life cycle. Although meeting proje ct time ( or duration), cost ( or budget), and quality ( or scope) requirements are most frequently referred to as the basic objectives of a successful project, further identification of main critical success factors (CSFs)

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22 and key performance indicators (KPI s) for project management is of significance for the project team to prioritize the resource constraints and then to have a correct focus (Ebbesen and Hope, 2013). The knowledge of CSFs and KPIs provides us with opportunities to add other important dimensi ons to the existing time cost quality trade off optimization analysis. Further, the project financial constraints are suggested to be included in the trade off analysis over the project life cycle. Considering uncertainties in different proje ct phases, fuzzy sets theory can be applied to help with the project management decision making process. The above mentioned efforts are made so that the simulation model can be closer to real engineering practice. Further, a dvanced modeling and algorithms are needed to solve such multi objective optimization problems as time cost quality trade off simulation. These include heuristics methods, linear regression, non linear programming, neutral network, genetic algorithms, etc. Among them, genetic algorithms (including improved genetic algorithms) have been widely used in recent years and seem to have advantages in identifying optimal or near optimal solutions to optimization and decision making problems with large search spaces based on linear or non linear programming. Another motivation of this research, introducing project life cycle assessment to the multi objective trade off analysis, requires two step work: firstly, identifying sustainability indicators, and secondly, integrating sustainability indicato rs into the existing trade off models. Social and environmental impacts on the project life cycle should be quantified and codified in some specific way so that they can be simulated in the model. The final motivation of this dissertation is to develop a framework for facilitation, through best project life cycle management of the proposed finance based fuzzy TCQT

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23 optimization model, of the positive feedback between project practice and corporate competitiveness. Application of this framework will enhance a whole. Research Questions This dissertation present s at least partially, solutions to the following questions: In general, w hat is the decision making process for infrastructure engineering development and how does it work ? (Chapter 3) What is the general form of a decision making problem? (Chapter 4) How do infrastructure engineering project sponsors target and select a specific project? For example, how should DOTs prioritize highway engineering projects? (Chapter 5 a nd Chapter 7) What strategies and techniques do DOTs adopt for project prioritization? (Chapter 5) What are critical factors and/or key performance indicators for a successful infrastructure engineering project and for successful project management? (Chapt er 2 and Chapter 3) What is the general form of a time cost quality trade off optimization problem? (Chapter 3 and Chapter 6) How can we optimize the project plan in terms of the trade off among project time, cost, and quality (so that a project can be del ivered on time, within budget, and with acceptable quality, and can create maximum benefits and utilities for stakeholders)? ( Chapter 2 and Chapter 6) How can we integrate financial constraints into the proposed model over the project life cycle? (Chapter 6 and Chapter 8) Research Objectives Based on the above research questions, the objecti ve of this research is to improve, through multi attribute project optimization, multi objective trade off optimization and best project management practice, the decision making process of and the connection between infrastructure engineering project succ ess and the competitiveness. The definitions of project management from different institutes and organizations are compared and

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24 summarized so that we can understand those factors or indicators that need to be focused on. Meta analyses is suggested to be conducted to filter out, among tens of possible factors, the critical success factors (CSFs) and the key performance indicators (KPIs) for project success, ding to the CSFs and the KPIs, potential infrastructure projects are first prioritized based on critical criteria that are selected. Then the project time cost quality trade off problem is analyzed in a wider and more general view of project life cycle as well as of project sponsor Considering the many uncertainties during the project life cycle, fuzzy sets theory is applied to help with the project management decision making process. Chapter Organization The chapters of the dissert ation are organized as shown in Figure 1 2. Chapter 2 provides an overview of the research background and findings from literature reviews. Chapter 3 explains the research methodology. Chapter 4 summarizes the theory on multi criteria decision making (MCDM ). Chapters 5 and 6 detail the MCDM methods by discussing applications of multi attribute decision making (MADM) optimization and multi objective decision making (MODM) optimization, respectively. Accordingly, Chapters 7 and 8 provide two case studies base d on the proposed MADM and MODM techniques, respectively. Finally, Chapter 9 discusses and summarizes the research findings and offers suggestions.

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25 Figure 1 1. Change of Project Features with Time Source: PMBOK (Fifth Edition, 2013, pp.40) Figure 1 2. Organization of Dissertation Chapters

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26 CHAPTER 2 BACKGROUND AND RELAT ED WORK Scope of Research on Infrastructure Engineering Projects resou rces pulled together to create something that did not previously exist and that will provide a With the increase in scale of engineering projects and in complexity of enginee ring design, it has become more and more difficult to meet pre defined objectives of engineering and construction projects. This makes it necessary to introduce optimization theories and techniques for project control. Research has indicated a variety of c ritical success factors. Among those factors, however, project time, cost, and quality are still the most widely recognized objectives to control. Other significant objectives, for example, project safety and sustainability (with regard to project environm ent), have gradually been added to the key control objectives. Meeting those objectives require: (1) properly selecting and planning potential projects in the very beginning, and (2) reasonably managing and controlling the project execution and operation. Accordingly, t h is dissertation research focuses on : (1) how to prioritize potential infrastructure projects, and (2) how to optimize the real world multi objectives of project time, cost, and quality over the whole project life cycle when dealing with the engineering and management of such infrastructure systems as highways, bridges, railways, water and sewage systems, energy facilities, and other civil engineering structures. These unique, large scale, and usually multimillion dollar involved infrastructu re engineering projects have increased in claims of economic, social, environmental, and technological leadership as infrastructure failures, ineffectiveness, and t he inability to properly plan, construct, manage, and maintain

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27 physical infrastructure. Therefore, the need has been extensively increased for properly managing the infrastructure engineering project over the whole project life cycle. In Chapters 5~8 high way engineering projects will be specifically chosen as the main reference for this dissertation research analysis. The frameworks and methodologies, however, may also be applied to the management of other infrastructure engineering projects. The Status o f Infrastructure in the United States and in Florida The United States has been leading the infrastructure development in the world for a long time since the end of World War II. The current status of infrastructure in the United States, however, brings mo Report Card for the major U.S. infrastructure and the cumulative grade was only D+ indicating a poor con dition with some risks The Report Card is updated every four years and its categories, assessment criteria, and grading scales are listed in Table 2 1 The highway and roadway systems in the U.S. are even under a slightly worse condition, with a grade of only D for roads and the improvement will require investment of $3.6 trillion by 2020 according to the estimation by Federal Highway Administration In a report to the White House, the National Economic Council and the infrastructure is not keeping pace with demands or the needs of our growing economy, for today appropri at e project prioritization system, as selecting appropriate projects at appropriate times is one of the keys to achieve goals of projects regarding time, cost, quality, and other important project objectives. The highway system faces the same challenge i n Florida. I n the 2012 Report Card for while its

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28 highways got a n above average grade of C. The funding or revenue sources have been considered one of the critical issues in both cases. This requires that decision makers select possible future infrastructure projects very carefully in the planning phase of project management. Researchers believe that the State of Florida is facing a transportation crisis. According to the est imation by Florida Transportation Commission (2014), an additional $136.3 billion is required in order to meet the mobility needs on the Strategic Intermodal System (SIS) 1 through 2040. In addition, in the 21 st Annual Report on the Performance of State Hig hway Systems (1984 2012) Hartgen et al. (2014) used spending and performance data from state highway agencies to track and rate the performance of the 50 state owned highway systems based on the following categories: expenditures, pavement conditions, bri dge conditions, congestion, fatality, and narrow rural arterial lanes. In 2012, the highway performance ranking for Florida was only and 33 in 2011; major issues that existed in the Florida highway system included disbursements (ranking 48th), capital and bridge disbursements (ranking 49th), maintenance disbursements (ranking 45th), admin disbursements (ranking 36th), and urban Interstate/freeway congestion (ranki ng 50th). Obviously, investments in infrastructure and the performance of the infrastructure systems are interactive. Both are also affected by economic activities such as the movement of people and goods. Part of this dissertation research concentrates sp ecifically on planning and optimization of highway engineering in the United States. 1 facilities and services, with all mode s of transportation, and with integrated transportation network. It focuses limited state resources on critical transportation facilities.

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29 U S Highway System Movement Take the U.S. highway system for example. With decades of highway construction the United States may ha ve established the most robust highway network and systems in the world. Accordingly, the emphasis of U.S. highway agencies has been moved from new construction to maintenance and asset management. Fwa (2006) summarized three phases of U.S. highway d evelopment (Table 2 2 ). The most recent improvement reflects the integration of big traffic data and mobile technologies with construction, maintenance, and management of highways and highway systems. Different from developing countries, who rely heavily o n debt sources (e.g., the World Bank) for financing of highway construction, the United States and most of developed counties have financed their highway systems primarily through both equity investment and bond issuance, in which calculation of financial risk and return has to be made. In addition, multi objective optimization analysis should also be conducted in order to incorporate non monetized elements with financial considerations. Overview of P roject Management Researchers from both the academia and the industry have attempted to define project management. Commonly cited are those published by different societies, associations, and institutes related to project management, as listed in Table 2 3 Some of those definitions have been accepted as national standards. These definitions clearly show that, while a variety of concepts have been made, the criteria for project success and project management success require balancing the objectives of time, cost and quality in general. Some researchers (e.g. Atkinson, 1999) refer to the three constraints as the Iron Triangle (Figure 2 1). Note that project quality and scope are used interchangeably in this research. This is reasonable because project quality is usually defined as

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30 meeting or exceeding the expectations of the customer and thus the customer gets what he or she asked for, i.e. the project scope. Three things are worth pointing out. Firstly, in a narrower view, project management success does not necessarily lead to project success, and sometime s (at least in some cases) a successful project does not indicate excellent project management for sure. Secondly, different people have different views on project success even for the same project. In addition debates on the Iron Triangle exist. Details are discussed as follows. Cooke Davies (2002) pointed out the importance of the distinction between project success and project management success. Further, he discussed and distinguished factors on project management success, on an individual successful p roject, and on consistently successful projects. He summarized the distinction between project success and project management success, the distinction between success criteria and success factors, and the distinction between project success and project per formance. Those distinctions are demonstrated Table 2 4 In order to differentiate views on project success from different people, Lim and Mohamed (1999) proposed to define the following two views of project success. 1. The macro viewpoint: Project end users and the general public usually evaluate the project performance from this viewpoint by asking whether the original project concept has been achieved or not at its operational phase. 2. The micro viewpoints: Project owners, sponsors, engineers, and contractor s define project success mainly from this viewpoint by asking whether their respective project objectives (e.g., project time, cost, and quality) have been achieved or not at the conclusion of the construction phase. Debates on the Iron Triangle do exist. Atkinson (1999) argued that the Iron Triangle (cost, time, and quality), which has been used usually, frequently and for a long time as a set of argument was base

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31 development life thin project management, i.e. Type I errors being the sin of commission (when something is done wrong), while Type II errors being the sin of omission (when something has not been done as well as it could have been or something was missed). So he concluded that using time, cost and quality as the criteria of success is an example of a Type II error and such criteria are not as good as they could be or something is missing. He proposed the Square Route of success criteria instead. Despite of those debates and arguments, it is still general expectation that a successful project should be delivered on time, within budget and meet q uality/scope specifications. However, projects meeting such goals sometimes may not necessarily be perceived as successful projects by key stakeholders (Shenhar and Dvir, 2007; Turner and Bredillet, 2009). Other factors (safety, adaptability, and sustainab ility, for example) have also been considered as indicators of successful projects. In t he PMBOK Guide (Fifth Edition 2013, pp.61 ), Project Management Institute provides a good summary of ten distinct Knowledge A reas of project management (Table 2 5) Critical Success Fa ctors and Key Performance Indicators The PMBOK Guide (Fifth Edition, 2013) suggests measuring project success by the following criteria: Product and project quality Timeliness Budget compliance Degree of customer satisfaction These criteria are consisten t with meeting pre determined objectives on project time, cost, and quality. Environmental issues and construction safety have also been of major concerns

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32 in recent decades. In fact, the development of the concept of project success has been a research foc us because researchers believe the setting of criteria and standards for project success measurements can benefit project managers to complete projects with the most favorable outcomes. The concept of project success, however, has remained ambiguously defi ned in the construction industry. Chan and Chan (2004) defined criteria of project success as the set of principles or standards by which favorable outcomes can be completed within a set specification. They argued that such definitions are dependent on pro ject type, size and sophistication, project participants and experience of owners, etc. and developed a set of key performance indicators (KPIs) for both objective and subjective measurements. Studies on project success factors or key performance indicator s have been conducted with focuses at or above the project level, on a variety of project types, on a specific country, or company/organization size, project size, organizati experience. Jugdev and Mller (2005) presented a shift or evolution of definition of project success from the implementation phase of the project life cycle to an appreciation of success over the project and product life cycle. Chan et al. (2002) developed a framework of success criteria for design/build projects by evaluation through performance measures developed from extensive research literature. Takim and Akintoye (2002) suggested dividing successful construction pro ject performance along procurement, process and result orientations. Regression analysis has been used to verify the relationship between project overall performance and success factors. For example, Lam et al. (2008) developed a project success index for design build projects in terms of time, quality, and functionality. Ling et al. (2008) used cost performance, time performance, quality performance, owner satisfaction, and profit

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33 margin as performance measures to develop models for prediction of project s uccess levels, based on project management practices adopted by foreign AEC firms in China. Researchers also use mathematical tools to categorize a huge number of success factors. Lu et al. (2008) grouped 35 success factors into eight clusters by factor an alysis. Tabish and Jha (2012) used structural equation modeling for measurement of human factors, management actions, success traits, and project success, concluding that human factors and management actions play a key role in making the project a success. Park (2009) identified a set of 10 common factors and 188 individual factors and grouped them into eight major categories as critical success factors for whole life performance assessment of construction projects. Chan et al. (2010) grouped 18 factors nec essary to conduct PPP projects into five categories. Although other factors or indicators have also been suggested, time, cost and quality remain the most considered criteria for measuring construction project success. As early as in 1972, the U.S. Governm ent Accountability Office (GAO, 1972) summarized the basic characteristics of credible cost estimates in their report of Theory and Practice of Cost Estimating for Major Acquisitions Those characteristics, listed as follows, can still be applied to the no wadays practice: Clear identification of task Broad participation in preparing estimates Availability of valid data Standardized structure for the estimate Provision for program uncertainties Recognition of inflation Recognition of excluded costs Independe nt review of estimates Revision of estimates for significant program changes

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34 The U.S. Government Accountability Office ( GAO, 20 12 ) also summarized ten best practices for development of a high quality, reliable schedule that is comprehensive, well construc ted, credible, and controlled. These ten best practices are: Capturing all activities Sequencing all activities Assigning resources to all activities Establishing the duration of all activities Verifying that the schedule can be traced horizontally and ver tically Confirming that the critical path is valid Ensuring reasonable total float Conducting a schedule risk analysis Updating the schedule using actual progress and logic Maintaining a baseline schedule In addition, the Integrated Master Schedule (IMS) is also suggested by GAO for the integration of planning, resource and budget assignment, and the project schedule. The importance of identifying CSFs and KPIs is at least two fold: first, it helps the management team develop effective strategies; and seco nd, incorporation of CSFs and KPIs with project success prediction models improves the project control process Russell et al. (1997) suggested using continuous variables (e.g., owner expenditures, contractor construction efforts hours expended, invoices p aid by contractor, total commitments for material and equipment, cost of owner project commitments and costs of contractor project commitments, and designer project cost) for project cost and schedule predictions. They found that success predictors are dif ferent at different points of project time. Ko and Cheng (2007) further created an Evolutionary Project Success Prediction Model by integrating genetic algorithms, fuzzy logic, and neural networks into the Continuous Assessment of Project Performance softw are developed by Russell et al. (1996).

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35 Time Cost Quality Trade off Optimization PERT (Program Evaluation and Review Technique) and CPM (Critical Path Method) are the most common tools associated with network analysis. They formed the foundation for schedu ling optimization with regard to minimizing project cost within pre determined project duration. Based on CPM, an early study on time cost trade off algorithm was conducted by Siemens (1971), in which he developed a Siemens Approximation Method (SAM). His method provided simple solutions (even suited for hand computation) to time cost trade offs on determining which activities to expedite and by what amount for minimizing the project cost by compressing the activity with the smallest slope (with regard to d irect cost) on the critical path. Another early effort was made by Philips and Dessouki (1977) for project time cost trade off optimization by using the minimal cut concept. Thomas and Ellis (2001) summarized 6 major causes of construction delay: (1) u tili ties (2) d iffering site conditions (3) d elays in environmental planning and permitting issues (4) d esign errors (5) o missions and changes and (6) w eather Stochastic methods are also used in the TCQT analysis. For example, Azaron and Tavakkoli Moghad dam (2007) used an interactive approach to covert a dynamic PERT into a stochastic network of queues and then to construct a continuous time Markov chain in the solution of multi objective time cost trade off problems. By introducing fuzzy numbers for the duration and cost of project tasks, Eshtehardian et al. (2009) proposed an optimization method for finding solutions to time cost trade off problems under uncertain conditions. Zhang and Xing (2010) further incorporated fuzzy numbers for project quality me asurement and provided solutions to fuzzy time cost quality trade off problems by using the particle swarm optimization (PSO) algorithm.

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36 Research has also been conducted where time, cost, and quality are treated as discrete variables. Tareghian and Taheri (2006) developed three binary integer programming models for optimization of one single objective with bounds on the other two objectives at each time. Literature has shown different types of models with regard to project quality. Existing models include t he cost of quality model (Ereiesleben, 2004; Schiffauerova and Thomson, 2006; Naidu, 2008; and Abdelsalam and Gad, 2009), the quality reliability model (Shi et al., 2009), the quality earned value model, and the time quality model (Babu and Nalila, 1996; P ollack Johnson and Mattew, 2006; and Tareghian and Taheri, 2007). Different modules have also been developed in trade off models. For example, Senouci and Al Derham (2008) presented such a model for the scheduling of linear construction projects, which con sists of a scheduling module, a cost module, and a multi objective module. Time cost quality trade off problems have attracted attention in the construction industry for many years. Frequently used as a set of project management success/performance criteri a, time, cost, and quality are almost always listed as controllable objectives by each AEC project team. And thus the three objectives/criteria are sometimes called the Iron Triangle. The mutual dependency and the quantitative trade off (assuming a higher quality index is better) among the three constraints are obvious: project quality and project time or project cost are usually positively correlated (i.e., requests for increasing project quality will increase the amount of time needed and will also cause in increase in project cost), while time and cost are usually negatively correlated (i.e., a tight/crashed time schedule requires more intensive labor and thus will lead to higher cost and usually a lower quality as well). It remains a puzzle, however, as of how to effectively quantify the three objectives in an appropriate model and then how to solve the model. The significance of such research is to maximize the project value (or in a wider extent,

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37 the social welfare) by providing better quality with less time and lower costs. Most of the existing studies, however, were conducted in a deterministic environment, and thus ignored or simplified uncertainties in real construction projects. The fact is that both the variables and objectives in project managemen t decision making are fuzzy due to uncertain underground conditions, non continual supply of equipment, etc. This gives possibilities for applying fuzzy logic into the tradeoff problems. Early attempts can be dated back to late 1950s, when Kelley and Walke r (1959) first developed the critical path method (CPM), an algorithm for scheduling a set of project activities. Until today it is still the most widely used tool for effective project management. Based on CPM, time cost trade off (TCT) analysis, as well as its extensive form, time cost quality trade off (TCQT) optimization, has been conducted in recent years (see Table 2 3 ). The time cost trade off methodology is used to obtain the optimization set of time or cost under the constraint of either a budget ( summarized by Brucker et al. (1999). This can be achieved by crashing those activities with more resources on the critical path, and finally a time cost curve can be constructed over the set of feasible project durations. In traditional studies on multi objective engineering optimizations, deterministic values linear and non linear programmi ng models were developed with certain assumption of time cost relationship (Brucker et al., 1999). Though widely used as forecasting tools, these traditional deterministic methods fail to provide the project team with sufficient information about the proba bility of meeting project goals. Such discrepancy with real engineering practice has long been realized, and thus uncertainty has been gradually introduced into simulation models. For

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38 example, efforts have been made on multi objective optimization under un certain circumstances. Those include: multi mode trade off optimization models; fuzzy logic based multi objective trade off optimization models; stochastic optimization models; etc. With the improvement of computers and computing sciences, advanced intelli gent algorithms have been adopted to solve the TCQT problem, as listed in Table 2 6 The difficulty of adding quality into the trade off analysis is how to quantify project [0,1] domain and then average them to get the project quality. Obviously, this only has a relative or comparative meaning. Babu and Suresh (1996) were among the first researchers who took project quality into consideration along with TCT optimization in a deterministic CPM network. The inter related linear programming models developed by Babu and Suresh were evaluated and applied to an actual cement factory construction project by Khang and Myrint (1999). Hegazy (1999) summarized the advantages and drawback s of different techniques used for TCT analysis, including heuristic methods, mathematical programming models, and genetic algorithms. Peng and Wang (2009) considered renewable resources in the discrete TCT problem and accordingly drew an example of time c ost curve. Table 2 6 listed most cited literatures on time cost quality trade off (TCQT) analyses in the past two decades. Typically, the following steps have been taken in existing studies on TCQT analysis: (1) making assumptions of the relationships amon g activity/project time, cost, and quality; (2) determining the variables; (3) suggesting the theoretical background and framework; (4) developing a TCQT model based on the assumptions and the framework; (5) comparing and selecting the algorithms; and (6) doing (scenario or real) case studies with numerical calculations.

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39 Other related studies provided general forms of multi objective optimization problems that can cover the elementary analysis of TCQT problems. For example, Konak et al. (2006) summarized the multiple objective o ptimization method using genetic algorithms (GAs) from existing studies. The authors compared the components, procedures, applications, advantages and disadvantages of well known (customized) multi objective GAs. Xu et al. (2012) took environment impact in to account for the trade off problem. They developed a fuzzy based adaptive hybrid genetic algorithm for analysis of the discrete trade off among time, cost, and environment. Zheng and Ng (2005) developed a stochastic time cost optimization model by integr ating the fuzzy sets theory and non replaceable front with genetic algorithms as a searching mechanism. proposed for TCQT optimization, and examples of these includ e the heuristic, linear programming, integer programming, and hybrid programming models. Again, one of the key points here is to tailor the assumptions, theories, models, and algorithms to the best need of the underlying question. The proposed dissertation research can provide new customization in the infrastructure engineering field to enrich the body of knowledge in TCQT analysis. In addition, another knowledge gap in existing literature is the missing of incorporation of other key performance indicators. Incorporating other factors, however, will greatly increase the complexity of the trade off analysis. Therefore, effort should be made in the proposed research to cautiously select the incorporated factors and to give them appropriate mathematical express ions. Moreover, the project life cycle performance has attracted more and more attention in the 21st century. For example, Jugdev and Mller (2005) argued that project management is perceived as providing only tactical (operational) value and not strategic value if project success

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40 is limited to the variables of time, cost, and scope. However, the definition of project success has now shifted from the implementation phase of the project life cycle to an appreciation of success over the project and product li fe cycle, so that project management can have strategic value when the links to product/service value exist. Assessing the project life cycle performance requires us to consider the series of project phases from its initiation to its closure. In this case, financial constraints in infrastructure engineering projects put great pressure on the project management team. In other words, financial availability has big impact on the project life cycle performance. In many organizations, however, predicting and ana lyzing the prospective financial performance Measurement of Subjective Factors In the trade off optimization analysis, attributes such as project time and cost are relatively easy to measure. Quantification and measurement of some other attributes, however, remain ambiguously determined. Project quality is an obvious example. Some studies suggested measuring quality subjectively by using a five or seven point scale. A relatively ob jective way, however, could be the measurement of the degree of conformance to all technical performance specifications (Chan et al., 2002) and to customer satisfaction. Similarly, environmental performance of a given project, also quite subjective, could be measured by the environmental impact assessment score through the application of ISO14000, and by the total number of complaints received during the construction. More accurately, fuzzy sets theory can be applied to deal with such uncertainty associated with linguistic imprecision. The proposed research will add to the knowledge base creative ways of quantifying and optimizing those subjective factors or indicators in the trade off analysis.

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4 1 A Possible Fourth Dimension: Sustainability A recent trend for similar trade off analysis is to take project life cycle into account. For example, the newest edition of PMBOK (Fifth Edition, 2013) has included and detailed the contents of the project management life cycle and its related processes, as well as the pro ject life cycle, which is defined as the series of phases that a project passes through from its initiation to its closure. Life cycle assessment is a more appropriate way to tell whether a project is really successful or not. After all, a bridge could not be viewed a successful project if it would collapse in 20 years while its design life were 50 years. Meanwhile, the view of project life cycle (and also, of project management life cycle) echoes the modern concept of sustainable development. However, one of the difficulties of taking sustainability into consideration is to develop a set of criteria with both effectiveness and efficiency. The current strategy usually proposes a rating system and suggests some up to date best practices. To capture the idea o f sustainability in the analysis of time cost quality trade off optimization is based on, to some extent, subjective judgments. The concept of Triple Bottom Line (TBL) has gained worldwide acceptance and will be integrated in the research model. The concep t of TBL was created by Elkington (1998). He argued that environmental, social and economic dimensions of sustainable development should be taken into consideration by corporations, government organizations and non government organizations (NGOs). Related to the ideas of corporate social responsibility, TBL requires that corporations pursue a balance in development among economic prosperity, environment protection, and social welfare. Traditionally, profit (or rather, the economic benefit of shareholders) i s the bottom line of not only by the traditional financial bottom line, but also by its social/ethical and environmental performance.

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42 The empirical study conduct ed by Ebbesen and Hope (2013) indicated disagreement of how to integrate sustainability into time, cost, and quality constraints, and of how to integrate sustainability principles into projects. They suggested sustainable project management as a process to Iron Triangle. Liu and Frangopol (2005) proposed a framework to formulate the life cycle maintenance planning of deteriorating bridges as a multi objective optimization problem. Genetic algorithms (GAs) and Monte Carlo simulation were applied to produce a pool of alternative maintenance solutions for the trade off among structure c ondition index, safety index, and life cycle maintenance cost. The 1987 World Commission on Environment and Development (WECD) report (later needs of the present w ithout compromising the ability of future generations to meet their own ge of meeting human needs for natural resources, industrial products, energy, food, transportation, shelter, and effective waste management while conserving and protecting environmental quality and the natural resource base essential for future development century civil engineer demonstrate an ability to analyze the sustainability of engineered systems and design accordingly. To incorporate sustainability in the proposed trade off analysis, however, we have to deal with at least two important things. Firstly, the concept of sustainability is too abstract and too general to be quantified and measured in the analysis, and thus identifying and adding specific,

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43 concrete and measurable indicators are of significance. Effort has been made on this issue. For example, Chen et al. (2010) identified sustainable performance criteria, composed of economic, social, and environmental criteria, for construction method selection in concrete buildings. However, there is still a lack of such identifica tion in infrastructure engineering in existing literature, not to mention to incorporate the identified indicators in the trade off analysis. Secondly, it is generally believed that sustainability increases costs in the short run, but can bring more benefi ts in the long run. This calls for the application of project life cycle assessment (LCA) and of project life cycle costing (LCC) analysis. Procedures of LCA and LCC have been suggested in existing studies (for example, see Ortiz et al. 2009), but customiz ing those procedures for the benefit of application in infrastructure engineering remains unsolved. In addition, issues associated with financing in LCA and LCC are often neglected or quite simplified in existing literature. One of the objectives of this d issertation is to bridge the above mentioned knowledge gap. Proctor et al. (2012) proposed the Asset Sustainability Index for measurement of critical budgeted for highway infrastructure preservation divided by the amount needed to adequately Finance based Scheduling ent among time, cost, and quality (some scholars also discussed resources, benefits and other factors in their studies). Some studies also included and discussed allocation and leveling of resources. Other than crashing non critical tasks, speeding up proj ect schedules can sometimes be achieved by investing more labors, using more equipment or higher efficient (and thus more expensive) equipment, and/or sacrificing some of the quality. Those have been discussed in existing studies.

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44 However, project financin g was neglected in most studies. This seems unusual because being short of cash flow is a common problem when project schedule is accelerated. Chih (2010, p.54) discussed advantages of the NPV based time cost trade off decision system. NPV is straightforwa rd in concept, simple in calculation, widely accepted, and most importantly, provides linkages between project duration and cost. Lucko and Thompson Jr. (2010) pointed out the importance of accurate determination of financing fees (particularly interest) f or planning and management of construction project cash flows. They considered construction project cash inflows as a quasi random function because contractors may undertake several projects of different sizes and activities in parallel subject to differen t payment terms. Elazouni and Metwally (2005) discussed the feasibility of applying genetic algorithms into a finance based scheduling model, and compared the model with an integer programming model developed by Elazouni and Gab Allah (2004). Both models, bank overdraft strategies, are aimed at searching for a schedule with maximum project profits by minimizing the total project duration under a cash constraint while minimizing financing costs. Ali and Elazouni (2009) int egrated cash flow models with CPM/LOB technique to devise financially feasible schedules through GAs technique for projects with repetitive non serial activities (which feature a uniform repetition of a unit work throughout the project, e.g. multiple simil ar houses and high rise buildings comprising similar floors). Elazouni (2009) also discussed the heuristic method for multi project finance based scheduling, subject specifically to cash constraints set up by line of credits. Uncertainty has also been cons idered in the research. Afshar and Fathi (2009) developed a finance based scheduling model for construction projects with uncertainties in cost by employing fuzzy multi objective optimization and the elitist non dominated sorting genetic

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45 algorithm techniqu es. They used the model to search the non dominated solutions considering total duration, required credit (specifically, bank lines of credits), and financing cost as three objectives. A time profit trade off optimization model, developed by Senouci and El Rayes (2009), is composed of a scheduling module, a profit module, and a multi objective module (based on genetic algorithm). The authors detailed the three modules step by step and evaluated the impact of subcontracting option, construction material, cre w size, and overtime policy on both construction time and profit. As a practical application in the engineering projects, Orabi and El Rayes (2011) discussed the optimization problem about the rehabilitation planning of aging transportation networks, inclu ding financial resource allocation, rehabilitation effect measurement, benefit cost estimation, and tradeoff analysis. All in all, there has been an increasing need for development of new approaches to model, analyze, and optimize financial constraints and cash flows in infrastructure engineering project management. A revised finance based TCQT model is developed in this dissertation to help support financial decision making in maximizing the net present value of a project within the project constraints. De velopment of a Finance Based Model Integrating scheduling and financing functions of construction project management has important because delivering the project withi n the agreed upon time and cost and maximizing the project profit are two vital objectives that often determine the project success or failure. Determination of debt structure is critical for both contractors and project owners, as borrowing can temporaril y cover the unbalance of cash outflow and inflow but with its financing fees impacting profitability. A trade off needs to be optimized within the financial constraints that are

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46 often faced by the project management team. However, the vast majority of cost optimization scheduling techniques in project management entirely discarded the financing costs. Finance cept of finance based scheduling achieves the sought for integration between the functions of scheduling and financing by incorporating financing costs into the project total cost as well as scheduling under cash constraints. Researchers have developed di fferent finance based models with different focuses on the project perspectives. For example, models have been developed based on different project types. Kong et al. (2008) established a quantitative model, which uses a conditional credit rating transitio n matrix to predict default probability and uses Net Present Value ( NPV ) to estimate the maximum default loss. Their model was based on BOT projects, whose credit risk depends on credit ratings, market data, and financial information. Orabi and El Rayes (2 011) discussed the optimization problem about the rehabilitation planning of aging transportation networks, including financial resource allocation, rehabilitation effect measurement, benefit cost estimation, and tradeoff analysis. Researchers have also in tegrated different scheduling techniques in their finance based models. For example, Ali and Elazouni (2009) integrated cash flow models with CPM/LOB technique to devise financially feasible schedules through GAs technique for projects with repetitive non serial activities. Others have proposed a variety of optimization or simulation techniques for the finance based models. Elazouni and Metwally (2005) discussed the feasibility of applying genetic algorithms into a finance based scheduling model, and compar ed the model with an integer programming model developed by Elazouni and Gab Allah (2004). Both models, especially

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47 maximum project profits by minimizing the tota l project duration under a cash constraint while minimizing financing costs. Elazouni (2009) also discussed the heuristic method for multi project finance based scheduling, subject specifically to cash constraints set up by line of credits. Afshar and Fath i (2009) developed a finance based scheduling model for construction projects with uncertainties in cost by employing fuzzy multi objective optimization and the elitist non dominated sorting genetic algorithm techniques. They used the model to search the n on dominated solutions considering total duration, required credit (specifically, bank lines of credits), and financing cost as three objectives. Lee et al. (2011) developed a stochastic project financing analysis system, integrating simulation based sched uling and cash flow analysis as well as incorporating the contract conditions relative to payment considerations. For simplification, however, they did not take into account the effect of interest rate change. Lucko and Thompson Jr. (2010) pointed out the importance of accurate determination of financing fees for planning and management of construction project cash flows. They considered construction project cash inflows as a quasi random function because contractors may undertake several projects of differ ent sizes and activities in parallel subject to different payment terms. The above mentioned studies focused more on the financing needs and cash flow management of contractors. General strategies about the trade off between financing and other critical pr oject objectives have been missed. However, there has been an increasing need for development of new approaches to model, analyze, and optimize financial constraints and cash flows in infrastructure engineering project management. A revised finance based T CQT model is developed in this dissertation to help support financial decision making in maximizing the net present value of a project within the project constraints.

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48 Summary A n infrastructure engineering project is typically a system of people, equipment, materials, and organizations. Good project managers (including civil engineers) must be able to see the project as a whole and drill down into the system and examine the detail of individual parts. This has been widely realized. For example, the Summit on the Future of Civil Engineering sustainable world and enhance the global quality of life, civil engineers serve competently, collaboratively, and ethically as master builders, environmental stewards, innovators and integrators, managers of risk and uncertainty, and leaders in shaping public (environmental and proposes a n integrated infrastructure engineering decision making procedure accordingly. After discussion about the current status of infrastructure development in the U.S. as well as related issues of project prioritization and project management, this chapter revi ewed the time cost quality trade off problem. Existing TCQT analyses focused on the trade off in a relatively limited scope, namely, only among time, cost, and quality in the project construction phase. Other critical factors and financial constraints over the project life cycle have been neglected. The proposed research aims to analyze the TCQT problem in infrastructure engineering in a

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49 Table 2 1. Report Ca Category Assessment Criteria Grading Scale Dams Drinking water Hazardous waste Levees Solid waste Wastewater Aviation Bridges Inland waterways Ports Rail Roads Transit Public parks and recreation Schools Ener gy Capacity Condition Funding Future need Operation and maintenance Public safety Resilience Innovation A (Exceptional): fit for the future B (Good): adequate for now C (Mediocre): requires attention D (Poor): at risk F (Failing/Critical): unfit for purpo se Source: ASCE (2013) Table 2 2. U.S. Highway System Development Phases Time Emphasis Achievements 1960~1985 New construction and expansion Interstate system was completed. Management systems (for pavement, bridge, maintenance, etc.) were introduce d. 1985~2000 Performance and expansion Budgeting, staff resource allocations, outsourcing and streamlining procedures were included in investment decisions. 2000~Present Maintenance and management Economics and engineering are strategically integrated. I T and mobile technology are applied. Source: Summarized from Fwa (2006), pp.17 1

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50 Table 2 3. Definition of Project Management Source Organization Definition / Concept Other Requirements A Guide to the Project Management Body of Knowledge (PMBOK Guide) Fifth Edition Project Management Institute, Inc. (2013) Project management is the application of knowledge, skills, tools, and techniques to project activities to meet the project requirements. Balance the competing project constraints, which include, bu t are not limited to: scope, quality, schedule, budget, resources, and risks. APM Body of Knowledge Sixth Edition Association for Project Management (2012) Project management is the application of processes, methods, knowledge, skills and experienc e to achieve the project objectives. A project is usually deemed to be a success if it achieves the objectives according to their acceptance criteria, within an agreed timescale and budget. Project Management (BS 6079 1: 2010) BSI (British Standard s Institution, 2010) Project management is planning, monitoring and control of all aspects of a project and the motivation of all those involved in it to achieve the project objectives on time and to the specified cost, quality and performance. Specificati on, schedule and cost always have to be bounded to ensure ongoing viability. ISO 21500: 2012 Guidance on Project Management International Organization for Standardization (2012) Project management is the application of methods, tools, techniques and competences to a project. Project management includes the integration of the various phases of the project life cycle. Project management is accomplished through processes. Delivery as promised, faster delivery, less surprises, and improved customer satis faction and less rework. A Guidebook of Project & Program Management for Enterprise Innovation Revision 3 Project Management Association of Japan (PMAJ, 2005) Project management is the professional capability to deliver, with due diligence, a proje ct product that fulfills a given mission, by organizing a dedicated project team, effectively combining the most appropriate technical and managerial methods and techniques and devising the most efficient and effective work breakdown and implementation rou tes. The objective is to generate specific project deliverables or results that fulfill requirements of project management such as scopes, technology (quality), cost and time, and to achieve profit goals as a business.

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51 Table 2 4. Distinctions Among Som e Concepts Project Success vs. Project Management Success Measured against the overall objectives of the project Measured against the widespread and traditional measures of performance against cost, time and quality Success Criteria vs. Success Fac tors The measures by which success or failure of a project or business will be judged Those inputs to the management system that lead directly or indirectly to the success of the project or business Project Success vs. Project Performance Cannot b e measured until after the project is completed Can be measured during the life of the project Table 2 5. PMI Knowledge Areas of Project Management Knowledge Area Utilization Integration Management To coordinate various project elements effectively To identify, define, combine, unify, and coordinate various processes and activities Scope Management To ensure all required work is enclosed To define and control what is and is not included in the project Time Management To provide an effective project s chedule To ensure the timely completion of the project Cost Management To identify needed resources and maintain budget control Quality Management To ensure project functional requirements are met and validated Human Resource Management To effectively d evelop, organize, manage, and lead the project team Communications Management To ensure timely, appropriate, effective internal and external communications as well as smooth project information flow Risk Management To analyze and control potential risks To increase the likelihood and impact of positive project events and decrease such of negative project events Procurement Management To purchase or acquire necessary resources or results from external sources Stakeholder Management To identify stakeholde rs and analyze their expectations To manage and control stakeholder engagement

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52 Table 2 6. Literature on TCT or TCQT Trade off Analyses Author Topic Model Algorithm Afshar et al. (2007) TCQT analysis Multi objective optimization model Multi objective an t colony optimization Afshar et al. (2009) TCT optimization Multi objective combinatorial optimization Non dominated archiving ant colony Babu and Suresh (1996) TCQT analysis Linear programming model Linear programming El Rayes and Kandil (2005) TCQT an alysis Multi objective optimization model Multi objective genetic algorithm Eshtehardian et al. (2009) Stochastic TCT analysis Discontinuous and multi objective fuzzy time cost model Multi objective genetic algorithm Hegazy (1999) Construction TCT analys is Discrete time cost relationships Genetic algorithms Iranmanesh et al. (2008) TCQT analysis Pareto optimality model with multi execution activity mode Fast Pareto genetic algorithm Kalhor et al. (2011) Stochastic TCT optimization Fuzzy approach Non dom inated archiving ant colony Khang and Myint (1999) TCQT analysis Linear programming model Inter related linear programming Li and Love (1997) TCT optimization Linear programming model Improved genetic algorithm Moussourakis and Haksever (2004) TCT probl em Flexible mixed integer programming model Integer programming Peng and Wang (2009) TCT problem Multi mode resource constrained discrete time cost trade off problem model Improved genetic algorithm Pour et al. (2010) TCQT problem Multi mode discrete TC QT model Novel hybrid genetic algorithm Pour et al. (2012) TCQT problem Discrete TCQT analysis with linguistic variables Novel hybrid genetic algorithm Shankar et al. (2011) Construction TCQT analysis Discrete decision making model Mean risk analysis and stochastic dominance Yang (2011) Stochastic TCT analysis Monte Carlo simulation Multi objective particle swarm optimization algorithm Zhang and Xing (2010) Construction TCQT analysis Fuzzy multi attribute utility model Particle swarm optimization Zheng and Mao (2010) Construction TCQT problem Multi objective optimization model Genetic algorithms Zheng and Ng (2005) TCT optimization Stochastic multi objective optimization model incorporating fuzzy sets theory and nonreplaceable front Genetic algorithms

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53 Figure 2 1 The Iron Triangle

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54 CHAPTER 3 METHODOLOGY Decision Making Process This dissertation focuses on the decision making process in infrastructure development. As Harris (1980) indicated, decision making has two folds of meanings: (1) the study of identifying and choosing alternatives based on the values and preferences of the decision maker; and (2) the process of sufficiently reducing uncertainty and doubt about alternatives to allow a re asonable choice to be made from among them. According to Baker et al. (2001), decision making should start with the identification of decision makers and stakeholders in the decision, reducing the possible disagreement about problem definition, requirement s, goals and criteria. Then, a general decision making process can be divided into the steps indicated in Figure 3 1 Generally, there are two types of decision making problems: the Multi Attribute Decision Making (MADM) problem and the Multi Objective Dec ision Making (MODM) problem. Both types are easily self explained. With regard to infrastructure engineering development, MADM is usually applied to project prioritization and evaluation, while MODM can be used for design and alternatives selection. Projec t owners or sponsors must properly make both types of decisions in order for the infrastructure project to be successful. Research Framework For an AEC firm, revenues from projects are the main source of corporate income and profits. Doing projects success fully is the foundation of a successful firm. Continual project success, however, depends largely on excellent project management practice. On the one hand, successful projects can provide the firm with good experience and enhance the overall reputation of the firm; on the other hand, the competitiveness and core competence enable the firm to win more successful projects. This is a positive feedback (Figure 3 2 ). The firm can increase the

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55 probability for project success through best project management pract ices, as well as by providing financial support, key resources (such as human and equipment resources), appropriate incentives, and appropriate organizational culture. Existing studies have been conducted separately on such project management issues as critical success factors, sustainability indicators, TCQT analysis, and finance based scheduling techniques. They have focused more on local op timization. The proposed research, however, suggests a system view on project management decision making procedures with identification of key indicators and sustainability criteria on project success and with integration of those indicators in a more gen eral and realistic TCQT optimization model over the project life cycle. The proposed research focuses more on global optimization. The basic time cost quality trade off (TCQT) optimization process proposed in the research will provide the project managemen t team of the contractor with direct guidance on optimal construction planning and scheduling. Based on existing studies on TCQT problems, the incorporation of other critical factors in the research will greatly expand the existing frameworks and methodolo gies and enrich the body of knowledge in the multi objective decision making analysis. The integration of financing function and sustainability indicators over the whole project life cycle will enlarge the application of the proposed model and benefit a gr eat many of the project stakeholders (e.g. the project owner, the government agency, and the project product end user) involved in the infrastructure engineering project. In other words, the proposed research aims to enhance the integrated decision making procedure for different project stakeholders in the infrastructure engineering field. This dissertation intends to first identify critical success factors (CSFs) and key performance indicators (KPIs) for project success and project management success. Thes e

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56 criteria are inputted in the proposed project prioritization model. Models for trade off among those factors or indicators will then be developed to optimize life cycle project management decision making processes. Financial constraints over the project life cycle will be incorporated in the model to develop financially feasible schedules with considerations of project sustainability objectives through the application of time value of money, cash flow management, and life cycle costing techniques. Fuzzy s ets theory will also be employed to model project uncertainties that have often been met in the infrastructure engineering field. Common advanced intelligent algorithms will be summarized and a new algorithm for the research model will be proposed to provi de solutions to the extensive TCQT optimization problem. An Excel and VBA based programming will finally be provided for the application of the proposed models. The research framework is demonstrated in Figure 3 3 Identification of CSFs and KPIs for Project Management Literature review indicates that the following four methodologies have often been selected for analysis of CSFs and KPIs: (1) Factor Analysis; (2) ANOVA; (3) AHP; and (4) Delphi Me thod. Some researchers have also performed regression analysis and case study on comparison of a variety of factors. Different mathematical tools have further been integrated in the analysis such as Fuzzy Delphi and Fuzzy AHP. There are plenty of studies a nd papers on project success factors and successful project management criteria. Surveys, interviews, investigations, and other qualitative or quantitative technique have been widely used as research methods for such studies. Although different results hav e been obtained, some factors are extensively accepted and most cited. Therefore, a meta analysis can be conducted to find out those factors that are often concluded. The terminology of meta anal

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57 (Borenstein et al. 2009). Though widely applied to biological, psychological, medical, and social sciences, meta analysis has not been used quite often in the civ il engineering industry. Kenley (1998) discussed the possible use of meta analysis in construction management research, taking two case studies, meta analysis of wasted time and meta analysis of the time cost relationship, for examples. Kenley suggested th at meta analysis should form a critical component of the research effort in the construction management research. Melo et al. (2013) conducted a meta analysis to investigate the output elasticity of transport infrastructure in different countries. Separate studies on CSFs and KPIs for project management have been accumulated in recent decades. This gives room for the application of meta analysis to summarize the effectiveness of those factors/indicators. Guidelines were summarized in the PRISMA (Preferred R eporting Items for Systematic reviews and Meta Analyses) Statement in 2009, which consists of a 27 item checklist and a four phase flow diagram, aiming to help authors improve the reporting of systematic reviews and meta analyses. The guidelines are reprod uced here in Figure 3 4 Research Methodology The first model proposed in the dissertation is a project prioritization model, which composes multi attribute decision making techniques to objectively rank potential projects for decision makers to prioritize pr ojects based on the criteria obtained as well as the project performance measures. This process provides key assurance for project time cost quality trade off optimization at the very beginning of the project life cycle. The original concept of the time co st trade off methodology is used to reduce the project duration incrementally with the smallest associated increase in incremental cost (Gido and Clemens, 2003, p.218). This methodology is based on the assumptions that each activity has both a normal and a crash duration and cost estimates. It also assumes linear relationship between

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58 resources. Integration of sustainability into the time cost quality trade off analysi s has at least two aspects of influences in the long run: firstly, a sustainable project requires investing some capitals for the improvement of the project and thus increases the total costs; and secondly, sustainability should be enclosed as one criterio n for project quality. The influence of sustainability on project cost and quality will, of course, has further impact on project duration. Life cycle costing, concerned with the interest rate, the borrowing cost, inflation, and other financial factors, is a methodology of sustainability calculation that combines both construction costs and operating costs in a model to get the net present value. Incorporation of financial constraints is critical because infrastructure engineering projects are usually capit al intensive businesses. The time value of money has to be considered since infrastructure engineering construction often takes a long time to complete, not to mention that the much longer project life cycle should also be considered. Cash flows of the pro jects must be optimized to achieve the project objectives. Therefore, a finance based model requires the application of the net present value method as well as the application of other advanced financial techniques. Fuzzy sets theory has been widely used a nd accepted for modeling of project scheduling uncertainty in recent decades. Although fuzzy sets are often used to reduce the bias of ambiguous statements, the membership function of fuzzy numbers is usually defined by subjective judgment. However, resear chers have claimed that fuzzy sets theory is more appropriate to model TCT or TCQT problems, given a good number of uncertain conditions in construction engineering and management. An appropriate membership function of the fuzzy sets will be

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59 suggested in t he research to closely reflect decision making processes in the infrastructure engineering practice. The fuzzy logic will then further integrated into the proposed model. Genetic Algorithm, with growing popularity in applications in the civil engineering f ield, is one of the major of evolutionary computing methods and has been proven to be very powerful in solving combinational problems. As a representative of advanced intelligent algorithms, the genetic algorithm will be compared with other algorithms, and one or more algorithms will be chosen for this research to provide solutions to the proposed model. As a last step, an Excel spreadsheet will be developed for calculation of the proposed model. As an application, case studies will be conducted to testify the effectiveness and the efficiency of the finance based fuzzy time cost quality trade off optimization model over the project life cycle. Comparisons with other existing models will also be made to verify if the proposed model can improve the integrated infrastructure engineering decision making procedure. Summary In this chapter, the decision making process has been reviewed. Based on specific decision making features, a research framework is proposed along with innovative research methodology. Two integ rated models, project prioritization model and project TCQT trade off model, have been proposed. The following chapters will discuss in detail the proposed models as well as their applications.

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60 Figure 3 1. Decision Making Proce ss Figure 3 2. Positive Feedback in an AEC Firm

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61 Figure 3 3. Research Framework

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62 Figure 3 4. Guidelines of Meta Analyses (Source: Moher, D., Liberati, A., Tetzlaff, J., & Altman, D. G. (2009). Preferred reporting item s for systematic reviews and meta analyses: the PRISMA statement. Annals of internal medicine 151 (4), 264 269.)

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63 CHAPTER 4 THEORY ON MULTI CRITERIA DECISION MAKING Decision making refers to the process of comparing, ranking, prioritizing, or selecting possible solutions from all the available alternatives in order to achieve optimal results. The alternatives usually have multiple attributes, while the results are expected to meet a single goal or multiple goals. The engineering processes have long been integrated with the decision making processes, from prioritization of potential projects at the very beginning of the planning phase to determination of labors and resources at the construction phase. Generally decision theory articulates the following k ey elements of decision making processes: Alternatives : identifying all viable options or choices Attributes : characterizing the conditions and performance of alternatives Objectives : indicating expectations on the outcomes Values : quantifying the results of selected alternatives Single Objective Optimization Model In a typical single objective optimization model, the Benefit Cost Analysis ( BCA ) is usually conducted to compare the costs and risks with benefits and rewards of alternatives for program evalua tion. This analysis method involves determination of costs and benefits, assignment of monetary values to both of them, and comparison of the two. It is a relatively simple and straightforward tool for go/no go decision making in investment and project sel ection. It is widely used by governments and other organizations, e.g., U.S. Army and California Department of Transportation, both of which have published guides on cost benefit analysis. The Economic Analysis Branch of California Department of Transporta tion has further developed a PC based life cycle benefit cost spreadsheet model of analysis of highway construction and operational improvement projects (Figure 4 1 ) FHWA has also developed a tool for operations benefit/cost analysis (Figure 4 2 ). In Flor ida, a Benefit Cost Analysis

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64 Template is suggested for roadway design (Figure 4 3 ). Many of those tools created spreadsheets using Microsoft Excel. In Table 4 1, a BCA worksheet is created. However, BC A has limitation on determination of monetary values of project quality and other long term objectives. In Table 4 2, common BCA tools that have been utilized in the United States are summarized. Note that when converting both benefits and costs to monetized values, we shall decide which type of dollars to use : constant dollars or current dollars. Constant dollars represent the purchasing power of the dollars in a specific year (i.e., base year). In other words, by using constant dollars the inflation effect has been removed, and thus real interest rates are us ed for calculation of discounted cash flows. Current dollars, on the other hand, are nominal dollars; they reflect the purchasing power of the dollars in the future. The link between constant dollars and current dollars is inflation. General Multi Criteria Optimization Model Instead of meeting onl y one single goal, in most decision making processes, decision makers must choose from all available alternatives based on a set of judgment criteria and a set of decision attributes a possible course of action that will optimize a set of different objec tives (Hwang and Masud, 1979). Concepts of alternatives, attributes, criteria, and objectives are self explained, although some scholars (e.g., Hwang and Masud, 1979) provided definitions of them. A multi criteria decision making problem with m alternative s and n criteria can be presented in a matrix format as follows: ( 4 1 )

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65 Where: is the feasible alternatives set; is the evaluation criteria set; is the criterion weight set; and is the performance rating set. The multi criteria optimization then becomes a procedure to find the best or optimal alternative among the feasible alternatives set based on evaluation criteria and re lative weights. Whatever method is used, the process of solving such multi criteria decision making (MCDM) problems involves five major steps: Selection of decision variables, judgment criteria, and alternatives Construction of decision matrix Normalizatio n of decision matrix Determination of criteria weights Prioritization of all alternatives Final decisions can be made according to the results obtained from the above process. Multi Criteria Decision Analys i s (MCDA) methods can be categorized in different ways based on different factors : constrained vs. unconstrained; linear vs. nonlinear; continuous vs. discrete; deterministic vs. stochastic; and single objective vs. multi objective etc For example, in discrete MCDA, criteria (either objectives or attrib utes) are countable in number and are well defined; while in continuous MCDA, mathematical programming is applied to functions that reflect multiple criteria. A common way for MCDA problems classification is to categorize them as either Multi Attribute Dec ision Making (MADM) problems or Multi Objective Decision Making (MODM) problems. Both categories are easily self explained Hwang and Yoon (1981) summarized the contrast of the features between the two. Simply put, MADM is usually applied to project priori tization and evaluation, while MODM can be used for design and alternative selection.

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66 Multi Objective Decision Making Optimization General Form In a typical multi objective decision making problem, the decision maker hopes to achieve more than one goal in selecting alternative components while satisfying the constraints and conditions that have been defined. Mathematically, such problems can be represented as: ( 4 2 ) Subject to: Where: is an n dimensional decision variable vector For a feasible solution of the i th decision variable, is an optimal value for the i th objective among the k objectives under m constraints. If some objective function is to be minimized, it is equivalent to maximize its negative. In multi objective decision making optimization, an optimal solution set usually does not exist that maximizes all objective functions at the same time, and thus Par eto optimal solutions are developed. When the Pareto optimal frontier is reached or approximated, any improvement in one objective will result in the worsening of at least one other objective The final suggested alternative is then selected from the Paret o solution that possesses the most desirable trade off properties. One of the traditional solutions to multi objective optimization problems first decompose the multi objective optimization problem into a series of single objective optimization problems and then use the solution to the preceding problem as a new constraint for the succeeding problem. The order for solving those sub problems is based on the relative importance of each objective. Therefore, the original problem has now been decomposed as t he following problem sets.

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67 ( 4 3 ) Subject to The Weighted Sum Method Another approach elicits decision maker preferences between hypothetical alternatives using mult i criteria trade offs in order to properly aggregate the attributes into a single criterion. In this way additive objective functions are constructed. In general, the process can be formulated as follows: 1. Choose appropriate weights, for m objectives, 2. Maximize ( 4 4 ) 3. Subject to Where V = value function for alternative i w = weight for objective s The key to additive objective functions development is to determine appropriate weights for different objectives according to their relative importance. Ideally, the decision maker has the knowledge and ability to assign weights of each objective b ased on the intrinsic feature of the problem. In practical use, however, the normalization of objectives is often applied to get a Pareto optimal solution. A common technique involves in use of normalization. Normalization makes the value of demand for eac h resource required by each task between [0, 1] and thus demand differences among tasks can be compared. Weights are then determined based on the degree of importance of each resource, or relative weights of each resource can be determined by AHP. However, in this approach, attribute weights are based on decision and thus selection of attribute weights will ha ve significant impact on the optimization results. In

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68 other words, it might be difficult to obtain satisfied Pareto optimality fo r decision makers. Pareto optimal solutions form a Pareto frontier, where any improvement in one objective has to be traded off by degrading the level of another objective. Additive objective functions can also be constructed for multi objective decision m aking problems. In this case, three objectives are included: project quality ( Q ) is maximized, while project time ( T ) and cost ( C ) are minimized. If we use the additive objective function that combines all the objectives into a single objective function an d that is to be minimized, the additive objective function ( Z ) is: ( 4 5 ) Where is the relative weights of the project objectives (i.e., project time, cost, and qu ality, respectively). Determination of the relative weights relies on different calculation approaches. Common methods include: Trade off evaluation between pairs of objectives may also be conducted For example, if two days increase in project time can be compensated by one unit gain in project quality, then we can determine that the relative weight of project time is 1 and the relative weight of project quality is 2. Sensitivity analysis can be enclosed as a powerful tool This method aims to find the ran ges of optimality through development of sensitivity tables for the relative weights for which the optimal solution does not change. A nother widely used practice for MODM optimization is through the introduction of utility theory. U tility theory can be app lied to prioritizing the development and construction of infrastructure engineering projects with multiple optimization objectives (mainly with trade off

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69 among project time, cost, and quality during the whole project life cycle). A value is assigned to the utility of a project and can be expressed as: ( 4 6 ) Where: = Overall value of the utility for Project X ; = The utility value for Index i of Project X ; and = The weight of the Index i After the development of different utility functions and the assignment of the utility value and the weight for ea ch index, the potential alternatives can be prioritized based on their overall utility values. Specifically when taking into consideration project constraints or boundary with regard to project time, cost, and quality, a multi objective optimization problem can be formulated as follows: Objective: ( 4 7 ) Constraints: Time: Cost: Quality: Where: Utility function; Decision variab les; Normalizing parameter; Project objectives; Relationships between decision variables and project objectives. At a maximum point, the partial derivatives of must be zero: ( 4 8 ) With the appearance of constraints, Lagrange multipliers can be introduced for making a system of equal equations and unknowns and thus the system can be solved.

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70 Generally speaking, m ulti objective decision making problems have been widely studied. Whichever method is used, the solution process typically includes: (1) normalization of decision making matrix, (2) determination of criteria weights, and (3) prioritization of all alterna tive solutions. Multi Attribute Decision Making Optimization General Form Given a set of plans P 1 P 2 P n each plan has its own attributes A 1 A 2 A m with the weights w 1 w 2 w m respectively, where w i confirms to the condition of normalization : The decision namely, P max The solution can be expressed as a matrix below: ( 4 9 ) where a ij is the value of the j th alt ernative on the i th index. Theoretically, we hope to find an optimal solution as a representative of best solutions. A unique optimal solution does not usually exist, however, in solving multi objective optimization problems, because we have to make trade offs among those multiple conflicting objectives. Usually, we can only help state the preferences over different objectives and attributes, and provide the decision maker with relevant information and priority suggestions. Thus the following possible solu tions are sought for: Non dominated Solution: A solution S 1 is dominated and thus should be eliminated if another solution is at least as good as S 1 with respect to every criterion. The remaining are non dominated solutions for final selection once all the dominated solutions are removed.

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71 Efficient Solution: A solution is said to be efficient (or, Pareto optimal) if there does not exist another solution such that the utility value (or other critical performance value) is larger than the utility value provid ed by the efficient solution. Accordingly, the set of all efficient solutions is called an efficient frontier. Preferred Solution: In order to get a preferred solution, multi attribute utility functions are usually developed to identify the most preferred alternative of a decision maker who has to trade off certain criteria for others. Satisfied Solution: A satisfied solution provides the decision maker with results that Ideal Solution: A solut ion is said to reach the (positive) ideal point if it provides the maximum for maximization problems and the minimum for minimization problems of each objective function. On the contrary, a negative ideal solution, or nadir point provides the minimum for maximization problems and the maximum for minimization problems of each object function among the points in the non dominated set. Therefore, the ideal solution can be expressed as: ( 4 10 ) Where: is the utility function of the i th attribute. On the contrary, the negative ideal solution can be expressed as: ( 4 11 ) Where: The ideal solution is infeasible in most cases, and thus the concept of a feasible Compromise Solution is generated, the solution that is closest to the ideal solution or farthest to

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72 the negative ideal solution. Zavadskas et. al (2006) provided a method for evaluating the accuracy of TOPSIS ranking in multi crit eria decisions. Quantification and Conversion of Criteria Both qualitative and quantitative criteria are common in multi objective optimization problems. Quantitative criteria, as its name indicates, can be measured objectively. Examples are distance, volu me, velocity, etc. Qualitative criteria, on the contrary, cannot be easily measured in an objective way. Examples are color, customer satisfactory, fairness, truth, etc. As one of the oldest methods of measuring subjective variables, bipolar scaling is sti ll popular and widely used, which establishes concepts that are opposite of one another, with degrees or steps between extreme poles (McCroskey and Richmond, 1989). When developing a bipolar scale we need to ask what (to be measured), how many (to be measu red), and what scale (to be used). The order of the scale values can be different, depending on whether the criteria (attributes) are related to benefits or costs (Figure 4 4 ). Simply put, we assign the largest number to those that bring the best/optimum r esults, and the smallest number to those that bring the worst/permimum results. Accordingly, the midpoint represents the breakpoint between favorable values and unfavorable values and thus forms the basis for calibration. The bipolar scale assignment is ob viously arbitrary, and thus other quantification approaches of fuzzy attributes should also be considered. Normalization is another widely used approach. On the other hand, normalization or standardization is often applied to decision criteria, as different criteria are usually measured in different units. Normalization is especially necessary for some decision making processes such as maxima x, maximin, and simple additive weighting. Commonly used normalization methods include : 1. Normalization based on maximum or minimum values This is the simplest normalization method in which the original value of each element is compared with the maximum or

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73 minimum value of all elements, depending on whether the attribute relates to benefit or cost. This normalization process can be expressed as: For benefit attribute: ( 4 12 ) For cost attribute: ( 4 13 ) 2. Normalization based on distance This method uses the concept of distance as the denominator and has the following expression: ( 4 14 ) 3. Normalization based on the difference between the ma ximum value and the minimum value. For benefits related criteria: ( 4 15 ) For costs related criteria: ( 4 16 ) Fuzzy numbers can also be used in the above calculation. Determination of Criteria Weights Determination of criteria weights is both necessary and important, because good solution to multi objective optimization problems also depends on the proper selection of weights and utility functions to reflect the decision ences. In practice, however, it is not easy to accurately assign weights to the selected criteria. This is due to: (1) different views of decision makers on the criteria; (2) unequal impacts of the criteria on the decision making process; and (3) different liabilities of the criteria. Therefore, weights need to be assigned to different criteria to catch their relative importance.

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74 Determination of criteria weights lies in two major categories: subjective assignments and objective assignments. The former tec hnique uses data collected from an expert system, in which the experts make subjective judgments and given their opinions on criteria weights accordingly. A typical example of subjective assignments is the Delphi method. The latter technique gathers data c ollected from the real practice. Common methods of objective assignments include Principal Components Analysis and Cluster Analysis. A nalytical H ierarchy P rocess First developed by Saaty ( 1990 ), the Analytical Hierarchy Process (AHP) has been widely used a nd been accepted as a popular system analysis tool since then. One major advantage of AHP is the integration of quantitative analysis with qualitative analysis for solving multi criteria optimization problems. In general, the process includes five steps: ( 1) create a hierarchy structure; (2) construct a judgment matrix; (3) compare decision elements in a pairwise manner; (4) assign relative weights to decision criteria; (5) check the consistency of the judgments; and (6) aggregate the relative weights to ca lculate alternative ranks. Consistency check is often neglected in practical use, but it actually is important in a way that understanding of the consistency relates the relationship and the magnitude of differences with various decisions (Tam et al., 2006 ). The steps of the process follow. Step 1: create a hierarchy structure The first step in the AHP is to form the hierarchy of the decision making problem in terms of an overall objective, aspects and criteria (or criteria and sub criteria), and different alternatives. The AHP model is structured in such a hierarchical way that the same assessment technique is used at each node of the hierarchy (Figure 4 5). Steps 2 and 3: construct a judgment matrix and make pairwise comparisons

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75 System analysis is based on information. The information collected for the AHP is the decision represented with numbers and thus form a judgment matrix. Constructing a judgment matrix is critical in the AHP. Assume Element A k in Level A is related with Elements B 1 B 2 n in Level B a judgment matrix can be developed in Table 4 3 In Table 4 3, b ij gives the relative importance or preference of B i over B j for Element A k designate the relative preference of one element over another) according to their relative importance, and their reciprocals are used for inverse comparisons. b ij =1: B i and B j are equally preferred (i.e., they have equal importance); b ij = 3: B i is moder ately preferred over B j (i.e., B i is moderately favored); b ij = 5: B i is strongly preferred over B j (i.e., B i is strongly favored); b ij = 7: B i is very strongly preferred over B j (i.e., B i is clearly dominant); b ij = 9: B i is extremely preferred over B j (i .e., B i is super dominant). In the AHP, a judgment matrix is suggested to meet the following two rules: and 2 Therefore, we only need to assign values to elements for a judgment matrix. The matrix of pairwise comparison is so constructed that the degrees of the decision 2 In this way the consistency condition is given by Another way for pairwise comparison is to assign values to for representation of preference difference between Criteria i and j Then the condition of reciprocity is and the consistency condition is given by See Ca vallo and http://www.researchgate.net/profile/Bice_Cavallo/publication/239920716_A_general_measure_of_consistency_for_ pairwise_comparison_matrices/links/00b4952e6d830d78b0000000.pdf

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76 This is essentially the same if we construct a matrix of pairwise comparisons for the weight of the alternative set : ( 4 17 ) Step 4: assign relative weights to decision criteria This step aims to assign weights to all the elements in a specific level rela tive to the level eigenvectors, which are used by the AHP to calculate weights of aspects, criteria and sub criteria, and alternatives for each factor based on the pairwi se comparisons. A simple weighted average is then used to determine final alternative weights. Mathematically, for the judgment matrix B, we calculate eigenvalues and eigenvectors that satisfy: ( 4 18 ) Where: is the maximum eigenvalue of matrix B and W is the corresponding normalized eigenvector. The element of W or is the relative weight. When three or more items are being compared, it is important to measure t he consistency of judgments. For example, if Alternative A costs two times of Alternative B and six times of Alternative C, the perfect consistency requires that Alternative B cost three times of Alternative C. Mathematically, Define the Consistency Index ( CI ) as: ( 4 19 )

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77 Obviously, if the judgment matrix has perfect consistency. The consistency becomes weaker as (and thus CI ) gets bigger. Therefore, we compare the CI with the average Random Consistency Index ( RCI ). For matrix of order 1~10, the RCI is listed in Table 4 4 Define the Co nsistency Ratio ( CR ) as: ( 4 20 ) When we consider the judgment matrix to be adequately consistent (Saaty, 1980). Otherwise we may need to improve the judgments until is satisfied. 3 Step 5: aggregate the relative weights to calculate alternative ranks Aggregation of ranking all levels needs to be done from upper levels to lower levels. Assume the ranking for all the elements in the upper level, A 1 A 2 m is co mpleted and the weights are a 1 a 2 m respectively. Then correspondingly, for elements in the current level, B 1 B 2 n the ranking result is: with respect to Further assume that if B j is irre levant to A i then Now we can get the aggregation of ranking as follows (Table 4 5 ) Obviously, the following condition is satisfied: ( 4 21 ) Similarly, the consistency of the judgment matrix should be checked using the following equations: 3 In many cases, we will need to go back to the decision makers and repeat the above mentioned steps in order to get corrected preference statements.

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78 ( 4 22 ) ( 4 23 ) ( 4 24 ) Where and are referred to in Level B The consistency requirement is satisfied if Entropy Weight In the AHP method and other similar evaluation methods, determination of criteria weights is critical. One issue about the weight assignment is that the calculation c ontains only the information of the individual indicator and thus ignores the relationship among other objectives. The entropy method has been proposed to solve such problems (Zou et al., 2006) because the entropy weight objectively reflects the original d ata in a more comprehensive way. Suppose there are m indicators and n alternative objects; the entropy of the i th indicator is defined as ( 4 25 ) Where k is a positive constant and thus Wher e: and Further, the entropy weight of the i th indicator is defined as: ( 4 26 )

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79 Again, and Now, construct to integrate the objective significance of the entropy weight, and the decision and thus reflects a comprehensive weight of an individual indicator as follows: ( 4 27 ) A simpler process can also be used, which gets the average of the two weights: ( 4 28 ) Application of Fuzzy Sets Theory In the real world, most of the time decision makers have to choose solutions where information and data are not precisely known. Many times it is also hard for decision makers to assign clearly defined (i.e., accurate) numbers for comparison o f different alternatives. Fuzzy numbers are then suggested to be assigned to weights and criteria measurement for alternatives. Certainly, deterministic assumptions largely simplify the problem statement and its solution, but can be so misunderstanding in the infrastructure engineering field that they might lead decision makers to make non optimal or even wrong decisions. Project owners and typical AEC firm s cannot suffer such losses. So introducing uncertainty in the TCQT analysis is of significance. Rathe r, an experienced project team is able to make an example estimate such as: the activity can be finished most likely within 10 days, but definitely not less than 7 days (with a crash schedule, due to labor/equipment/budget/other constraints) and not more t han 15 days (due to schedule requirements). In addition, the description and measurement of project quality are usually linguistic and thus filled with vagueness and subjectivity. In order to reflect such

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80 uncertainties, fuzzy sets theory can be applied and is viewed as one of the effective ways to solve the uncertain problem. Here a critical step for application of fuzzy sets theory is to define the membership function. Different membership functions will be considered and compared in the dissertation to fi nd one that mostly conforms to the real infrastructure engineering practice. The project quality relies on qualities of a series of tasks, and the task quality relies on its work activities or sub work items, whose qualities show fuzziness as discussed in previous chapters. Therefore, it is inappropriate to use ordinary (single value) numbers for activity (and thus project) quality evaluation. Instead, linguistic evaluation is implemented in this research. This requires converting linguistic variables, gene numbers. The relative, overall project quality can then be assessed from the sum product of each expert weight and each activity quality. One of the big issues for the decision making process in the construction ind ustry is incomplete information caused by the complexity and uncertainty of engineering projects. This makes construction engineering decision making a typical fuzzy multi objective optimization problem and gives space for the application of fuzzy sets the ory in the engineering field, or, fuzzy engineering decision making. In addition, e ffective project financing decisions also require judgment, either objectively or subjectively, which involves figuring out a way for the project team to accept ambiguity, c onflict and confusion. Fuzzy Sets The vagueness and uncertainty in the decision making process can be addressed by the fuzzy set theory. First proposed and introduced by Zadeh (1965), fuzzy sets are an extension of classic crisp sets. According to Zadeh (1 965), the definition of a fuzzy set is: Let X be a space of points (objects), with a generic element of X denoted by x Thus X = {x}

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81 A fuzzy set (class) A in X is classified with a continuum of grades of membership and is characterized by a membership (ch aracteristic) function f A (x) which associates with each point in X a real number in the interval [0,1], with the values of f A (x) at x x in A Thus, the nearer the value of f A (x) to unity, the higher the grade of me mbership of x in A on opinion polls of human thoughts (Chiu & Park, 1994). Accordingly, is a fuzzy set on U or is the membership function of the fuzzy set A For the value is called the grade of membership of x in the fuzzy set A As two special cases, indicates that the elemen t x belongs to set A for sure, while indicates that the element is clearly not one of the elements in set A. Here a character Triangular Fuzzy Number Fuzzy numbers can be obtained wi th different forms. One of the most widely used forms utilizes triangular fuzzy numbers. For example, a triangular fuzzy number is denoted as by using the smallest possible value, the most promising value, and the largest possible value of a fuzzy event. Its membership function can be written as follows. ( 4 29 ) The parameter is the center point, and are two base points. Therefore, the degrees of membership of , and are 0, 1, and 0, respectively. Obviously, it holds that

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82 The larger the value of is, the fuzzier the membership. For example, the following figure shows a typical triangular fuzzy number where , and Therefore, its membership function is: The difference between a triangular probability distribution and a triangular fuzzy number rests on the aspect from different views: the former being objective probabilistic occurrence of an event, and the latter being subjective judgment in human thoughts of an event. In addition, the graded mean integration representation (GMIR) is often adopted to rank fuzzy numbers and a larger GMIR means a larger fuzzy number. For a triangular fuzzy number the GMIR can be com puted as follows: ( 4 30 ) 0 0.2 0.4 0.6 0.8 1 0 2 4 6 8 10 12 x

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83 Another way of de fuzzification is to calculate the best non fuzzy performance (BNP) value: ( 4 31 ) One of the widely used linguistic scales introduces t riangular fuzzy numbers for pairwise comparison. The meaning of such fuzzy numbers and their membership functions are listed in Table 4 6 Operations of Triangular Fuzzy Numbers Zadeh (1965) also discussed and defined operation rules involving fuzzy sets by extending the corresponding definitions for ordinary sets. Let and the following operations can be performed: Addition: ( 4 32 ) Subtraction: ( 4 33 ) Multiplication: ( 4 34 ) Division: ( 4 35 ) level ( ), a triangular fuzzy number, can be decomposed into an interval set as: ( 4 36 ) Where:

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84 Please note that some different expressions for fuzzy number operations have also been proposed (Gani and Assarudeen, 2012). For the purpose of simplification, the above defined operations are used in this research. Measuring Fuzziness Fuzzy numbers need to be ranked for practical use (Cheng, 1996). A common approach to measuring fuzziness refers to the concept of distance, which measures the degree of separation between two identical objects (e.g., points, lines, surfaces, and in this case, fuzzy numbers). The smaller the defined distance, the closer two fuzzy numbers or fuzzy sets are. A variety of fuzzy distance measures have been summarized and proposed in literature (e.g., Cheng, 1996; Klir, 1987; and Tran and Duckstein, 2002). Three dist ance expressions that are widely used are: Hamming Distance: ( 4 37 ) Euclidean Distance: ( 4 38 ) Minkowski Distance: ( 4 39 ) Note Hamming Distance and Eucli dean Distance are special cases of Minkowski Distance when and respectively. Specifically, define the distance between triangular fuzzy numbers and as follows: ( 4 40 ) It does not always make sense to use distance for description of degrees of fuzziness. An improved method is further developed where ( r elatively) Weighted Hamming Distance is first defined:

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85 ( 4 41 ) Where the weights on , shall satisfy: Take fuzzy sets for example, where denote three different project features (e.g., project location, local weather condition, and project size), respectively. Assume: And satisfies To compare the similarity between a new Project A and completed Projects B and C, we can calculate weighted hamming distances as follows: Since it is probably a wise decision to predict features of Project A based on those of Project C.

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86 Generally, the multiplication or division of two triangular fuzzy numbers does not necessarily results in triangular fuzzy numbers. In the fuzzy decision making process, however, we still view such results as triangular fuzzy numbers. There are also some other methods commonly used for comparison of fuzzy sets, such as cut, fuzzy scoring, and linguistic expression. Fuzzy Modeling Some commo nly used multi objective decision making problem solving techniques are (Konak et al., 2006; other literature): Simple Additive Weighting (SAW): This method begins with constructing and normalizing the decision making matrix. Then optimal values of each pa rameter and attributes weights are determined. After calculation of the weighted normalized matrix and determination of simple additive weighting optimality criterion, the final results of alternatives ranking can be obtained according to the SAW criterion values. For example, Shevchenko et al. (2008) used this method for analysis of investments risk alternatives in construction. The mechanism for SAW calculation is relatively simple: (4 42) Where: Weighted score for alternative i ; Weight for criterion j ; Rating score for alternative i on criterion j Weighted Sum Method (WSM): Simply put, an alternative ( ) is scored for the product sum of the performance of each alternative under each criterion ( ), among criteria, multiplied by its relative weight ( ). And thus the alternative, with the highest score, is selected: (4 43) It is understandable that the WSM is a suitable application to single objective decision making problems where all measurement units are identical. It is not an accurate approach, however, to multi criteria decision making optimization.

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87 Weighted Product Method (WPM): In essence, this method is a revised WSM. Instead of calculating product sum scores, WPM compares alternatives one pair at a time according to the following defined ratios: (4 44) Where: number of decision criteria; value of Alternative K in terms of the j th criterion; value of Alternative L in terms of the j th criterion; weight assigned to the j th criterion. An advantage of the WPM over WSM lies in the elimination of measurement units to make different measures comparable. Technique for Orde r Preference by Similarity to the Ideal Solution (TOPSIS) The Analytical Hierarchy Process (AHP) The Simple Multi Attribute Rating Technique (SMART) Analytic Network Process (ANP) The vagueness in the decision making process makes it necessary to introduce fuzzy logic for decision assistance. Because of its effectiveness and calculation efficiency, recently, criteria decision making (Saghafian and Hejazi, 2005; Shih et al., 2006; Wang and Lee, 2007; and Behzadian et al., 2012). As a common step, when using TOPSIS, relative closeness from each alternative to ideal solution has to be determined and then compared; therefore, the distance between two fuzzy numbers mu st be pre defined if a fuzzy TOPSIS is used. Literature has also proposed different equations for fuzzy numbers distance calculation. Fuzzy AHP Analytic Hierarchy Process (AHP), first developed by Saaty (1990), is now widely used as a multi objective decis ion making tool. AHP shows effectiveness in relevant factor selection and ranking in a hierarchic structure through a way of combining both qualitative and quantitative analyses. Saaty (1990) suggested what to include in the AHP when constructing

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88 hierarchi es: appropriately thorough representation of the problem; consideration of the environment; identification of attributes; and identification of participants. Zahedi (1986) summarized in which areas AHP was applied, suggested extensions of AHP, and addresse d criticisms of AHP. Essentially, AHP reflects strategic thinking of human beings in which subjective judgment is quantized through analysis Degrees of importance for each relevant factor are compared in such a hierarchic way that a complex decision makin g problem is decomposed Saaty ( 1990 ) suggested that the key to decision making problems should be evaluation and selection of behaviors, schemes, and objectives, in which objectives need to be ranked and then good objectives need to be selected. Further, the fuzzy AHP takes into consideration fuzzy numbers, based on the decision comparisons. As has been discussed in the previous section, a consistency check is required in the application of AHP. Bec ause lack of consistency in the decision making process (e.g., inconsistency in preference relations among attributes) often brings inconsistent conclusions, failure in the consistency check will lead to re assignment of comparable ratios. Fuzzy numbers wi ll further increase the likelihood of inconsistency. In a crisp context, the preference transitivity is straightforward: In a fuzzy model, the preference transitivity is anticipated as:

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89 Basically, i n the fuzzy context, this is saying that if an alternative a is preferred to alternative b and is b to c, then a should be preferred to c. In the real decision making process, however, such easy preference transitivity can be seldom guaranteed. Herrera Vie dma (2004) summarized two widely used preference relations: multiplicative preference relations and fuzzy preference relations. 1. In a multiplicative preference relation, the preference of alternative over is defined by the ratio, of their preference intensity with 1~9 scale (Saaty, 1990). Hence, represents that is no different from while represents that is maximally better than Obviously such a preference relation is assumed multiplicative reciprocal: (4 45) 2. In a fuzzy preference relation, the preference of alternative over is defined by the preference degree, an element characterized by a membership function. Hence, represents that is almost as good and important as ( ), while represents that is maximally better than Generally, indicates that is preferred to ( ), and such a preference relation is assumed additive reciprocal: (4 46) Fuzzy TOPSIS TOPSIS was first developed by Hwang and Yoon (1981). TOPSIS selects the alternative that is the closest to the ideal solution and farthest from negative ideal solution. The solution is considered optimal when it is closest to the positive ideal point and farthest to the negative ideal point. The original TOPSIS used ordinary single value numbers for both evaluation and weight assignments. The Washington State Department of Transportation adopts TOPSIS for benefit cost analysis calculation o f highway mobility project prioritization. WSDOT estimates benefits on the basis of 24 hour user travel time savings and costs on the basis of expenses of ROW, engineering, construction, and operation and maintenance. TOPSIS has been improved by many

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90 resea rchers to fuzzy TOPSIS, taking into account fuzzy effects in the practical decision making procedures. Fuzzy TOPSIS has been applied to a variety of decision making areas. For example, Moradpour et al. (2011) used the method for ranking highway constructio n project risks and their questionnaire resulted in a weight vector of In essence, the selection of the optimal alternative in the TOPSIS process is based on the highest score from the following equation (Finnie et al. 2007): ( 4 47) Where: = the score x for the alternative i under the attribute j ; and = the weight of attribute j Application of fuzzy TOPSIS is discussed step by step as fo llows. Step 0: Finding attribute weights and attribute ratings, and construct decision table. Denote the j th criterion for the i th alternative as In other words, with m alternatives and n criteria, the decision (evaluation) mat rix is: (4 48) Define attribute ratings as follows ( for l inguistic variables and fuzzy scores of the ratings of alternatives ): The range of fuzzy scores for the ratings of alternatives have been pre defined as

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91 [0,1] and thus already been standardized; otherwise the decision matrix have to be further standardized. Similar to the determination of criteria weights Weighted Arithmetic Averaging (WAA) operators are also applied to get the weighted fuzzy evaluation scores: ( 4 49) where is the WAA vector. Step 1: Standardize the Decision Matrix. This step transforms various attribute dimensions into non dimensional attributes, which allows comparisons acro ss criteria. For standardizing, each column of decision matrix is divided by the root of sum of square of respective decision attributes. Step 2: Construct weighted standardized decision matrix by multiplying attributes weight to each rating. The weighted standardized decision (evaluation) matrix is now: where is the weight for the j th criterion. Step 3: Determine ideal solution and negative ideal solution. (A set of maximum values for each criterion is i deal solution.) Positive ideal solution (based on benefit): (4 50) Negative ideal solution (based on cost): (4 51) Step 4: Determine separation from ideal solution. Distance to the positive ideal solution: (4 52) Step 5: Determine separation from negative ideal solution. Distance to the negative ideal solution: (4 53)

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92 Step 6: Determine relative closeness to ideal solution. ( 4 54) Barnes and Rutherford (1997) identified such closeness as Priority Index when they developed the State of Washington highway mobility project ranking procedure by using TOPSIS. Step 7: Rank the order. Summary In a typical multi criteria optimization problem, there are a variety of attributes (associated with alternatives) and/or objectives (both interactive and contradictive with one another), under a set of constraint resource conditions. Solution to such a problem reflect s the decision a set of alternatives with multiple, potentially conflicting criteria. Trade offs always exist in such project management decision making processes: We have to put more labor or provide highly priced, advanced equipment on the project to achieve the project quality requirement within a shorter time; otherwise we have to wait longer for the project or task to complete. Challenges that are often encountered in the multi criteria decision making process include selection of proper criteria, evaluation of alternatives, assignment of attributes weight, and determination of strength of preferences. In this chapter, theory on multi criteria decision making was discus sed. As a widely used method for single objective optimization, benefit cost analysis tools were first summarized. Two types of multi criteria decision making problems, multi objective decision making optimization and multi attribute decision making optimi zation, were then discussed in detail. Lastly, fuzzy set theory was introduced along with its application in the decision making field.

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93 Table 4 1. Benefit Cost Analysis Worksheet Action i (Short Term / Long Term) Using / Doing Not Using / Not Doing Bene fits + Rewards Costs + Risks Table 4 2. Summary of Widely Used BCA Tools Document Agency Year Real rate Category Impact (costs or benefits) Tools Economic Analysis Primer USDOT 2003 7% Agency costs Design and engineering HERS ST (Highway Economic R equirement s System) by FHWA Land acquisition Construction Reconstruction/Rehabilitation Preservation/Routine maintenance Mitigation User costs/benefits associated with work zones Delays Crashes Vehicle operating costs User costs/benefits associated with facility operations Travel time and delay Crashes Vehicle operating costs Externalities Emissions Noise Other impacts Macro economic Analysis of Florida's Transpo rtation Investments FDOT 2015 4% Costs Travel time The Regional Economic Models, Inc. (REMI) economic simulation model Vehicle operating costs Accident cost Increased capacity Modal shifts Capacity spending Operatio ns and maintenance Administration and support Benefits Reduced cost of doing business Household cost savings Modal shifts Income Jobs Gross state product Personal travel user benefits Safety

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94 Table 4 2. Continued Document Agency Year Real rate Category Impact (costs or benefits) Tools Benefit Cost Analysis Analyses Guidance for TIGER Grant Applicants TIGER 2014 3% Quality of life Land use changes that reduce VMT TIGER BCA Resource Guide Increased accessibility Property value increases Economic competitiveness Travel time savings Operating cost savings Safety Prevented accidents, injuries, and fatalities State of go od repair Deferral of complete replacement Maintenance and repair savings Reduced VMT from not closing bridges Environmental sustainability Environmental benefits from reduced emissions WSDOT Mobility Project Prioritization Process WS DOT 2000 4% Benefits Travel time savings for passenger and freight movement Operating savings Accident reduction Costs Construction Environmental retrofit Preliminary engineering Annual operating and maintenan ce Benefit Cost Analysis for Transportation Projects MnDOT Online Not specified, but used 3.6% in an example Benefits Travel time savings Vehicle operating cost savings Safety Costs Capital costs Major rehabilitation costs Routine annual maintenance costs Remaining capital value California Life Cyce Benefit/Cost Analysis Model Caltrans 2009 4% Travel time savings Cal B/C Vehicle operating cost savings Project costs Safety (Acciden t cost savings) Emissions reductions (air quality and greenhouse gas benefits) Major Corridor Investment Benefit Analysis System INDOT 1998 7% Travel time savings NET BC Safety cost savings Vehicle operating cost savings Business cost savings Business attraction impacts Tourism impacts Construction Operations and maintenance

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95 Table 4 3. Pairwise Comparisons A k B 1 B 2 B n B 1 b 11 b 12 b 1n B 2 b 21 b 22 b 2n B n b n1 b n2 b nn Ta ble 4 4. RCI values for different values of n Order 1 2 3 4 5 6 7 8 9 10 RCI 0.00 0.00 0.58 0.90 1.12 1.24 1.32 1.41 1.45 1.49 Table 4 5. Aggregation of Ranking Level A A 1 A 2 A m Aggregation of Ranking in Level B a 1 a 2 a m B 1 B 2 B n Table 4 6. Triangular Fuzzy Numbers for Pairwise Comparison Importance strength Fuzzy number Membership function Linguistic variables 1 (1,1,3) Equally important 3 (1,3,5) Weakly important 5 (3,5,7) Strongly more important 7 (5,7,9) Very strongly important 9 (7,9,9) Extremely more important

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96 Table 4 7. Application of Fuzzy Methods Author (Year) Methodology Fuzzification and Decision Making Techniques Application Pan (2008) Fuzzy AHP Fuzzy importance scale by a combination of triangular and trapezoidal fuzzy numbers cut representing degr ees of uncertainty Bridge construction method selection Huang et al. (2008) Fuzzy AHP Integration of degree of optimism with triangular fuzzy numbers for consideration of decision risks Government sponsored R&D project selection Gumus (2009) Fuzzy AHP an d TOPSIS Criteria obtained with modified Delphi method Extent analysis Hazardous waste transportation firms evaluation Amiri (2010) AHP and Fuzzy TOPSIS Group working for structuring decision hierarchy, AHP for criteria weights, and fuzzy TOPSIS for proje ct selection Oil fields development project selection Sun (2010) Fuzzy AHP and Fuzzy TOPSIS Vagueness and subjectivity handled with linguistic values by using triangular fuzzy numbers Company performance evaluation Figure 4 1. Cover Sheet of Californi a Life Cycle Benefit/Cost Analysis Model

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97 Figure 4 2. Cover Sheet of FHWA Tool for Operations Benefit/Cost Figure 4 3. Cover Sheet of FDOT Benefit Cost Analysis Template

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98 Benefits Small 1 2 3 4 5 6 7 Large Costs Large 1 2 3 4 5 6 7 Small Figure 4 4. Example of Order of Scale Values Figure 4 5. AHP Hierarchy Structure

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99 CHAPTER 5 APPLICATION OF MULTI ATTRIBUTE DECISION MAKING OPTIMIZATION: PRIORITIZATION OF HI GHWAY PROJECTS IN FL ORIDA The Needs for Project Prioritizati on When deciding allocation of available funds, transportation agencies must keep in mind the budget constraints imposed both locally and nationally. Gaps almost always exist between the required funds and the available funds. Decision makers must evaluate comprehensively the impact of infrastructure engineering projects on investments, operation expenses, network, traffic level of service, as well as on land development and environmental conditions. Take highway engineering projects for example: Prioritiza tion of potential highway projects development plays an important role on the significance of the impact stated above. Prioritizing project development, or comparing a variety of potential project and then choosing a specific one, is essentially a multi at tribute optimization problem. Therefore, research must be done with regard to economy, technology, and environment. A case in point in Florida is the Long Range Transportation Plan in which the North Florida TPO (Transportation Planning Organization) defi nes the goals and objectives as enhancing economic competitiveness, livability, safety, mobility and accessibility, equity in decision making, and system preservation. They further provide details about the performance measures and benchmarks for the above goals and objectives. Usually, benefit cost analysis ( BC A) is conducted to evaluate the financial performance of highway projects by calculations of net present value (NPV), internal rate of return (IRR), payback period, and other economic indicators. In addition, multi criteria performance should also be assessed with incorporation of non monetized elements. Accurate p rojection of future trip and travel demand is critical to the highway and transportation planning process. The four step process (NCHRP, 20 12) has long been the

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100 conventional method for transportation demand estimation. The process begins with estimation of trip generation from socio economic characteristics, land use patterns, and transportation system characteristics, and is then followed by trip distribution and mode choice, and is concluded with network assignment such as link flows, speeds, travel times, and transit ridership. Further, FDOT (2013) based the process for construction opportunities prioritization on highway capacity, preserva tion, and safety. The Strategic Investment Tool (SIT) is developed and used by FDOT to rank capacity projects on Strategic Intermodal System (SIS) facilities. The following sections describe main project attributes and objectives and how we analyze them. E conomic Attribute Analysis The project economic analysis can be done through a benefic cost analysis for evaluation of the rationale and feasibility of potential projects. This provides the foundation of investment analysis, plan comparison, and project pr ioritization. In such an analysis the roadway network must be considered as a whole. The difficulty of economic analysis for transportation projects also lies in their impacts on not only direct users but also indirect users, and thus we must conduct such analyses in a view of system management over the project life cycle. Kockelman et al. (2013) summarized the impacts of investment in transportation infrastructure (Table 5 1). Principles for Federal Infrastructure Investments (1994) requires systematic ana lysis be conducted of expected benefits and costs (including both quantitative and qualitative measures) for investment/performance analysis of transportation systems. Although the methods used for benefit cost analysis are different among the Highway Econ omic Requirements System (HERS), the National Bridge Investment Analysis System (NBIAS), and the Transit Economic Requirements Model (TERM), all of the three models introduce and incorporate benefit cost analysis into the investment/performance evaluation. FDOT published Macroeconomic Analysis in January 2015, which provides methodology for

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101 economic effect analysis for highway investments. The following figure (Figure 5 1) briefly summarizes the analysis approach. In a report prepared for Utah Department of Transportation Research Division, Schultz and McGee (2009) conducted an economic development analysis and developed a project evaluation and prioritization method. The scoring system they proposed for economic development assessment consists of four aggregate criteria and one bonus criterion, a total of 110 points (Figure 5 2). Environmental, congestion, and safety objectives were further added to the succeeding economic evaluation framework. They suggested picking a set of indices for different project types from the following possible indices on a pr oject by project basis: AADT Truck AADT v/c ratio v/c ratio improvement safety index functional class transportation growth vehicle hours saved B/C ratio Adjacent interchange v/c ratio Average adjacent interchange distance Investment in highway and transportation system helps the competitiveness of local and regional economic growth in such a way that labor productivity and market access are improved by decrease in travel time and cost, as well as b y increase in reliability. Project Life Cycle Costs The life cycle cost s of a highway project are composed of investment costs and operation expens es. Investment costs are costs incurred during the planning, engineering, and construction phases of the project. Operation expenses cover costs incurred during the operation, maintenance, and renovation phases, and may also include the demolition costs if necessary.

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102 Transportation Equity Act for the 21 st Century provides a definition of Life Cycle Cost Analysis initial costs and discounted future costs, such as m aintenance, user, reconstruction, rehabilitation, using an LCCA driven cost effectiveness ranking to inform the STIP (Statewide Transportation Improvement Pr ogram) and TIP (Transportation Improvement Program). In addition, FHWA ocess begins with establishment of alternatives and follows by determination of activity timing and estimation of agency and user costs; after computation of life cycle costs, the results are finally analyzed. In most evaluations, construction costs and ma intenance costs are sufficient to consider, since they typically account for most of the project life cycle costs. According to FHWA, user costs, based on capacity flow analysis, can be estimated from vehicle operating costs, delay costs, and crash costs. In addition, the FHWA suggests including 5~10% project contingency to account for unforeseen changes. Project Economic Benefits Corresponding to the project life cycle costs, the project economic benefits should also cover the whole life cycle of the proj ect. Main categories of benefits are listed as follows. Vehicle operation cost savings Benefits due to reduce in mileage Benefits due to reduce in operation expenses Benefits of time saving due to increase in vehicle velocity Benefits due to decrease in truck travel time Benefits due to decease in congestion Accident cost savings Environmental cost savings

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103 Above mentioned are examples of direct benefits. Major indirect benefits include land use impacts, employment, and other non user benefits. Other categories of benefits or costs have also been studied. Examples of such categories include changes (positive or negative) in the environment and changes (loss or improvement) of recreational facilities. Among these economic benefi ts, travel time savings (TTS) is usually the principal benefit of a highway project. USDOT (2003) suggested using the value of travel time savings (VTTS) in all DOT benefit cost analyses. There has been no unique formula for VTTS calculation; however, per person hour values are often recommended as a percentage of total earnings. An estimate for travel time savings (TTS) can be made as follows: ( 5 1 ) Where: = Traffic volumes on the i th and j th roads on current and future roadway networks, respectively. = The lengths of the i th and j th roads on current and future roadway networks, respectively. = The average speeds on the i th and j th roads on current and future roadway networks, respectively. The value of travel time reflects the opportunity cost for a traveler in terms of dollar values that the traveler is willing to pay for savings of time. The USDOT recommends a 2013 U.S. per person hour dollar value of $13 for local travel and of $19 for intercity travel, combining both personal and business travels.

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104 Economic Analysis Net Present Value : Net present value (NPV) is the present value of all cash flows, both positive (i.e., cash inflows) an d negative (i.e., cash outflows), associated with the project investment and expenses. In other words, it is the present value of the benefits minus the present value of the costs over the project life cycle. The higher the NPV, the more attractive and des irable the project being evaluated is. Given the project life cycle of n years, the NPV can be expressed as follows: ( 5 2 ) Where r is the interest rate per period. If in Year t NPV = 0 then we say t is the payback period. If a specific r* satisfies the equation NPV = 0, then we call r* the internal rate of return (IRR) of the project. Benefit Cost Analysis : As has been discussed in Chapter 4, the Benefit Cost Analysis (BCA) is usually conducted to compare the proj ect benefits and rewards with project costs and risks in order to evaluate alternatives. Table 5 2 lists some components of such analysis. Specifically for transportation project, t he USDOT proposes a ten step BCA process: 1. Establish objectives 2. Identify constraints and specify assumptions 3. Define base case and identify alternatives 4. Set analysis period 5. Define level of effort for screening alternatives 6. Analyze traffic effects 7. Estimate benefits and costs relative to base case 8. Evaluate risk 9. Compare net benefits and rank alternatives 10. Make recommendations Main benefits and costs associated with transportation projects are listed in the Table 5 3.

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105 Inflation has to be adjusted when we conduct the BCA. The Federal Highway Administration provides National H ighway Construction Cost Index, or NHCCI (former Bid Price Index, or BPI), for inflation adjustments. Specifically: Base year dollars = Data year dollars x Base year price index / Data year price index ( 5 3 ) Data year dollars = Base year dollars x Data year price index / Base year price index ( 5 4 ) Table 5 4 further lists the key highway financials in the United States. The data were extracted in 2010. Technological Attribute Analysis The purpose of technological objective analysis is to evaluate the quality of the network by identifying the impact of the potential project devel opment on the improvement of network traffic quality and level of service. Change in Network Connectivity Connectivity reflects the relative degree of connectedness within a transportation network. Connectivity is a measure of accessibility without regard to distance: The higher the connectivity, the lower the isolation and the higher the accessibility. Places with high connectivity are often considered important since they are the best connected. Consequently, changes in the highway network connectivity re flect the impact of new projects on the existing network. The highway network changing ratio (NCR) can be calculated as follows: ( 5 5 ) Where: C = Degree of network connectivity with the new project C 0 = Degree of net work connectivity without the new project Invest = Total construction costs and operation and maintenance expenses The degree of network connectivity in a specific area, C i can be estimated as:

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106 ( 5 6 ) Where: L = To tal highway mileage within the area H = Average distance between two nodes N = Number of total nodes in the area Change in Accessibility Highway node accessibility reflects the mean travel time (or distance, or expenses) from a certa in point in the area through the highway network to a certain destination. Highway Accessibility can be measured by the degree of a node, the total accessibility matrix, the Shimbel accessibility matrix (aka. The D matrix), or the valued graph matrix. Accessibility mainly relies on location and distance. Location can be identified by th e combination of its population, economic activity level, tourist attraction, etc. Distance can be measured by length, time, cost, or energy spent. Environmental Attribute Analysis Construction and operation of highways may inevitably cause dama ges to the environment, and thus integration of environmental impact assessment (EIA) into highway development is crucial. Development of highways, from land acquisition through road construction to operation and maintenance, can bring many potential adver se impacts on the environment. An EIA process is typically composed of three key elements as shown in Figure 5 3 (Fwa 2005, p.3 1~p.3 22).

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107 Similarly, environmental objective analysis needs to enclose an alysis for both potential costs and benefits to the environment brought by the new project. Externalities also need to be estimated in terms of costs associated with controls over waste materials, pollution, noise, etc. Sustainability appraisal methods can be applied to such analysis. Ugwu et al. (2006a, 2006b) proposed a framework for infrastructure projects sustainability assessment, using both the weighted sum model and the additive utility model. Their procedure leads to the Sustainability Index (SI) of infrastructure projects and the highest corresponding value of SI is thought to be preferred as it maximizes the sustainability of a design proposal. Here they define the SI as a crisp, additive/commutative utility value of performance measurement based o n sustainability appraisal decision matrix in terms of indicators of environment, health and safety, economy, societal, resource utilization, and project administration. The statutory authority of the Federal Highway Administration (FHWA) developed a frame work with six principles for the National Environmental Policy Act (NEPA) review purpose in transportation decision making. Generally, the NEPA process begins with identification of purpose and need and consideration of project impacts, followed by develop ment and evaluation of alternatives. The process also requires interagency coordination and public involvement. Mitigation of adverse project impacts is the final step of the NEPA process. Obviously, such a decision making process has to be based on correc t prediction about transportation demand as well as on reasonable judgment for roadway deficiency, and this is a critical component of the big picture for highway engineering projects decision making. When using BCA as a method to assess the environmental impact, Heinzerling and Ackerman (2002) argued that BCA usually leads to biased and misleading results for

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108 environmental protection analysis. Specifically, they held the view that cost benefit analysis suffers from four fundamental flaws: 1. The standard eco nomic approaches to valuation are inaccurate and implausible. 2. The use of discounting improperly trivializes future harms and the irreversibility of some environmental problems. 3. The reliance on aggregate, monetized benefits excludes questions of fairness an d morality. 4. The value laden and complex cost benefit process is neither objective nor transparent. Instead, they recommended some alternatives to the use of BCA for environmental protection, such as technology based regulation, market based regulation, an d environmental right to know programs. sustainable construction evaluation, among other things, only if it is available, reliable, and measurable. They further developed pr ocedures of applying Technique for Order Preference by Similarity to Ideal Solution ( TOPSIS ) or Simple Additive Weighting ( SAW ) for construction sustainability assessment. Goh and Yang (2013) identified, between traditional models with benefit cost analysi s and life cycle cost analysis and proposed models with sustainability based financial decision support analysis, the knowledge gap, including difficulties in measuring sustainability, inconsistency in measurement standard, ambiguity in identifying sustain ability related costs and impacts, and omission of social and environmental related costs. They also summarized from the literature three sustainability related cost categories for highway infrastructure as agency costs, social costs, and environmental cos ts; each of them has several main components and sub factors. Generally, EIA must be carried out in all the project phases for development of sustainable highways and must be fully integrated with different project phases.

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109 Safety The FDOT Mission Statemen system that ensures the mobility of people and goods, enhance economic prosperity and 4 been continuous ly improved due to the efforts of FDOT and many other organizations. The Highway Safety Improvement Program (HSIP) provides methodology for highway safety improvement projections. A simple way to look into project safety is to evaluation project alternati ves by estimating monetary value of project benefits, number of total crashes reduced, number of fatal and incapacitating injury crashes reduced, number of fatal and injury crashes reduced, and cost effectiveness index (Layton, 2010). Development of an Ind ex System for Highway Engineering Projects Priority Ranking Principles The factors to be considered in the projects priority ranking should reflect the objectives of the road investment program (Thagesen 2003, p.65). Those factors should be measurable and be able to indicate the significance of the project. Therefore, the following principles should be considered when constructing an index system for highway engineering projects priority ranking. Fwa (2005, p.1 11 and p.1 12) listed some of the common reaso ns that lead to project failure in developed countries, such as poor public relations, unrealistic budgets, inappropriate design, lack of cooperation, wrong placement of expertise, distrust, as well as sensitive environmental and social issues. 4 http://www.dot.state.fl.us/publicinformationoffice/moredot/mvv .shtm accessed April 24, 2015

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110 Pertinence : The index system must be pertinent to the solution to the highway network requirement. In the United States, sufficiency ratings have been developed in most states to help determine which highway sections should be improved under budgetary constraints. For example, the 2014 Florida Statutes (Chapter 335, Section 335.07) requires that the FDOT adopt a sufficiency rating system for roads on the State Highway System and the determination of rating be based on structural adequacy, safety, and service and fur ther on a series of considerations (Figure 5 4 ). Please note that road improvement costs are not taken into account; sometimes this is believed a drawback of the sufficiency rating method. Based on the sufficiency rating or other similar rating scales, a priority index (PI) can be developed as follows together with consideration of incremental costs: ( 5 7 ) Wher e: R i = improved condition rating; R e = existing condition rating; w = importance weight; and C = incremental costs. Practice of State DOTs : Many State DOTs have adopted some form of project prioritization process, although the applied prioritization crit eria vary. Table 5 5 shows the application developed by DelDOT. The North Carolina Department of Transportati on (NCDOT) developed highway scoring criteria 6 for strategic transportation investments prioritization, measured on a 0 to 100 point scale (Table 5 6) Construct of a Comprehensive Index System There are a great number of fa ctors that can influence the priority of highway engineering projects construction, and thus selection of appropriate factors has to be made so that the selected 6 https://connect.ncdot.gov/projects/planning/STIData/Highway_CriteriaSummaryReport.pdf

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111 ones can accurately reflect the project condition in different aspects, such as necessity, imp ortance, benefits, costs, and traffic impacts of the construction of the highway engineering criteria and calculated utility values to rank highway infrast ructure rehabilitation projects within budget constraints. Ziara et al. (2002) proposed a risk based AHP model for infrastructure projects prioritization by using project importance, sector importance, finance suitability, execution suitability, operation suitability, reliability, and consequence of failure as multiple criteria. Degrees of Urgency : Flow ratio (v/s ) can be used as a measurement of degrees of urgency. It is the ratio of the actual flow rate or projected demand v on an approach or lane gro up to the saturation flow rate s. Degree of saturation is used to compare traffic demand with the total capacity of a road. It is calculated as a ratio of demand to capacity on each approach to the junction. A 100% degree of saturation (i.e., equal demand and capacity) indicates that no further traffic is able to progress through the junction. Values over 85% are typically regarded as suffering from traffic congestion, with queues of vehicles beginning to form. Classification of Roadways : As early as in 19 89, FHWA developed a classification system of roadways according to their functions. The revised functional classification categories, identified by FHWA (2013), consist of four roadway classes: Local roads: have low operating speeds, serve local residence s and businesses, and provide access to collectors. Collectors: have intermediate travel speeds, channel traffic from local roads to arterials, and trade off the demands between land access and mobility. Minor arterials

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112 Principal arterials (including inter state highways, freeways, and expressways): provide mobility (i.e., safe, reliable, and efficient travel) between towns and cities, and are used for long distance travel at high speeds. Obviously, such a classification system partly reflects the degree of urgency of different roadways and thus po tentially indicates the construction priority in a sense. This gives us an priorities. The following coefficients have been assumed in this dissertation: Loca The degrees of urgency for the highway engineering projects are obtained by calculating the weighted average of th e degree of saturation and the coefficient of the roadway classification. Also note the distinction between highways in Florida (which include all roads in Florida) and highways on the Florida State System (which consists of highways maintained by FDOT). A variety of terminology exists for highway construction projects. Degrees of urgency can also be connected with the status of congestion. FDOT (2011) identified congested roadways and bottlenecks on Florida SIS by using a combination of planning time ind ex and frequency of congestion. Here congested roadways and bottlenecks were quantified by the duration, extent, intensity, and reliability of the congestion. Importance of Highway Engineering Projects : The importance of highway engineering projects also needs to be taken into account when we prioritize the development and construction of the projects. It makes sense that priority should be given to those highway projects that have large impacts on the roadway network, the function of the network, and the level of service. The degree of importance of the roadway can be reflected by the importance of the nodes that connect different roads or links.

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113 The importance of the nodes indicates the contribution of the corresponding area to traffic demands, and such c ontribution can be decomposed of both direct traffic demand statistics (e.g., freights) and indirect social economic statistics (e.g., population, average vehicles per household, per capita GDP, average income, etc.). Therefore, the degree of importance of the nodes can be expressed as follows: ( 5 8 ) Where: = The degree of importan ce of Node = The j th traffic st atistics of Node i = The j th social economic statistics of Node i = The average of the j th traffic statistics, = The average of the j th social economic statistics, = The weights of each statistics Further, the importance of the link between Nodes i and j can be determined as follows: ( 5 9 ) Where: = The degree of importance of the link between Nodes i and j = The degrees of importance of Nodes i and j, respectively = The nu mbers of links that are directly connected with Nodes i and j, respectively

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114 Economical Assessment of Highway Construction : As a critical part of highway construction feasibility analysis, the economical feature of highway construction must be assessed. Th e cost benefit analysis should be conducted on the basis of traffic demand forecast and engineering characteristics. Among others, NPV and IRR are usually calculated with regard to the highway construction economical assessment. A case in point is Florida which uses the following key performance indicators: Affordability Index: a measure of toll revenue to annual vehicle miles traveled. Operating Expense Percentage: a calculation of operations and maintenance expense as a percentage of r evenue. System Transportation Asset Reinvestment (STAR): a ratio of income before contributions to toll revenue. Traffic Effects of Highway Construction : The traffic effects of highway construction are reflected by the degree to which the roadway network system is improved in terms of level of service. Such improvements include the improvements on both the degree of congestion and the travel time. In other words, we want to know the impacts of construction of a specific highway on the improvements of the r oadway network operation efficiency and quality. The impact on the roadway network operation efficiency can be assessed by the change in total travel time. Reduce in total travel time is obviously a sign of traffic improvement and can be estimated. We must notice that the investment level can have huge impact on the level of improvement, and thus we may want to know the total time savings per dollar value, i.e., the roadway network operation efficiency improvement rate: ( 5 1 0 )

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115 Where r O is the efficiency improvement rate, and I is the invested dollar amount of money. Similarly, we can calculate the roadway network congestion improvement rate, based on the calculation of the congestion degree for the roadway network. Preference for mode choice is often designated by a utility function composed of both trip cost and trip time. A typical utility function for a specific transportation mode can be simply developed as a linear relationship as follows: ( 5 1 1 ) Where: = Utility, trip cost, and trip time for mode I, respectively = Constant = Relative weights of each service variable Apparently, a passenger is most likely (and thus has the largest probability) to choose the trip mode with the highest utility. A logit model further estimates the probability , that a user with a utility value , will select mode i from n modes being considered ( 5 1 2 ) Highway maintenance costs can be budgeted according to historical trends for remedial maintenance and according to the pavement management system (PMS) outputs for preventative maintenance. The estimated annual costs ranges for remedial and preventative maintenances are $1,000~$5,000/lane kilometer and $4,000~$8,000/lane kilometer, respectively, and the sum of both costs can account for 1%~4% of the initial highway construction costs (Fwa, 2005). Selecting a specific value from both ranges should depend on the age of the road, the importance,

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116 the traffic levels, the location, etc. In a National Cooperative Highway Research Program (NCHRP) report, Markow (2011) suggested a full co st determination process. Summary The main goal of the prioritization process is to select projects that will generate maximum value, both monetary and non monetary, resulting from trade off optimization under budget constraints. To simplify the process, we assume that the best design alternative for each project has been submitted and been used in the process. Projects to be prioritized should be those listed in the long range planning and in the future work program and thus the prioritization is an on go ing process. In practice, the most widely used prioritization methods include NPV, IRR, B/C ratio, incremental B/C analysis, cost effectiveness measures, as well as optimization methods. The purpose for ranking highway engineering projects priorities is to effectively and efficiently use the highway development capital. Specifically, we aim to achieve a trade off optimization of project time, cost, and quality for the whole project life cycle. We expect to achieve optimum economic benefits and optimum highw ay network traffics with least and reasonable capital investment for highway planning, construction, operation, and maintenance. Based on those economic, technological, environmental, and safety attribute, an index system for highway engineering projects p riority ranking has been developed in this chapter. Chapter 7 will follow on the proposed index system with a case study.

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117 Table 5 1. Importance of Transportation Infrastructure Category Possible Indicators User Impact Traveling costs reflected by time safety, comfort, and reliability Economic Impact Changes in employment, personal income, property values, business sales volume, and business profit Government Fiscal Impacts Changes in public revenues and expenditures Other Social Impacts Air quality and other environmental conditions Table 5 2. Components of Benefit Cost Analysis Benefits Costs Increase in personal income Increase in personal auto benefits Increase in consumer surplus Construction costs Operations and maintenance costs General o verhead and administration costs Table 5 3. Benefits and Costs Associated with Transportation Projects Agency Costs User Costs/Benefits Associated with Work Zones User Costs/Benefits Associated with Facility Operations Externalities Design and engineeri ng Land acquisition Construction Reconstruction/Rehabilitation Preservation/Routine maintenance Mitigation (e.g., noise barriers) Delay Crashes Vehicle operating costs Travel time and delay Crashes Vehicle operating costs Emissions Noise Other impacts Sou rce: USDOT (2003) Table 5 4. Key Highway Financials in the United States Revenue Sources Expenditure Source Percentage (%) Type Percentage (%) General funds: 26.5 Capital outlay: 48.8 Motor fuel taxes: 26.0 Maintenance and traffic services: 23.8 Bonds : 14.9 Highway patrol and safety: 8.8 Motor vehicle taxes: 12.2 Administration: 7.9 Tolls: 4.3 Bond retirement: 6.0 Other: 16.1 Interest on debt: 4.8 Data Source: USDOT (2013)

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118 Table 5 5. DelDOT Project Prioritization Process Criteria Weight Descripti on DelDOT 7 Safety 33.0% The ability of the transportation system to allow people and goods to move freely, without harm System operating effectiveness 24.8% The ability of the transportation system to efficiently move people, goods and services without excessive delay or inconvenience Multi modal mobility, flexibility/access 15.6% The ability of a project to provide efficient movement of people and goods between destinations by motor vehicle, pedestrian, bicycle and transit modes Revenue generation/ economic development/jobs & commerce 7.9% The ability of a project to facilitate or support business development and employment Impact on the public/social disruption/economic justice 7.2% The assessment of the project on the transportation system as it relates to existing communities and population centers Environmental impact/stewardship 6.5% The effect of the transportation system on energy use and the natural environment System preservation 5.0% Fix It First/State of Good Repair addresses the impr ovement of the physical condition of existing transportation assets 7 See: https://www.deldot.gov/information/pubs_forms/CTP/pdf/DelDOT_project_prioritization_criteria_summary.pdf

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119 Table 5 6 NCDOT Project Prioritization Process Criteria Formula Weight Congestion (Existing traffic volume/Roadway capacity ratio*100*60%) + (Existing traffic volume/1000*40%) State wide mobility 30% Regional impact 25% Division needs 20% Benefit/Cost Travel time savings/Project costs Statewide mobility 30% Regional impact 25% Division needs 20% Economic competitiveness Number of long term jobs created (50%) + Value adde d in dollars based on productivity change in division economy (50%) Statewide mobility 10% Safety For segments: (Crash density*33%) + (Severity index*33%) + (Critical crash rate*33%) For intersections: (Crash frequency*50%) + (Severity index*50%) State wide mobility 10% Regional impact 15% Division needs 10% Multimodal ((V/C Ratio [STRAHNET] x 100) x 25%) + ((V/C Ratio [Route to Transportation Terminal] x 100) x 25%) + (Truck Volumes / 100 x 50%) Statewide mobility 20% Accessibility / Connecti vity Measured by county tier designation, upgrade roadway function, and commute times Regional impact 10% Lane width The existing lane width DOT design standard lane width Regional impact 10% Division needs 10% Shoulder width The existing paved s houlder width DOT design standard paved shoulder width Regional impact 10% Division needs 10%

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120 Figure 5 1. FDOT Highway Analysis Approach Source: FDOT

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121 Figure 5 2. Scoring System Developed by Utah Department of Transportation Source: Schultz and McGee (2009)

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122 Figure 5 3 EIA Process Figure 5 4. Sufficiency rating system for roads on Florida State Highway System

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123 CHAPTER 6 APPLICATION OF MULTI OBJECTIVE DECISION MAKING OPTIM IZATION: PROJECT TIME COST QUALITY TRADE OFF ANALYSIS Basic Assumptions and Notations A general linear, deterministic time cost quality trade off analysis is based on the following assumptions: Direct cost is negatively related with project/activity time. Indirect cost (general overhead and administration expense) is positively related with project time. High project/activity quality is achieved when the project/activity is executed within reasonable (efficiency) time. A job task can be completed with a va riety of modes, and each mode varies in time, cost, and quality due to the selection of crews, materials, equipment, and other fuzzy factors. Linear relationships are also assumed in the linear model analysis. The following notations will be used: : number of activities : early start date of activity i (assume ) : duration of activity i : normal (accepted longest) time for activ ity i : crash time for activity i : normal cost for activity i : crash cost for activity i : normal quality for activity i : c rash quality for activity i : total time (duration) of the project

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124 : total project cost : overall project quality Given these assumptions and notations, linear relationships bet ween project time and cost and between project time and quality can be drawn in Figures 6 1 and 6 2 Basic Problem Statement The duration of each activity i is bounded by its normal time and by its crash time: ( 6 1 ) For each activity i : ( 6 2 ) Total project duration: ( 6 3 ) where CP is the activity set on the critical path. Total project cost: ( 6 4 ) where a nd according to the (negative) linear relationship between project cost and time. Overall project quality: ( 6 5 )

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125 where and according to the (po sitive) linear relationship between project quality and time. The linear programming model is developed to get the Pareto optimal solution set by minimizing T and C and maximizing Q For different budget constraints and quality tolerances, minimizing T yie lds the shortest project completion times. Similarly, minimizing C yields the lowest project cost given completion due dates and quality tolerances. Maximizing Q yields the best project quality subject to a function of budget levels and project duration. F urther Development of Models The basic problem statement is based on the assumption of linear relationships, and without consideration of other indicators and uncertainties that have often been met in real engineering practice. It is also limited in the c onstruction phase of a project. Further development of optimization models should take into account those constraints. Revision to the C ost T ime L inear R elationship The expression of project cost ( C ) in the above section assumes increasing cost linearly by reducing project time. This is questionable in two major aspects: firstly, in a project, while direct cost is probably negatively related with activity time (and thus crash cost is higher than normal cost), indirect cost (e.g., general overhead and admi nistration expense) increases with project time. As a starting point, a simplified non is: ( 6 6 ) Where and can be obtained from the corresponding time cost curve. ) is:

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126 ( 6 7 ) where is the indirect cost rate ($/ day) and is a constant. The total project cost is now: ( 6 8 ) Revision to the Quality Time Linear Relationship The quality time relationship is not linear because of at least two reasons: Firstly, optimal quality can seldom crash time) or delayed (i.e., the project duration is close to the longest accepted time); and ity. More reasonable assumptions should be made that optimal activity quality can be achieved when the activity is finished within some commonly expected time, and that the overall project quality can be expressed by a reliability function of each activity relative to the overall project quality, determined by historical data or expert opinions. Therefore, the adjusted expression of overall project quality is: ( 6 9 ) Where and Other, more complicated expressions of Q will be discussed in the dissertation. For example, a reliability function can be applied to define activity j s quality ( q j ) based on its q i ):

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127 ( 6 10 ) where is the set of activity j Application of Time Value of Money Infrastructure engineering projects are us ually capital intensive, requiring large amounts of money and other financial resources. Cash flows of the projects and the impact of time value of money, although often neglected, must be optimized within the constraints of time, cost, and quality objecti ves. Essentially, financing and its impact on project profits should be treated as a cost accrued, which most optimization models fail to reveal. The net present value (NPV) method is usually believed an effective way to count the time value of money. NPV is defined as the discounted sum of all expected future revenues minus the initial cost and the discounted sum of all expected future costs (Hirst 2001; Newan et al. 2004). The concept of NPV has been employed by a number of researchers to solve project s cheduling and time/cost trade off problems. Based on expressions discussed above the present value of the project cost ( ), under a discount rate of r, is: ( 6 11 ) Now the cost objective is to minimize Of course, a more accurate way to deal with financing costs requires developing a cash flow model of each activity at each project phase over the project life cycle. A comprehensive finance based scheduling (in terms of time cost quality trade off optimization) model over the project life cycle will be presented in this dissertation.

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128 Existing literature implies continuous changes among project time, cost, and quality; however, they often perform in a discrete way in p ractice. Meanwhile, one of the optimization objectives is to minimize project costs; however, minimum costs do not necessarily indicate maximum benefit for decision makers. Most of the existing models also do not take the time value of money into considera tion. Decisions on project time cost quality trade offs affect, both directly and indirectly, the time, cost, and quality. The project duration is T (in years) The price (value) in the contract is V The payment, occurs at the end of the i th month. The pre payment percentage is and thus the pre payment is Similarly, assume the per centage for quality (performance?) bond is and thus the performance bond (quality warranty?) is which will be paid at Time (in years). The net present value of the contract va lue, V is: ( 6 12 ) Now we consider bonus and punishment allocated by the project owner. Bonus and punishment have been applied by the project owner for the purpose of project control. They should not be neglected by th e contractor, as the dollar amount of bonus and/or punishment may payment method of bonus and punishment, along with the impact of time value of money, are analyze d and modeled in this research. Assume the project deadline is D (or rather, the project is required to be completed within D days). The contract price, V will be paid in full to the contractor if the project is completed

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129 within the timeline If the project is completed at time T before time the contractor will receive an additional amount of money, as bonus. If the project is completed at time T after time however, the contractor will get punished by an additional amount of money, as punishment. The multi objective optimization function of the total project can be summarized as: ( 6 1 3 ) Intro ducing Multiple Attribute Utility Functions Utility analysis has also been conducted to help make better decisions by building mathematical models of a decision function ( U ) for the time cost quality trade off analysis can be written as: ( 6 1 4 ) where: is the weight for the performance P (time T cost C or quality Q in this case) and is the single attribute utility function for the performance P For a risk neutral person, the utility function can simply be defined as: ( 6 1 5 ) where and are constants and can be determined based on the best and worst performances, and y denotes the performances for an alternative. Zhang and Xing (2010) suggested the following form of utility function for the TCQT analysis:

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130 ( 6 1 6 ) For the consistence purpose, the above expressions use superscripts N and C to denote normal and crash schedules, respectively. Now the solution to the TCQT problem is to find t he optimal alternative that has the largest multiple attribute utility, namely: ( 6 1 7 ) Project Time Cost Quality Optimization Project quality relies on the quality of each task. Completing a task within different time sched ules, however, results in different levels of quality. The following assumptions are made: Reducing normal time of a task will degrade the task quality. Lengthening normal time of a task, however, will not necessarily upgrade the task quality; conversely, a slightly degraded quality is expected. Therefore, the quality level for the i th task can be calculated as: (6 18) Where is the output quality level for the i th task. is the input quality level of the j th predecessor and task I has m predecessors. Please note that Further, the fact that project time, cost, and quality compose an Iron Triangle gives indication that changes to any of the three va riables will affect the other two. Specifically: Reducing project time will most likely result in increase in cost and decrease in quality. Reducing project cost will most likely result in increase in time and decrease in quality. Increasing project qualit y will most likely require increase in both cost and time. Two more presumptions are made before analysis is conducted in the following chapters:

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131 Orders of each task as well as its predecessors and successors remain the same. Therefore, if time for each ta sk is known, the project time can be calculated with the Critical Path Method. Quality (or rather, level of quality) is relatively scaled and rated within [0,1], with 0 representing the minimum quality level and 1 representing the maximum quality level. Th is makes the level of project quality comparable under different engineering conditions. A variety of time cost trade off models have been proposed by researchers with the development and progress of network program techniques. Two categories are generally referred to in the literature: One assumes unconstrained resources with constrained schedule; the other assumes unconstraint time with constrained resources. The first category is more practical and is the focus of this research. It is also necessary to p ropose different expressions for direct cost and indirect cost, as they change with project time not in the same mode (way). Generally speaking, shortening project duration, no matter how it is achieved, will increase direct costs, as more labors or equip ment have to be used, or labors have to work overtime. Assuming a quadric relationship, a curve for direct costs vs. project time can be plotted. On the other hand, indirect costs (mostly overheads and general administration expenses) decrease with the dec rease in project time. A linear relationship between indirect costs and project time is assumed in this research. Therefore: (6 19) Where: is the normal cost. is the n ormal duration for task i is the actual duration for task i

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132 Summary In this chapter, a project time cost qua lity trade off optimization model is proposed based on the multi objective decision making theory discussed in Chapter 4. Compared with single objective decision problems, multi objective problems are much more complicated, as those multiple objectives are potentially such conflicting that measures for improving one objective would most likely worsen the performance of other objectives. Therefore, instead of seeking for a unique optimization solution (as is the case for single attribute decision problems), we have to put effort to find an optimization set, i.e., the Pareto optimality, for multi objective optimization problems (Zio and Bazzo, 2012). Figure 6 1. Linear Relationship Between Time and Cost Figure 6 2. Linear Relationship Between Time an d Quality

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133 CHAPTER 7 CASE STUDY I: SIS HIGHWAY PROJECTS PRIORITIZATION IN FDOT DISTRICT 2 In this case study, potential highway development projects on Strategic Intermodal System ( SIS ) highway routes in FDOT District 2 are selected as samples Particip ants in the decision making process may include stakeholders representing FDOT, planning authorities, and local government agencies. Project goals, criteria, weights, and alternatives should be established by those stakeholders. This case study does not, h owever, incorporate all direct inputs from those stakeholders because the purpose of this case study is to evaluate the efficacy of the proposed model. Therefore, the inputs here rely to a large extent on the researcher to serve the above stakeholder roles Case Description In July 2014, the FDOT adopted the Strategic Intermodal System (SIS) 1 st Five Year SIS funded projects for the current fiscal ye is extracted and displayed in Figure 7 1 The information about project limits, location, major Strategic Investment Tool (SIT) scores are also summarized. The SIT is used for project prioritization and selection purposes by measuring the following six major goals in a total of 120 points ( Figure 7 2 ): (1) safety & security; (2) maintenance & operations; (3) mobility & connectivity; (4) economic competitiveness; (5) livable communities; and (6) environmental stewardship. those critical projects that were picked based on the e valuation and prioritization processes, and in such processes SIT was developed as one of the tools for determining highway project

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134 priorities. The SIT highway and connector measures are listed as follows. Figure 7 3 illustrates the decision making process of FDOT and its partners for funding SIS investments. In comparison, High Country Rural Planning Organization (RPO) of North Carolina Department of Transportation (NCDOT) proposed a project solicitation and ranking process NCDOT 2015) to evaluate STIP transportation projects For highways, RPO assigns a total of 100 points to 9 prioritization criteria, as shown in Table 7 1 The FDOT is decentralized in 7 districts (Figure 7 4) District 2 is located in Northeast Florida and includes the following 18 counties: Alachua, Baker, Bradford, Clay, Columbia, Dixie, Duval, Gilchrist, Hamilton, Lafayette, Levy, Madison, Nassa u, Putnam, St. Johns, Suwannee, Taylor, and Union. As of now, this district has 2,556 centerline miles and 8,197 lane miles on the State Highway System, with more than 43.2 million miles daily travel 8 Data Sources Natio nally, the USDOT Bureau of Transportation Statistics developed the National Transportation Atlas Database (NTAD), a database of transportation network data in the United States. Evaluation of conditions of bridges and highways can be collected from the Nat ional Bridge Inventory (NBI) and the Highway Performance Monitoring System (HPMS), respectively. In additional, a number of states have established their own pavement management systems and safety reporting systems. Also nationally, the Fatality Analysis R eporting System (FARS) documents all country wide fatal crashes. Table 7 2 lists major national data sources. FDOT and some other Florida agencies maintain a number of data bas e. Data used in this dissertation research were obtained from the following sources. 8 See http://www.dot.state.fl.us/publicinformationoffice/moreDOT/districts/dist2.shtm for details.

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135 Project environmental impact analysis data are obtained with the Environmental Screening Tool on the Efficient Transportation Decision Making (ETDM) Web site : https://etdmpub.fla etat.org/est/ ETDM published on the website information about proposed transportation projects, information including environmental data and discussion, sociocultural data, and agency environmental comments, etc. The Florida Traffic Safety Portal, developed by the State Safety Office of the FDOT, makes information available about tools, data, and ideas about traffic safety in Florida. Safety information and data (e.g., crash statistics) can then be obtained from this Portal: https://fdotewp1.dot.state.fl.us/TrafficSafetyWebPortal/ Updated project information can be checked through the Office of Work Program and Budget of FDOT. Projects in the Five Year Work Program are displayed t here, information including project description, type of work, item number, length, scheduled activities, fiscal year budgets, and map of item. http://www2.dot.state.fl.us/fmsupportapps/workprogram/WorkProgram.aspx Among them the map of item is made available through the interactive FDOT WPA / PSM online tool. http s://wpagis.fla etat.org/viewer.htm

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136 Brief Description of Selected Projects Figure 7 5 shows the major highway projects being planned in FDOT District 2. They are at different project planning phases. Nine out of those projects were randomly selected for p rioritization analysis using the methodology proposed in the dissertation. Travel demand in District 2 was first analyzed. Prioritization criteria were chosen from the discussion in Chapter 5 Weights of each criterion were calculated using the suggested A HP Entropy method as well as the Fuzzy AHP method. The weights were then inputted in the TOPSIS spreadsheet. Based on the TOPSIS result, a prioritization list of the 9 projects was suggested. Demand Analysis: Trip Generation Regional Travel Demand Model: Descriptive Statistics Samples for District 2 are first extracted out from the overall data file ( i.e., the Florida samples from the 2 009 National Household Travel Survey ). Cases are then sorted by district. This results in 1879 cases in total for District 2 Before cleaning the data, we may want to review the data so that we can later clean the data and create the explanatory variables reasonably. An overview of the original data from those households in District 2 is described in detail in Appendix A. Some of the observations are listed as follows. Count of Household Members : Two member households are common in District 2 Almost half of the households are comprised of two members (49.3% in District 2). Few households (less than 2% of total households) in the district have more than five members in them. Count of Adult Household Members at Least 18 Years Old : Two adult households are typical (64.8% in District 2). Followed are one adult households (23.8% in District 2). Around 10% of the households have more than two adults.

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137 Number of workers in HH : 43.3% of the households in District 2 have no workers in them More than half of the households in District 2 have one (34.4% ) or two (19.5%) m embers employed. Life Cycle for the HH : The life cycle for the households is indicated in the frequency table. As we may see, households with two or more retired adults but without children are very common in District 2 (32.9%). Number of Drivers in Household : Two driver households are common (57.3% in District 2). This is consistent with the observation in count of adult household members. Similarly, followed are one driver households (27.9% in District 2). Count of Household Vehicles : Two vehicle households a re common in District 2 (42.4%) Few households have more than 5 vehicles in this district Derived Total Household Income : Assume low income households are those with derived total income less than $30,000, med income $30,000~$7 9,999, and high income more than $80,000. T here are 23.6% high income households in District 2 36.6% low income households in District 2. Housing Unit Owned or Rented : Most households in District 2 (more than 90%) own their houses, and detached single hou ses are typical (around 70%). Other Observations : Most of the households in District 2 are white (accounting for around 90%). More than half (52.3%) of the households in District 2 report that their home addresses are located not in an urbanized area. I t seems that households in District 2 generate more trips on Mondays than other weekdays or weekends. Most of the households in District 2 are permanent residents, namely, they lives more than 6 months a year in Florida. Seasonal travelers are less than 2 % in both districts.

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138 Count of Household Vehicles by Count of Household Members Crosstabulation : Crosstabs for HHVEHCNT by HHSIZE are also run for analysis. Observations for both districts are similar: Households that have only 1 adult typica lly own only 1 car. Households that have 2 or more adults typically own 2 cars; in such cases, increase in number of adults in a household does not lead to significant increase in number of cars. New Variables Creation : Other than the existing variables t hat have been defined in the original data, the following new variables are created based on the observations from the descriptive statistics. Variables for household life cycle are created, broken down by retired households, working households without chi ldren, and working households with children. A binary variable for seasonal residents and permanent residents is created. A household is considered seasonal if they live in Florida more than one month but less than six months a year. Market segmentation va riables are created for increment of cars, from zero to 3 or more (3+). The number of children variable was created by subtracting the number of adults from the household size. New variables for income are created, broken down by low, medium, and high. Low income households earn less than $30,000. Medium income households earn incomes ranging from $30,000 to $80,000. High income households earn greater than $80,000. Binary choice variables are created for both the small city and big city variables. A small city has a population under 500,000, where a large city is any population greater than this. Binary choice variables are created for trips made on a weekday versus a weekend, as well as for trips made on Monday versus other days. Binary choice variables ar e also created for households owning a housing unit versus renting a housing unit. These variables are listed in Table 7 3

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139 Considering possible connections between household income and number of vehicles and between household income and number of adult household members, the following interaction variables are further created. One set of interaction variables are created by multiplying the three income levels by the number of vehicles in the household. Another set of interaction varia bles are created by multiplying the income levels by the number of adult members in the household. See the following table. Data Cleaning : The possible explanatory variables, including the existing variables and the newly created variables, make the following data cleaning process necessary. FL1: Remove invalid cases based on number of months that the house hold lives in FL. Cases with negative values are removed. HHFAMINC: Remove invalid cases based on derived total household income. Cases that included the values 9, 8, or 7 are removed. URBANSIZE: Remove invalid cases based on size of urban area. Cases w ith a value of 1 are removed. After data cleaning, we have a total of 1734 valid cases in District 2. Cleaned Data Splitting : about 80% (drawn randomly) of all the data for the district. The validation sample comprises the remaining 20% of the data for each district. The cleaned data from District 2 are split into an estimation sample with 1418 cases and a validation sample with 316 cases. Discussion of the Empirical Model Results The model is presented in this section. Interpretation and discussion follow. District 2 Model : The best District 2 model is presented in T able 7 5

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140 District 2 Model Interpretation : In the specification, the base categories used are high income households and weekdays. In other words, t his model is based on a high income household that takes trips on weekdays. Generally, those explanatory variables are meaningful with regard to household trips. Those parameters, as well as their signs, are intuitively correct. For example, we can reasona bly expect more household trips if the number of adults, children, or drivers in a household increase. There are also some other interesting points demonstrated as follows. Presence of children in households has larger impact than presence of adults. While increase in one adult in a household will increase 0.948 household trips per day, increase in one child (less than 18 years old) in a household will increase 1.999 household trips per day. Presence of drivers in a household has positive impacts on househo ld daily trips. On average, one more driver makes 1.269 more trips. Household income has positive impact on trips in general. The richer the household is, the more trips they will make. On a daily average, a low income household makes 2.473 less trips than a high income household, and a medium income household makes 1.586 less trips than a high income household. Households make fewer trips on weekends than on weekdays. The average difference is 0.817 trips. According to the results of linear regression, cou nt of household vehicles and size of urban areas are statistically insignificant with regard to household trip making. Possible interpretation might be that it is the household member who makes trips, regardless of how many vehicles he/she owns or where he /she lives. Besides, at the significance level of 0.1, households do not make more trips on Monday. There is also no evidence showing difference between seasonal and permanent households. The model show s the impact of household child members, income levels and travel days on the household daily trips. Generally, a household with more adult members, with a higher income level, and who travels on weekdays is expected to make more trips. The model also

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141 indicates positive impacts of household children and driv ers on daily trips. Another interesting point is that the interaction variables that are created do not show statistical significance in the model. Predictive Assessments In this section, the predictive performance of the locally estimated models against that of the transferred models is compared. For validation samples from each district and for each case (household) in the validation sample we have (1) the true trip generation rates, (2) the predicted rate from the locally estimated model, and (3) the pr edicted rate from the transferred model. Prediction Expression : The District 2 model generates the following prediction expression: Pred_trip = 1.999*NCHILD 2.473*LowInc 1.586*MedInc 0.817*WKEND + 0.948*NUMADLT + 1.269*DRVRCNT + 3.657 Model Validation : The regression models generated from the estimation samples in District 2 are validated based on their validation samples, respectively. Mean Absolute Deviation (MAD), Root Mean Square Error (RMSE), and Mean Absolute Percent Error (MAPE) are calculated (see the following formula) for measures of overall prediction accuracy of each model. Where: F i Predicted trip rates; y i True trip rates; and n Sample nu mber. Generally, the MAD (Mean Absolute Deviation) measures the size of the error in units, the RMSE (Root Mean Square Error) represents the sample standard deviation of the differences between predicted values and observed values, and the MAPE (Mean Absol ute Percent Error) measures the size of the error in percentage terms. Results are shown in the following tables.

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142 Discussion The mean absolute percent errors for model validations are all above 50%, indicating lack of accuracy in the model prediction abilities. However, the results are consistent with the small R square values for both models The model for District 2 show s the impact of household child members, income levels, and travel days on the household daily trips. Generally, a household with more adult members, with a higher income level, and who travels on weekdays is expected to make more trips. The District 2 model also indicates positive impacts of household children and drivers on daily trips. Another interesting point is that the interaction variables that are created do not show statistical significance in both models. Since the errors are high (e.g., with the mean absolute percent errors above 50%) when applying both models for prediction, the transferability of the trip generation models does not make much sense. In the future, variables should be created and selected in a more reasonable effort based on existing theories and current research findings. Determination of Criteria Weights For those nine selected projects, eight evaluation criteria were created, and raw data from the measures of each criterion were collected. Those d ata can be either directly obtained or inferred from the data sources listed above. Criteria were determined based on the data that were readily available or reasonably projected. Those eight evaluation criteria are listed as follows: 1. Facility Type 2. Area Ty pe 3. Average Crashes per Mile per Year 4. Existing Level of Service 5. v/c Ratio

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143 6. Two Way AADT per Mile 7. Present Value of Available Project Funds per Mile 8. Environmental Impact For facility type, the numerical values were assigned in Table 7 7 For area type, the numerical values were assigned in Table 7 8 For level of service, the numerical values were determined in Table 7 9 Note that s ome of these data should be positively correlated with the development priority. For example, the bigger the ratio of traffic volume over capacity, the more urgent the need for improvement of the highway. Two of these data, present value of project funds per mile and environmental impact, are negatively correlated with the development priority. In the AHP analysis, linguistic terms were assigned values as listed in Table 7 10 Both fuzzy and non fuzzy methods were used for calculati on and then results compared. Pairwise comparison results were assumed as in Table 7 11 After processing of the raw data in Table 7 12 numerical values were obtained for critical project information, as listed in Table 7 13 The tables that follow show t he calculation process of AHP. Among them Table 7 14 simply gives results of the original, non fuzzy AHP, while results in Tables 7 15~19 are from the fuzzy AHP calculation. Tables 7 20~25 show the calculation process for entropy weights. The final criteri a weights are results that integrate the fuzzy AHP weights with the entropy weights (Table 7 26 ). Finally, we obtained the weight for each criterion as follows: Prioritization Based on TOPSIS The criteria weights obtained from the above AHP Entropy calculation were then inputted in the TOPSIS model developed with MS Excel. Tables 7 27~29 that follow display the

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144 calculation process for the TOPSIS. The final ranking for the potential projects is listed in Table 7 30 based on the calculated distance. Summary This chapter presented a case study using the proposed model in Chapter 5 to prioritize potential SIS highway projects in FDOT District 2. Trip generation was first analyzed in order to forecast the future travel demand. After selection of criteria based on data availability, the criteria weights were determined by the proposed fuzzy AHP Entropy method. Criterial weights were further inputted in the proposed TOPSIS model. The TOPSIS calculation results in final project prioritization. The proposed methodology proved to be effective.

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145 Table 7 1. NCDOT Project Prioritization Criteria Measure Maximum Score Volume to Capacity 15 Crash Incidence 15 Upgrade Ex isting Facility 15 CTP or Thoroughfare Plan Consistency 10 Project Status 10 Connectivity 5 Access to Community Facilities 5 Truck Traffic 5 Local Priority Project 20 Table 7 2. National Highway and Transportation Data Sources Database Developed b y Contents National Transportation Atlas Database (NTAD) USDOT Bureau of Transportation Statistics (BTS) National transportation network data United States Geological Survey USGS Topographic maps, land use, and land cover maps, including information abou t ownership and political boundaries, transportation, and hydrography Topologically Integrated Geographic Encoding and Referencing (TIGER) U.S. Census Bureau Socioeconomic and demographic data, census tract boundary files and street centerline networks

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1 46 Table 7 3. List of New Variables for Travel Demand Analysis Name Label RetiredHH Hourseholds that include at least one retired household member and no full time employed members WorkHH_NC Households, other than retired households, with no household mem bers under the age of 16 WorkHH_C Households, other than retired households, with at least one household members under the age of 16 SeasonalHH Households whose residents live in the region more than one month, but less than six months per year Car0 Hou seholds that have 0 cars Car1 Households that have 1 car Car2 Households that have 2 cars Car3 Households that have 3 or more cars NCHILD Count of HHMs less than 18 years old LowInc Low income households less than $30,000 MedInc Med income households $30,000 through $80,000 HighInc High income households more than $80,000 SCity Small cities with a population under 500,000 LCity Large cities with a population above 500,000 MON Monday WKEND Weekend OwnHouse Housing unit owned RentHouse Housing un it rented Table 7 4. List of Interaction Variables Name Label Low_veh Number of vehicles if the household has low income Med_veh Number of vehicles if the household has med income High_veh Number of vehicles if the household has high income Low_adlt Number of adults if the household has low income Med_adlt Number of adults if the household has med income High_adlt Number of adults if the household has high income Table 7 5: District 2 Model Explanatory Variable Parameter t Statistic Count of HHM s less than 18 years old 1.999 13.375 Low income households less than $30,000 2.473 6.865 Med income households $30,000 through $80,000 1.586 5.073 Weekend .817 2.965 Count of adult HHMs at least 18 years old .948 3.237 Number of drivers in Hous ehold 1.269 4.499 Constant 3.657 7.344 R 2 .306 Adjusted R 2 .303

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147 Table 7 6. District 2 Validation Sample (316 Cases) Prediction from local model Prediction from transferred model MAD 3.52 3.63 RMSE 4.89 4.89 MAPE 50.80% 55.72% Table 7 7. Values A ssigned for Facility Type Facility Freeway Highway Arterials Value Assigned 1.5 1.0 1.0 Table 7 8. Values Assigned for Area Type Area Type Urbanized Areas over 500,000 Urbanized Areas under 500,000 Transitioning Urban Community Rural Value Assigned 6 5 4 3 2 1 Table 7 9. Values Assigned for Level of Service LOS A B C D E F Value Assigned 5 4 3 2 1 0 Table 7 10. Values Assigned for Linguistic Terms Linguistic Terms Abbreviation Value (Non Fuzzy) Fuzzy Score (TFN) l m u Absolutely Strong AS 9 8 .000 9.000 10.000 Very Strong VS 7 6.000 7.000 8.000 Fairly Strong FS 5 4.000 5.000 6.000 Slightly Strong SS 3 2.000 3.000 4.000 Equal EQ 1 1.000 1.000 1.000 Slightly Weak SW 1/3 0.250 0.333 0.500 Fairly Weak FW 1/5 0.167 0.200 0.250 Very Week VW 1/ 7 0.125 0.143 0.167 Absolutely Weak AW 1/9 0.100 0.111 0.125 Intermediate Values 2,4,6,8

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148 Table 7 11. Pairwise Comparison Assumed Facility Type Area Type Average Crashes per Mile per Year Existing Level of Service v/c Ratio Tow Way AADT per M ile PV of Project Funds per Mile Environmental Impact C1 C2 C3 C4 C5 C6 C7 C8 Facility Type C1 EQ EQ SW SW FW SW AW AW Area Type C2 EQ SW SW FW EQ VW AW Average Crashes per Mile per Year C3 EQ SS EQ FS SW SW Existing Level of Service C4 EQ SS VS EQ EQ v/c Ratio C5 EQ VS EQ EQ Tow Way AADT per Mile C6 EQ FW FW PV of Project Funds per Mile C7 EQ EQ Environmental Impact C8 EQ

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149 Table 7 12. Raw Data about Project Information Project Project 1 Project 2 Project 3 Project 4 Project 5 Project 6 Project 7 Project 8 Project 9 FDOT Financial Project ID 208001 1 209301 3 209537 4 209658 4 209659 3 210711 2 213323 1 213345 7 428865 1 Transportation System Intrastate State Highway Intrastate Inters tate Intrastate State Highway Intrastate Interstate Intrastate Interstate Intrastate State Highway Intrastate Interstate Intrastate Interstate Intrastate Interstate Type of Work Preliminary engineering Add lanes and reconstruct New Road Constructio n Add L anes and Reconstruct Interchange Improvement Add Lanes and Reconstruct New Interchange Ramp Add Lanes and Reconstruct Interchange Improvemen t Length (miles) 2.985 4.212 7.335 6.075 3.224 2.167 7.885 4.299 1.99 County Bradford Duval Duval Duval Duval Nass au Duval Duval Duval SIS Y Y Y Y Y Y Y Y Y PV of Project Funds 2,000 50,835,049 67,501,750 7,204,134 1,624,671 45,362,268 188,586,867 13,106,618 91,028,935 Facility Highway Freeway Arterial Freeway Freeway Highway Freeway Freeway Freeway Area Type Tran sition Urbanized Urbanized Urbanized Urbanized Transition Urbanized Urbanized Urbanized Speed (mph) 55 65 45 65 70 55 70 65 70 2013 Traffic 1566 8595 702 4500 4005 1729 9585 10080 4005 Max Service Volume 4460 10060 3580 6700 10060 4460 13390 10060 6700 LOS/STD C/C D/D D/D D/D D/D C/C D/D D/D D/D LOS B D C C B B C E B 2035 Traffic 1674 12348 846 6939 4806 2133 12465 12888 4806 LOS in 2035 B F C E B B D F C Two Way AADT 18500 99000 5600 59500 4600 11400 20500 117500 9700 2011~2013 Total Crashes 126 2 35 7 263 69 76 62 523 75 Mile Post Distance (miles) 3 4 2 6 2 3 3 4.5 2 Average Crashes per Mile per Year 14.0 19.6 1.2 14.6 11.5 8.4 6.9 38.7 12.5

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150 Table 7 13. Numerical Values for Critical Project Information Project ID 208001 1 209301 3 209537 4 2096 58 4 209659 3 210711 2 213323 1 213345 7 428865 1 Project # P1 P2 P3 P4 P5 P6 P7 P8 P9 Facility Type C1 1 1.5 1 1.5 1.5 1 1.5 1.5 1.5 Area Type C2 4 6 6 6 6 6 6 6 6 Average Crashes per Mile per Year C3 14.0 19.6 1.2 14.6 11.5 8.4 6.9 38.7 12.5 Existi ng Level of Service C4 1.33 1.00 1.50 1.50 2.00 1.33 1.50 0.50 2.00 v/c Ratio C5 0.351 0.854 0.196 0.672 0.398 0.388 0.716 1.002 0.598 Tow Way AADT per Mile C6 6198 23504 763 9794 1427 5261 2600 27332 4874 PV of Project Funds per Mile C7 23,013,889 12,0 69,100 9,202,693 1,185,866 503,930 20,933,211 23,917,168 3,048,760 45,743,184 Environmental Impact C8 44 30 40 32 45 34 32 36 44 Table 7 14. Original AHP Calculation Facility Type Area Type Average Crashes per Mile per Year Existing Level of Service v/c Ratio Tow Way AADT per Mile PV of Project Funds per Mile Environmental Impact C1 C2 C3 C4 C5 C6 C7 C8 normalization Facility Type C1 1.00 1.00 0.50 0.50 0.33 0.50 0.13 0.13 0.40 0.04 0.35 0.32 1.10 Area Type C2 1.00 1.00 0.33 0.50 0.25 1.00 0.11 0.13 0.39 0.04 0.33 0.31 1.05 Average Crashes per Mile per Year C3 2.00 3.00 1.00 2.00 1.00 5.00 0.50 0.50 1.40 0.14 1.20 1.11 1.08 Existing Level of Service C 4 2.00 2.00 0.50 1.00 2.00 6.00 1.00 1.00 1.49 0.15 1.36 1.18 1.15 v/c Ratio C5 3.00 4.00 1.00 0.50 1.00 7.00 1.00 1.00 1.60 0.16 1.35 1.26 1.07 Tow Way AADT per Mile C6 2.00 1.00 0.20 0.17 0.14 1.00 0.25 0.20 0.38 0.04 0.33 0.30 1.08 PV of Project Fund s per Mile C7 8.00 9.00 2.00 1.00 1.00 4.00 1.00 1.00 2.21 0.22 1.84 1.75 1.05 Environmental Impact C8 8.00 8.00 2.00 1.00 1.00 5.00 1.00 1.00 2.24 0.22 1.84 1.77 1.04 10.12 1.00 8.63 CI 0.09 RCI 1.41 CR 0.06

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151 Table 7 15. Fuzzy AHP Calculation I Middle Facility Type Area Type Average Crashes per Mile per Year Existing Level of Service v/c Ratio Tow Way AADT per Mile PV of Pro ject Funds per Mile Environmental Impact C1 C2 C3 C4 C5 C6 C7 C8 normalization Facility Type C1 1.00 1.00 0.33 0.33 0.20 0.33 0.11 0.11 0.31 0.03 0.26 0.24 1 .08 Area Type C2 1.00 1.00 0.33 0.33 0.20 1.00 0.14 0.11 0.37 0.03 0.29 0.28 1.02 Average Crashes per Mile per Year C3 3.00 3.00 1.00 3.00 1.00 5.00 0.33 0.33 1.40 0.13 1.29 1.06 1.22 Existing Level of Service C4 3.00 3.00 0.33 1.00 3.00 7.00 1.00 1.00 1.68 0.16 1.57 1.27 1.24 v/c Ratio C5 5.00 5.00 1.00 0.33 1.00 7.00 1.00 1.00 1.66 0.16 1.37 1.26 1.09 Tow Way AADT per Mile C6 3.00 1.00 0.20 0.14 0.14 1.00 0.20 0.20 0.39 0.04 0.32 0.29 1.10 PV of Project Funds per Mile C7 9.00 7.00 3.00 1.00 1.00 5.0 0 1.00 1.00 2.35 0.22 1.86 1.78 1.04 Environmental Impact C8 9.00 9.00 3.00 1.00 1.00 5.00 1.00 1.00 2.43 0.23 1.93 1.83 1.05 10.60 1.00 8.86 CI 0.12 R CI 1.41 CR 0.09

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152 Table 7 16. Fuzzy AHP Calculation II Lower Facility Type Area Type Average Crashes per Mile per Year Existing Level of Service v/c Ratio Tow Way AADT per Mile PV of Project Funds per Mile Environmental Impac t C1 C2 C3 C4 C5 C6 C7 C8 normalization Facility Type C1 1.00 1.00 0.25 0.25 0.17 0.25 0.10 0.10 0.27 0.02 0.21 0.19 1.09 Area Type C2 1.00 1.00 0.25 0.25 0 .17 1.00 0.13 0.10 0.33 0.03 0.24 0.23 1.02 Average Crashes per Mile per Year C3 4.00 4.00 1.00 4.00 1.00 6.00 0.25 0.25 1.49 0.13 1.46 1.06 1.38 Existing Level of Service C4 4.00 4.00 0.25 1.00 4.00 8.00 1.00 1.00 1.83 0.16 1.74 1.31 1.33 v/c Ratio C5 6.00 6.00 1.00 0.25 1.00 8.00 1.00 1.00 1.71 0.15 1.37 1.22 1.12 Tow Way AADT per Mile C6 4.00 1.00 0.17 0.13 0.13 1.00 0.17 0.17 0.36 0.03 0.30 0.26 1.15 PV of Project Funds per Mile C7 10.00 8.00 4.00 1.00 1.00 6.00 1.00 1.00 2.57 0.23 1.98 1.84 1.08 Environmental Impact C8 10.00 10.00 4.00 1.00 1.00 6.00 1.00 1.00 2.65 0.24 2.04 1.89 1.08 11.20 1.00 9.23 CI 0.18 RCI 1.41 C R 0.12

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153 Table 7 17. Fuzzy AHP Calculation III Upper Facility Type Area Type Average Crashes per Mile per Year Existing Level of Service v/c Ratio Tow Way AADT per Mile PV of Project Funds per Mile Environmental Impact C1 C2 C3 C4 C5 C6 C7 C8 normalization Facility Type C1 1.00 1.00 0.50 0.50 0.25 0.50 0.13 0.13 0.39 0.04 0.34 0.31 1.09 Area Type C2 1.00 1.00 0.50 0.50 0.25 1.00 0.17 0.13 0.44 0.04 0.37 0.35 1.05 Average Crashes per Mile per Year C3 2.00 2.00 1.00 2.00 1.00 4.00 0.50 0.50 1.30 0.13 1.14 1.05 1.09 Existing Level of Service C4 2.00 2.00 0.50 1.00 2.00 6.00 1.00 1.00 1.49 0.15 1.39 1.20 1.16 v/c Ratio C5 4.00 4.00 1.00 0.50 1.00 6.00 1.00 1.00 1.62 0.16 1.38 1.31 1.06 Tow Way AADT per Mile C6 2.00 1.00 0.25 0.17 0.17 1.00 0.25 0.25 0.41 0.04 0.36 0.33 1.07 PV of Project Funds per Mile C7 8.00 6.00 2.00 1.00 1.00 4.00 1.00 1.00 2.10 0.21 1.75 1.70 1.03 Environmental Impact C8 8.00 8.00 2 .00 1.00 1.00 4.00 1.00 1.00 2.18 0.22 1.83 1.76 1.04 9.93 1.00 8.59 CI 0.08 RCI 1.41 CR 0.06 Table 7 18. Normalization of Fuzzy AHP Weights l m n Facility Type R1 0.267 0.313 0.386 Area Type R2 0.327 0.370 0.436 Average Crashes per Mile per Year R3 1.488 1.403 1.297 Existing Level of Service R4 1.834 1.678 1.488 v/c Ratio R5 1.707 1.662 1.622 Tow Way AADT per Mile R6 0.361 0.386 0.414 PV of Project Funds per Mile R7 2.573 2.355 2.104 Environmental Impact R8 2.646 2.430 2.181 Sum 11.202 10.597 9.928

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154 Table 7 19. Final Weight from AHP Calculations BNP Normalized AHP w1 0.027 0.030 0.034 0.030 0.030 0.03 9 w2 0.033 0.035 0.039 0.036 0.035 0.039 w3 0.116 0.132 0.150 0.133 0.132 0.139 w4 0.133 0.158 0.185 0.159 0.158 0.147 w5 0.145 0.157 0.172 0.158 0.157 0.158 w6 0.036 0.036 0.037 0.037 0.036 0.038 w7 0.188 0.222 0.259 0.223 0.222 0.219 w8 0.195 0.22 9 0.266 0.230 0.229 0.222 1.005 1.000 Table 7 20. Data Used for Entropy Weights Calculation 208001 1 209301 3 209537 4 209658 4 209659 3 210711 2 213323 1 213345 7 428865 1 A1 A2 A3 A4 A5 A6 A7 A8 A9 Facility Type C1 1 1.5 1 1.5 1.5 1 1.5 1.5 1.5 x/max(x) Area Type C2 4 6 6 6 6 6 6 6 6 x/max(x) Average Crashes per Mile per Year C3 14.0 19.6 1.2 14.6 11.5 8.4 6.9 38.7 12.5 x/max(x) Existing Level of Service C4 1.33 1.00 1.50 1.50 2.00 1.33 1.50 0.50 2.00 x/max(x) v/c Ratio C5 0.351 0.854 0.196 0.672 0.398 0.388 0.716 1.002 0.598 x/max(x) Tow Way AADT per Mile C6 6198 23504 763 9794 1427 5261 2600 27332 4874 x/max(x) PV of Project Funds per Mile C7 23,013,889 12,069,100 9,202,693 1,185,866 503,930 20,933,211 23,917,168 3,048,7 60 45,743,184 min(x)/x Environmental Impact C8 44 30 40 32 45 34 32 36 44 min(x)/x

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155 Table 7 21. Entropy Weights Calculation I Normalization A1 A2 A3 A4 A5 A6 A7 A8 A9 C1 0.667 1.000 0.667 1.000 1.000 0.667 1.000 1.000 1.000 C2 0. 667 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 C3 0.362 0.506 0.031 0.377 0.297 0.217 0.178 1.000 0.323 C4 0.667 0.500 0.750 0.750 1.000 0.667 0.750 0.250 1.000 C5 0.350 0.853 0.196 0.670 0.397 0.387 0.714 1.000 0.597 C6 0.227 0.860 0.028 0.358 0. 052 0.192 0.095 1.000 0.178 C7 0.022 0.042 0.055 0.425 1.000 0.024 0.021 0.165 0.011 C8 0.682 1.000 0.750 0.938 0.667 0.882 0.938 0.833 0.682 Table 7 22. Entropy Weights Calculation II R(delta) A1 A2 A3 A4 A5 A6 A7 A8 A9 Sum C1 0.111 0.000 0.111 0.000 0.000 0.111 0.000 0.000 0.000 0.333 C2 0.111 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.111 C3 0.407 0.244 0.939 0.388 0.494 0.613 0.675 0.000 0.458 4.218 C4 0.111 0.250 0.063 0.063 0.000 0.111 0.063 0.563 0.000 1.222 C5 0.422 0.022 0.647 0.109 0.363 0.376 0.082 0.000 0.163 2.183 C6 0.598 0.020 0.945 0.412 0.898 0.652 0.819 0.000 0.675 5.019 C7 0.957 0.918 0.893 0.331 0.000 0.952 0.958 0.697 0.978 6.685 C8 0.101 0.000 0.063 0.004 0.111 0.014 0.004 0.028 0.101 0.426 Ta ble 7 23. Entropy Weights Calculation III f(ij) A1 A2 A3 A4 A5 A6 A7 A8 A9 C1 0.333 0.000 0.333 0.000 0.000 0.333 0.000 0.000 0.000 C2 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 C3 0.097 0.058 0.223 0.092 0.117 0.145 0.16 0 0.000 0.109 C4 0.091 0.205 0.051 0.051 0.000 0.091 0.051 0.460 0.000 C5 0.193 0.010 0.296 0.050 0.166 0.172 0.037 0.000 0.075 C6 0.119 0.004 0.188 0.082 0.179 0.130 0.163 0.000 0.135 C7 0.143 0.137 0.134 0.049 0.000 0.142 0.143 0.104 0.146 C8 0.238 0.000 0.147 0.009 0.261 0.033 0.009 0.065 0.238

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156 Table 7 24. Entropy Weights Calculation IV lnf(ij) A1 A2 A3 A4 A5 A6 A7 A8 A9 C1 1.099 0.000 1.099 0.000 0.000 1.099 0.000 0.000 0.000 C2 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 C3 2.337 2.852 1.502 2.387 2.145 1.929 1.832 0.000 2.220 C4 2.398 1.587 2.973 2.973 0.000 2.398 2.973 0.776 0.000 C5 1.643 4.611 1.216 3.000 1.793 1.759 3.287 0.000 2.596 C6 2.127 5.545 1.670 2.501 1.720 2.041 1.813 0.000 2.006 C7 1.944 1.985 2.012 3.006 0.000 1.949 1.942 2.261 1.922 C8 1.436 0.000 1.918 4.691 1.343 3.426 4.691 2.729 1.436 Table 7 25. Entropy Weights Calculation V f(ij)lnf(ij) A1 A2 A3 A4 A5 A6 A7 A8 A9 Sum Hi w' C1 0.366 0.000 0.366 0.000 0.000 0.366 0.000 0.000 0.000 0.732 0.667 0.094 C2 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.283 C3 0.226 0.165 0.334 0.219 0.251 0.280 0.293 0.000 0.241 0.725 0.660 0.096 C4 0.218 0.325 0.152 0.152 0.000 0.218 0.152 0.357 0.000 0.695 0.632 0.104 C5 0.318 0.046 0.360 0.149 0.298 0.303 0.123 0.000 0.194 0.724 0.659 0.097 C6 0.253 0.022 0.314 0.205 0.308 0.265 0.296 0.000 0.270 0.590 0.537 0 .131 C7 0.278 0.273 0.269 0.149 0.000 0.278 0.278 0.236 0.281 0.820 0.746 0.072 C8 0.342 0.000 0.282 0.043 0.351 0.111 0.043 0.178 0.342 0.623 0.567 0.122 4.468 Table 7 26. Determination of Final Weights F uzzy AHP Entropy Product Final Weight Facility Type C1 0.030 0.094 0.003 0.027 Area Type C2 0.035 0.283 0.010 0.095 Average Crashes per Mile per Year C3 0.132 0.096 0.013 0.120 Existing Level of Service C4 0.158 0.104 0.016 0.155 v/c Ratio C5 0.157 0. 097 0.015 0.143 Tow Way AADT per Mile C6 0.036 0.131 0.005 0.045 PV of Project Funds per Mile C7 0.222 0.072 0.016 0.150 Environmental Impact C8 0.229 0.122 0.028 0.265 1.000 1.000 0.106 1.000

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157 Table 7 27. TOPSIS Input Data Project ID 20800 1 1 209301 3 209537 4 209658 4 209659 3 210711 2 213323 1 213345 7 428865 1 Criteria Project # P1 P2 P3 P4 P5 P6 P7 P8 P9 Weights Criteria Criterion # Optimum Facility Type C1 Max 1 1.5 1 1.5 1.5 1 1.5 1.5 1.5 0.027 Area T ype C2 Max 4 6 6 6 6 6 6 6 6 0.095 Average Crashes per Mile per Year C3 Max 14 19.6 1.2 14.6 11.5 8.4 6.9 38.7 12.5 0.120 Existing Level of Service C4 Max 1.3 1.0 1.5 1.5 2.0 1.3 1.5 0.5 2.0 0.155 v/c Ratio C5 Max 0.351 0.854 0.196 0.672 0.398 0 .388 0.716 1.002 0.598 0.143 Two Way AADT per Mile C6 Max 6,198 23,504 763 9,794 1,427 5,261 2,600 27,332 4,874 0.045 PV of Project Funds per Mile ($) C7 Min 23,013,889 12,069,10 0 9,202,693 1,185,866 503,930 20,933,211 23,917,168 3,048,760 45,743,184 0.150 Environmental Impact Score C8 Min 44 30 40 32 45 34 32 36 44 0.265 Table 7 28. TOPSIS Normalized Criterion Matrix Project ID 208001 1 209301 3 209537 4 209658 4 2 09659 3 210711 2 213323 1 213345 7 428865 1 Criteria Project # P1 P2 P3 P4 P5 P6 P7 P8 P9 Weights Criteria Criterion # Optimum Facility Type C1 Max 0.246 0.369 0.246 0.369 0.369 0.246 0.369 0.369 0.369 0.027 Area Type C2 M ax 0.229 0.344 0.344 0.344 0.344 0.344 0.344 0.344 0.344 0.095 Average Crashes per Mile per Year C3 Max 0.269 0.377 0.023 0.281 0.221 0.162 0.133 0.745 0.241 0.120 Existing Level of Service C4 Max 0.301 0.226 0.339 0.339 0.452 0.301 0.339 0.113 0.4 52 0.155 v/c Ratio C5 Max 0.187 0.455 0.104 0.358 0.212 0.207 0.381 0.534 0.318 0.143 Two Way AADT per Mile C6 Max 0.160 0.608 0.020 0.253 0.037 0.136 0.067 0.707 0.126 0.045 PV of Project Funds per Mile ($) C7 Min 0.370 0.194 0.148 0.019 0.008 0. 336 0.384 0.049 0.735 0.150 Environmental Impact Score C8 Min 0.387 0.264 0.352 0.282 0.396 0.299 0.282 0.317 0.387 0.265

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158 Table 7 29. Weighted Criterion Matrix Project ID See Tables 7 27 and 7 28. Criteria Max Min Project # P1 P2 P3 P4 P5 P6 P7 P8 P9 Weights Weight Weight Criteria Criterion # Optimum Facility Type C1 Max 0.007 0.010 0.007 0.010 0.010 0.007 0.010 0.010 0.010 0.027 0.010 0.007 Area Type C2 Max 0.022 0.033 0.033 0.033 0.033 0.033 0.033 0.033 0.033 0.095 0.033 0.022 Average Crashes per Mile per Year C3 Max 0.032 0.045 0.003 0.034 0.027 0.019 0.016 0.089 0.029 0.120 0.089 0.003 Existing Level of Service C4 Max 0.047 0.035 0.053 0.053 0.070 0.047 0.053 0.018 0.070 0.155 0.070 0.018 v/c Rat io C5 Max 0.027 0.065 0.015 0.051 0.030 0.030 0.055 0.076 0.046 0.143 0.076 0.015 Two Way AADT per Mile C6 Max 0.007 0.027 0.001 0.011 0.002 0.006 0.003 0.032 0.006 0.045 0.032 0.001 PV of Project Funds per Mile ($) C7 Min 0.056 0.029 0.022 0.003 0 .001 0.051 0.058 0.007 0.111 0.150 0.111 0.001 Environmental Impact Score C8 Min 0.103 0.070 0.093 0.075 0.105 0.079 0.075 0.084 0.103 0.265 0.105 0.070 Distance to the P ositive I deal S olution 0.105 0.064 0.116 0.067 0.091 0.104 0.101 0.055 0.135 Distance to the Negative Ideal Solution 0.070 0.115 0.096 0.128 0.125 0.076 0.083 0.153 0.067 Relative Closeness to Ideal Solutions 0.401 0.643 0.453 0.656 0.580 0.421 0.449 0.736 0.333 Table 7 30. Final Ranking from TOPSIS Ranking Project # Project ID Relative Closeness to Ideal Solutions 1 P8 213345 7 0.736 2 P4 209658 4 0.656 3 P2 209301 3 0.643 4 P5 209659 3 0.580 5 P3 209537 4 0.453 6 P7 213323 1 0.449 7 P6 210711 2 0.421 8 P1 208001 1 0.401 9 P9 428865 1 0.333

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159 Figure 7 1. An Example of a FDOT SIS Project Listed in the 1 st Five Year Plan

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160 Figure 7 2. FDOT Strategic Investment Tool Highway and Connector Measures Source: S trategic Investment Tool Highway Component. (2015). FDOT Systems Planning Office

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161 Figure 7 3. Decision Making process of FDOT for funding SIS investments Figure 7 4. Map of FDOT Districts

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162 Figure 7 5. Map of Major Projects B eing Planned in District 2

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163 CHAPTER 8 CASE STUDY II: MULTI OBJECTIVE OPTIMIZATI ON FOR PROJECT DEVEL OPMENT Case Description and Inputs In recent decades, transportation infrastructure in the United States has been thought to be deteriorated due to unbala nced transportation supply and demand, underfunding, and lack of financial resources (Kim, 1998, p.4). After a specific project is sel ected through the prioritization process discussed in Chapters 5 and 7, the project sponsor and the project manager must f urther optimize the trade off among project time, cost, and quality within the financial constraints. The MODM techniques discussed in Chapter 6 can now be applied to a case study. Consider a simple project with 18 activities as shown in Table 8 1 and Fi gure 8 1 with pre defined activity predecessors, normal duration, normal cost per day, and normal quality index Threshold quality index and maximum days that can be crashed for each activity are al so determined. These variables are shaded in Table 8 1 as original inputs. Baseline Calculation The project baseline sets the normal project schedule. In Table 8 2 the normal project time is calculated. These include the early start (ES), early finish (EF ), late start (LS), late finish (LF), total float (TF), and free float (FF) of each activity. The bolded activities in Table 8 2 indicate those activities on the critical path based on the calculation results (i.e., ) Prior to optimization (see Table 8 3 as well) the project can be completed within 424 days with a total constru ction cost of $17,808,000 The normal activity quality index (0.9) has been set generally above the threshold quality index (0.6) Optimization Assumptions Optimization of the suggested model aims to : (1) minimize the total cost, (2) reduce the project duration, and (3) still meet the project quality requirements

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164 The key conditions for this case project include (see Table 8 3) : Maximum days that can be crashed for each activity has been determined Time constraint: The project duration should be less than 365 days Cost constraint: Crash cost per day for each activity is 20% higher than normal cost Quality constraint: Each quality index should be above the threshold quality index Quality assumption: The activity quality shows linear relationship with the activity durat ion. Optimization Results The optimization, based on the suggested model in this dissertation, results in a total cost reduction from $ 17,808,000 to $ 14,955,000 a 1 6 % saving in total cost. Meanwhile, the total project time has been reduced from 424 days to 300 days a decrease of 29% from normal project time. Th e quality indexes for some activities have to be sacrificed in order to achieve both cost savings and time reduction, but they are still well above the threshold index. See Table 8 3 for details. The optimization results have validated the effectiveness and efficiency of the proposed model. Construction Financing and Project Development Budget From the above calculation, the total construction costs have been reduced to $14,955,000 and the project duration has been decreased to 300 days, or 10 months. Usually, the proje ct sponsor or the project manager then needs to seek construction financing, either by getting construction loans from lenders or by issuing project bonds. Therefore, the financing costs must be calculated and included in the project development budget. Th ere are two specific ally important challenges, among many other challenges when a project development budget is modeled: 1. Construction costs distribution: Construction costs can be easily forecasted using a straight line distribution in which the construc tion costs are evenly assigned to each month. In the real world, however, this is often not the case. Instead, cumulative construction costs tend to show an S curve distribution. Specifically, construction costs

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165 are usually low er both at the beginning and at the end of a project, but are higher in the middle when the project goes on. 2. Financing costs minimization: In each month, the financing costs rely on the beginning balance of the construction loan in the same month while the beginning balance is the su m of the ending balance in the previous month and the financing advances drawn in the same month which partially depends on the total development costs in the same month, including the financing costs. This causes iterative calculation problems. An innova tive mechanism has been designed in t he proposed model in this dissertation to solve the two problems discussed above. Assumptions on construction contingency interest only construction loan costs and project sponsor equity contributions are made as foll ows: Contingency: 5.0% of construction costs Interest Only rate for construction financing: 4.0% Sponsor equity: 35% of total funds Calculation of construction financing costs is shown in Table 8 4 which also encloses a comprehensive project development budget. Figures 8 2~8 4 illustrate the construction costs S curve distribution and the funds draw schedule, respectively. The financing cost optimization process results in total project development expenditures of $15,818,383, including financing costs o f $115,633. Using the sponsor equity as 35% of total funds needed this requires sponsor equity contribution of $5,536,434 and a total of $10,281,949 in construction loans or project bonds. Summary This chapter presented another case study using the mul ti objective decision making optimization model proposed in Chapter 6. The case study aims to find the best solution to the trade off of major project objectives along with the consideration of construction financing costs optimization The calculation re sults indicated that the proposed model is effective and provides a quick solution to project optimization.

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166 Table 8 1. Example Project Activity # Activity Predecessor Normal Duration Normal Cost per Day ($1,000) Normal Quality Index Thresho ld Quality Index Max Days Crashed 1 A 4 $30.00 0.9 0.6 1 2 B 1 48 $25.00 0.9 0.6 7 3 C 2 24 $35.00 0.9 0.6 4 4 D 3 72 $38.00 0.9 0.6 28 5 E 4 62 $40.00 0.9 0.6 21 6 F 5 102 $43.00 0.9 0.6 34 7 G 6 4 $40.00 0.9 0.6 1 8 H 7 4 $39.00 0.9 0.6 1 9 I 6 34 $45.00 0.9 0.6 14 10 J 9 17 $38.00 0.9 0.6 11 11 K 6 24 $42.00 0.9 0.6 7 12 L 10,11 17 $35.00 0.9 0.6 4 13 M 8,12 7 $50.00 0.9 0.6 2 14 N 13 14 $55.00 0.9 0.6 4 15 O 14 4 $40.00 0.9 0.6 1 16 P 15 11 $37.00 0.9 0.6 4 17 Q 16 4 $ 36.00 0.9 0.6 1 18 R 17 4 $30.00 0.9 0.6 1 Table 8 2. Project Schedule Activity # Activity Predecessor Normal Duration Early Start (ES) Early Fin ish (EF) Late Start (LS) Late Finish (LF) Total Float (TF) Free Float (FF) 1 A 4 0 4 0 4 0 0 2 B 1 48 4 52 4 52 0 0 3 C 2 24 52 76 52 76 0 0 4 D 3 72 76 148 76 148 0 0 5 E 4 62 148 210 148 210 0 0 6 F 5 102 210 312 210 312 0 0 7 G 6 4 312 316 372 376 60 0 8 H 7 4 316 320 376 380 60 60 9 I 6 34 312 346 312 346 0 0 10 J 9 17 346 363 346 363 0 0 11 K 6 24 312 336 339 363 27 27 12 L 10,11 17 363 380 363 380 0 0 13 M 8,12 7 380 387 380 387 0 0 14 N 13 14 387 401 387 401 0 0 15 O 14 4 401 405 401 405 0 0 16 P 15 11 405 416 405 416 0 0 17 Q 16 4 416 420 416 420 0 0 18 R 17 4 420 424 420 424 0 0

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167 Table 8 3 Project Optimization Duration Time Quality Cost Activity Normal Duration Max Days Crashed Days Crashed Crash Duration Normal ES Crashed E S Original EF Crashed EF Normal Quality Index Threshold Quality Index Crash Quality Normal Cost per Day ($1,000) Total Normal Cost ($1,000) Crash Cost per Day ($1,000) Total Crash Cost ($1,000) A 4 1 1 3 4 3 0.9 0.6 0.68 $30.00 $120 $36.00 $108 B 48 7 7 41 4 3 52 44 0.9 0.6 0.77 $25.00 $1,200 $30.00 $1,230 C 24 4 4 20 52 44 76 64 0.9 0.6 0.75 $35.00 $840 $42.00 $840 D 72 28 24 48 76 64 148 112 0.9 0.6 0.60 $38.00 $2,736 $45.60 $2,189 E 62 21 21 41 148 112 210 153 0.9 0.6 0.60 $40.00 $2,480 $48.00 $1, 984 F 102 34 34 68 210 153 312 221 0.9 0.6 0.60 $43.00 $4,386 $51.60 $3,509 G 4 1 1 3 312 221 316 224 0.9 0.6 0.68 $40.00 $160 $48.00 $144 H 4 1 1 3 316 224 320 227 0.9 0.6 0.68 $39.00 $156 $46.80 $140 I 34 14 11 23 312 221 346 244 0.9 0.6 0.60 $45.00 $1,530 $54.00 $1,224 J 17 11 6 11 346 244 363 255 0.9 0.6 0.60 $38.00 $646 $45.60 $517 K 24 7 7 17 312 221 336 238 0.9 0.6 0.64 $42.00 $1,008 $50.40 $857 L 17 4 4 13 363 255 380 268 0.9 0.6 0.69 $35.00 $595 $42.00 $546 M 7 2 2 5 380 268 387 273 0.9 0.6 0.64 $50.00 $350 $60.00 $300 N 14 4 4 10 387 273 401 283 0.9 0.6 0.64 $55.00 $770 $66.00 $660 O 4 1 1 3 401 283 405 286 0.9 0.6 0.68 $40.00 $160 $48.00 $144 P 11 4 4 7 405 286 416 294 0.9 0.6 0.60 $37.00 $407 $44.40 $326 Q 4 1 1 3 416 294 420 297 0.9 0.6 0.68 $36.00 $144 $43.20 $130 R 4 1 1 3 420 297 424 300 0.9 0.6 0.68 $30.00 $120 $36.00 $108 TCQT Optimization Summary Project Time 424 300 Satisfied: Crash quality not less than threshold Total Cost $17,808 $14,955 Days Saved 124 Cost Savings $2,853 Days Saved (%) 29.2% Cost Savings (%) 16.0%

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168 Table 8 4 Project Development Budget Month Total 0 1 2 3 4 5 6 7 8 9 10 Expenditures : Financing Costs $115,633 $ $ $ $ $ $ $7,716 $17 ,890 $25,893 $30,848 $33,286 Construction $14,955,000 $ $250,473 $667,159 $1,390,861 $2,269,677 $2,899,329 $2,899,329 $2,269,677 $1,390,861 $667,159 $250,473 Contingency $747,750 $ $12,524 $33,358 $69,543 $113,484 $144,966 $144,966 $113,484 $69,543 $33,358 $12,524 Total $15,818,383 $ $262,997 $700,517 $1,460,404 $2,383,161 $3,044,295 $3,052,012 $2,401,051 $1,486,298 $731,365 $296,283 Construction Loan Beginning Balance $ $ $ $ $ $ $2,314,941 $5,366,953 $7,768,004 $9,254,301 $9,985,666 Cash Flows : Sponsor Equity $5,536,434 $ $262,997 $700,517 $1,460,404 $2,383,161 $729,354 $ $ $ $ $ Financing Advances $10,281,949 $ $ $ $ $ $2,314,941 $3,052,012 $2,401,051 $1,486,298 $731,365 $296,283 Total Sources $15,818,383 $ $262,997 $700,517 $1,460,404 $2,383,161 $3,044,295 $3,052,012 $2,401,051 $1,486,298 $731,365 $296,283 Net Cash Flow $ $ $ $ $ $ $ $ $ $ $ Cash Balance $ $ $ $ $ $ $ $ $ $ $ Total Project Cost $ $262,997 $963,514 $2,423,918 $4,807,080 $7,851,375 $10,903,387 $13,304,438 $14,790,736 $15,522,100 $15,818,383 Construction Loan Ending Balance $ $ $ $ $ $2,314,941 $5,366,953 $7,768,004 $9,254,301 $9,985,666 $10,281,949 Loan to Cost NA 0% 0% 0% 0% 29% 49% 58% 63% 64% 65%

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169 Figure 8 1. Project Schedule

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170 Figure 8 2. Construction Costs S Curve Distr ibu tion (Cumulative) Figure 8 3. Construction Costs S Curve Distribution (Monthly ) $0 $2,000,000 $4,000,000 $6,000,000 $8,000,000 $10,000,000 $12,000,000 $14,000,000 $16,000,000 Month 1 Month 2 Month 3 Month 4 Month 5 Month 6 Month 7 Month 8 Month 9 Month 10 Construction Hard Costs S Curve Distribution Cumulative $0 $500,000 $1,000,000 $1,500,000 $2,000,000 $2,500,000 $3,000,000 $3,500,000 Month 1 Month 2 Month 3 Month 4 Month 5 Month 6 Month 7 Month 8 Month 9 Month 10 Construction Hard Costs S Curve Distribution Monthly

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171 Figure 8 4. Funds Draw Schedule $0 $500,000 $1,000,000 $1,500,000 $2,000,000 $2,500,000 $3,000,000 $3,500,000 Month 1 Month 2 Month 3 Month 4 Month 5 Month 6 Month 7 Month 8 Month 9 Month 10 Funds Draw Schedule Sponsor Equity Draws Loan Draws

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172 CHAPTER 9 CONCLUSIONS Conclu ding Remarks State highway agencies struggle to provide t he public with timely, qualified, and environment friendly construction of highways with high safety requirements and with limited budgets. Construction delays, cost overrun, and poor project quality may cause significant inconveniences to the public and s hould be avoided through proper planning practices (e.g., proper project prioritization process es ) and through project time cost quality optimization processes. Development of global construction, alongside with advancement of construction engineering and management, facilitates the needs for trade off optimization among multiple objectives such as project time, cost, quality and other indicators. Most of previous studies have followed the steps below: 1. Quantify one single objective or define the boundaries both qualitatively and quantitatively, between two different objectives 2. Set up models based on Step 1 3. Solve models using common mathematical tools and techniques. Such models usually have to make assumptions that are not practical in real engineering a Besides, traditional mathematical tools have also been proven complicated, unproductive, inaccuracy, and uni versatile. This dissertation aimed to improve such d ecision making procedures in the development of infrastructure engineering projects. Specifically, t his dissertation center ed upon the study of methodology in decision making of infrastructure engineering development and management. It further propose d com prehensive finance based time cost quality trade off optimization models to help infrastructure engineering decision makers enhance their integrated decision making procedures. After a literature review

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173 on the theory and methods of multi criteria decision making (MCDM), two types of applications were discussed: (1) multi attribute decision making (MADM) optimization, and (2) multi objective decision making (MODM) optimization. The MADM method was proposed to be applied in the prioritization process of highw ay projects by constructing an index system through analysis of economic attributes, technological attributes, and environmental attributes of potential projects. The MODM method was proposed to be applied in the optimization of multiple objectives trade o ff for a selected project through identification and modification of relationships among multiple objectives and through advanced optimization techniques. The former was then applied in Case Study I which aims to prioritize the Strategic Intermodal System highway projects in Florida Department of Transportation District 2, and the latter was then applied in Case Study II which provides the project sponsor with a finance based multi objective trade off optimization model. An integration of analytic hierarchy process, entropy weight, and technique for order of preference by similarity to ideal solution was modeled to solve the MADM problem, while the genetic algorithm was suggested to solve the proposed MODM optimization model. In addition, some critical succe ss factors and key performance indicators for successful projects and successful project management were identified and incorporated in the proposed models with consideration of financial constraints over the project life cycle. Uncertainties and imprecisi ons that have often been encountered in the infrastructure engineering decision making practice were modeled through the application of fuzzy sets theory. The two case studies testified the effectiveness and the efficiency of the proposed models. Generally this dissertation research has provide d infrastructure engineering decision makers (e.g., project sponsors and project managers) with a look into the existing methods and their applications to MCDM problems.

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174 Table 9 1 summarizes the gap between this diss ertation and the existing body of knowledge in the research on general time cost quality trade off problems. Suggestions The proje ct prioritization procedure proposed in the dissertation can be improved by filtering and including more appropriate variables and parameters that best indicate the features and performance of potential projects. Other than fuzzy sets techniques, probabil istic models may also show advantages over the proposed model. In addition, t he effectiveness of the proposed model should be further tested if more available data are obtained. Most of the existing TCQT models have been developed as if the contractor perf orms all the project activities on its own. In other words, the management of subcontractor work is seldom enclosed in the TCQT analysis. In practice, however, the general contractor often trades time with subcontractors in sequential projects, and accordi ngly management of the een the project manager from the general contractor and the subcontractor makes room for the application of cooperative game theory (Asgari and Afshar, 2008; Sacks and Harel, 2006). For example, the numerical calculation of the expected utilities, develop ed by Sacks and behavior, given neither the project manager nor the subcontractor has any knowledge of the probability distribution of the work load. In this case, a perfect equilibrium exists that the project manager demands more work while the subcontractor allocates fewer resources. Similar analyses should be incorporated in the TCQT problem to get a more comprehensive optimization solution.

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175 A finance based fuzzy time cost quality trade off optimization model over the project life cycle has been proposed in this research. This model can be used as a tool to enhance the integrated decision making procedure of project owners/sponsors as well as of architecture, engin eering, and construction firms in the infrastructure engineering field. Discussion of critical success factors and key performance indicators of successful infrastructure engineering projects adds more fuel to the proposed model. A methodology to integrate potential indicators with project time cost quality trade off analysis has also been developed. A framework has been created that facilitates the positive feedback from project success through project management Th e next step in the future may start with modeling project quality in a more realistic and effective way, either through the proposed AHP Entropy TOPSIS integration process or through creation of advanced mathematical functions. In addition, an integrat ed approach should be further studied that connects the MADM optimization with the MODM optimization over the project life cycle. Such an approach should be able to offer project decision makers more values as a whole

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176 Table 9 1. Knowledge Gap between the Existing Research and the Proposed Research Existing Research Proposed Research Project Prioritization Focused on development of weighted criteria according to expert opinions. Integrates AHP and entropy weights to assign criteria weights and then apply them to TOPSIS for final ranking. System Approach No; conducted research separately on different project management issues. Yes; proposes a system view on project management decision making procedures. Identification of CSFs Focused on a variety of proje ct types, on a specific country, or on different project phases. Conducts meta analysis to statistically synthesize results from existing studies; focuses at and above the project level. Sustainability Identified sustainable performance criteria mainly in building construction; no suggestions on incorporation of those criteria in the trade off analysis. Identifies sustainability indicators in infrastructure engineering; integrates indicators in the trade off analysis by customizing LCA and LCC procedures. TCQT Analysis Developed common procedures; focused on the trade off in a relatively limited scope, only among time, cost, and quality in the project construction phase; neglected other critical factors and financial constraints over the project life cycle Incorporates other critical factors; integrates project life cycle performance and financing needs; analyzes the TCQT problem in a wider and more general view of project life constraints. Finance based Model Foc used on financing needs and cash flow management of contractors; missed general strategies about the trade off between financing and other project objectives. Seeks for integration between the functions of scheduling and financing; develops new approaches to model, analyze, and optimize financial constraints and cash flows in infrastructure engineering project management. Optimization Focused on local optimization within a specific project phase. Focuses on global optimization over the whole project life cycle.

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177 APPENDIX A TRAVEL DEMAND DATA A NALYSIS The travel demand data analysis was conducted using SPSS Statistics, a software package used for statistical analysis. Descriptive Statistics Details District 2 Frequency Tables Count of HH members a Fr equency Percent Valid Percent Cumulative Percent Valid 1 418 22.2 22.2 22.2 2 926 49.3 49.3 71.5 3 245 13.0 13.0 84.6 4 201 10.7 10.7 95.3 5 63 3.4 3.4 98.6 6 17 .9 .9 99.5 7 5 .3 .3 99.8 8 1 .1 .1 99.8 9 1 .1 .1 99.9 11 1 .1 .1 99.9 1 3 1 .1 .1 100.0 Total 1879 100.0 100.0 a. FDOT district of HH location = 2 Count of adult HHMs at least 18 years old a Frequency Percent Valid Percent Cumulative Percent Valid 1 447 23.8 23.8 23.8 2 1218 64.8 64.8 88.6 3 160 8.5 8.5 97.1 4 49 2.6 2.6 99.7 5 4 .2 .2 99.9 8 1 .1 .1 100.0 Total 1879 100.0 100.0 a. FDOT district of HH location = 2

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178 Number of workers in HH a Frequency Percent Valid Percent Cumulative Percent Valid 0 813 43.3 43.3 43.3 1 646 34.4 34.4 77.6 2 366 19 .5 19.5 97.1 3 47 2.5 2.5 99.6 4 7 .4 .4 100.0 Total 1879 100.0 100.0 a. FDOT district of HH location = 2 Life Cycle for the HH a Frequency Percent Valid Percent Cumulative Percent Valid one adult, no children 169 9.0 9.0 9.0 2+ adults, no ch ildren 382 20.3 20.3 29.3 one adult, youngest child 0 5 9 .5 .5 29.8 2+ adults, youngest child 0 5 121 6.4 6.4 36.2 one adult, youngest child 6 15 18 1.0 1.0 37.2 2+ adults, youngest child 6 15 205 10.9 10.9 48.1 one adult, youngest child 16 21 2 0 1.1 1.1 49.2 2+ adults, youngest child 16 21 87 4.6 4.6 53.8 one adult, retired, no children 249 13.3 13.3 67.1 2+ adults, retired, no children 619 32.9 32.9 100.0 Total 1879 100.0 100.0 a. FDOT district of HH location = 2 Number of drivers i n Household a Frequency Percent Valid Percent Cumulative Percent Valid 0 56 3.0 3.0 3.0 1 524 27.9 27.9 30.9 2 1076 57.3 57.3 88.1 3 172 9.2 9.2 97.3 4 44 2.3 2.3 99.6 5 6 .3 .3 99.9 6 1 .1 .1 100.0 Total 1879 100.0 100.0 a. FDOT district of HH location = 2

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179 Count of HH vehicles a Frequency Percent Valid Percent Cumulative Percent Valid 0 72 3.8 3.8 3.8 1 495 26.3 26.3 30.2 2 797 42.4 42.4 72.6 3 338 18.0 18.0 90.6 4 123 6.5 6.5 97.1 5 37 2.0 2.0 99.1 6 9 .5 .5 99.6 7 3 .2 .2 99.7 8 3 .2 .2 99.9 9 1 .1 .1 99.9 10 1 .1 .1 100.0 Total 1879 100.0 100.0 a. FDOT district of HH location = 2 Derived total HH income a Frequency Percent Valid Percent Cumulative Percent Valid Don't know 48 2.6 2.6 2.6 Refused 94 5. 0 5.0 7.6 less than $5,000 27 1.4 1.4 9.0 $5,000 $9,999 94 5.0 5.0 14.0 $10,000 $14,999 99 5.3 5.3 19.3 $15,000 $19,999 105 5.6 5.6 24.9 $20,000 $24,999 94 5.0 5.0 29.9 $25,000 $29,999 126 6.7 6.7 36.6 $30,000 $34,999 76 4.0 4.0 4 0.6 $35,000 $39,999 115 6.1 6.1 46.7 $40,000 $44,999 55 2.9 2.9 49.7 $45,000 $49,999 113 6.0 6.0 55.7 $50,000 $54,999 51 2.7 2.7 58.4 $55,000 $59,999 98 5.2 5.2 63.6 $60,000 $64,999 39 2.1 2.1 65.7 $65,000 $69,999 87 4.6 4.6 70. 3 $70,000 $74,999 42 2.2 2.2 72.5 $75,000 $79,999 72 3.8 3.8 76.4 $80,000 $99,999 147 7.8 7.8 84.2 more than $100,000 297 15.8 15.8 100.0 Total 1879 100.0 100.0 a. FDOT district of HH location = 2

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180 Housing unit owned or rented a Freque ncy Percent Valid Percent Cumulative Percent Valid own 1698 90.4 90.4 90.4 rent 181 9.6 9.6 100.0 Total 1879 100.0 100.0 a. FDOT district of HH location = 2 Type of housing unit a Frequency Percent Valid Percent Cumulative Percent Valid Don't kn ow 2 .1 .1 .1 Refused 3 .2 .2 .3 Detached single house 1377 73.3 73.3 73.5 Duplex 53 2.8 2.8 76.4 Rowhouse or townhouse 130 6.9 6.9 83.3 Apartment, condominium 311 16.6 16.6 99.8 Mobile home or trailer 3 .2 .2 100.0 Total 1879 100.0 100.0 a FDOT district of HH location = 2 Hispanic status of HH respondent a Frequency Percent Valid Percent Cumulative Percent Valid Not ascertained 1 .1 .1 .1 Don't know 3 .2 .2 .2 Refused 4 .2 .2 .4 yes 48 2.6 2.6 3.0 no 1823 97.0 97.0 100.0 Tota l 1879 100.0 100.0 a. FDOT district of HH location = 2

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181 Race of HH respondent a Frequency Percent Valid Percent Cumulative Percent Valid Not ascertained 1 .1 .1 .1 Don't know 1 .1 .1 .1 Refused 8 .4 .4 .5 White 1664 88.6 88.6 89.1 African A merican, Black 127 6.8 6.8 95.8 Asian Only 19 1.0 1.0 96.9 American Indian, Alaskan Native 18 1.0 1.0 97.8 Native Hawaiian, other Pacific 6 .3 .3 98.1 Multiracial 15 .8 .8 98.9 Other specify 5 .3 .3 99.2 Other specify 15 .8 .8 100.0 Total 187 9 100.0 100.0 a. FDOT district of HH location = 2 Size of urban area in which home address is located a Frequency Percent Valid Percent Cumulative Percent Valid 50,000 199,999 193 10.3 10.3 10.3 500,000 999,999 704 37.5 37.5 47.7 Not in an ur banized area 982 52.3 52.3 100.0 Total 1879 100.0 100.0 a. FDOT district of HH location = 2 Travel day day of week a Frequency Percent Valid Percent Cumulative Percent Valid Sunday 267 14.2 14.2 14.2 Monday 303 16.1 16.1 30.3 Tuesday 269 14.3 14.3 44.7 Wednesday 274 14.6 14.6 59.2 Thursday 247 13.1 13.1 72.4 Friday 257 13.7 13.7 86.1 Saturday 262 13.9 13.9 100.0 Total 1879 100.0 100.0 a. FDOT district of HH location = 2

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182 Number of months lives in FL a Frequency Percent Valid P ercent Cumulative Percent Valid Not ascertained 1 .1 .1 .1 Don't know 2 .1 .1 .2 2 1 .1 .1 .2 4 2 .1 .1 .3 5 1 .1 .1 .4 6 10 .5 .5 .9 7 6 .3 .3 1.2 8 3 .2 .2 1.4 9 5 .3 .3 1.6 10 5 .3 .3 1.9 11 11 .6 .6 2.5 12 1830 97.4 97.4 99.9 9 9 2 .1 .1 100.0 Total 1879 100.0 100.0 a. FDOT district of HH location = 2 Summary of Crosstabs FDOT district of HH location = 2 Case Processing Summary a Cases Valid Missing Total N Percent N Percent N Percent Count of HH vehicles Count of HH members 1879 100.0% 0 0.0% 1879 100.0% a. FDOT district of HH location = 2

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183 Count of HH vehicles Count of HH members Crosstabulation a Count of HH members Total 1 2 3 4 5 6 7 8 9 11 13 Count of HH vehicles 0 Count 50 16 3 3 0 0 0 0 0 0 0 72 % within Count of HH members 12.0% 1.7% 1.2% 1.5% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 3.8% 1 Count 298 154 27 13 2 1 0 0 0 0 0 495 % within Count of HH members 71.3% 16.6% 11.0% 6.5% 3.2% 5.9% 0.0% 0.0% 0.0% 0.0% 0.0% 26.3% 2 Count 50 526 95 93 2 0 9 4 0 0 0 0 797 % within Count of HH members 12.0% 56.8% 38.8% 46.3% 31.7% 52.9% 80.0% 0.0% 0.0% 0.0% 0.0% 42.4% 3 Count 12 164 88 50 21 1 1 0 0 1 0 338 % within Count of HH members 2.9% 17.7% 35.9% 24.9% 33.3% 5.9% 20.0% 0.0% 0.0% 100.0% 0.0% 18 .0% 4 Count 8 46 21 29 14 2 0 1 1 0 1 123 % within Count of HH members 1.9% 5.0% 8.6% 14.4% 22.2% 11.8% 0.0% 100.0% 100.0% 0.0% 100.0% 6.5% 5 Count 0 13 10 8 2 4 0 0 0 0 0 37 % within Count of HH members 0.0% 1.4% 4.1% 4.0% 3.2% 23.5% 0.0% 0.0% 0 .0% 0.0% 0.0% 2.0% 6 Count 0 3 0 3 3 0 0 0 0 0 0 9 % within Count of HH members 0.0% 0.3% 0.0% 1.5% 4.8% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.5% 7 Count 0 1 0 2 0 0 0 0 0 0 0 3 % within Count of HH members 0.0% 0.1% 0.0% 1.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.2% 8 Count 0 1 1 0 1 0 0 0 0 0 0 3 % within Count of HH members 0.0% 0.1% 0.4% 0.0% 1.6% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.2% 9 Count 0 1 0 0 0 0 0 0 0 0 0 1 % within Count of HH members 0.0% 0.1% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.1% 10 Count 0 1 0 0 0 0 0 0 0 0 0 1 % within Count of HH members 0.0% 0.1% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.1% Total Count 418 926 245 201 63 17 5 1 1 1 1 1879 % within Count of HH members 100.0% 100.0% 100.0% 100.0% 100.0% 10 0.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% a. FDOT district of HH location = 2

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184 Regression Model Details Model 1 Variables Entered/Removed a Model Variables Entered Variables Removed Method 1 Housing unit owned or rented, Households whose residents live in the region more than one month, but less than six months per year, Count of HHMs less than 18 years old, Monday, Med income households $30,000 through $80,000, Count of adult HHMs at least 18 years old, Number of workers in HH, High income househol ds more than $80,000, Number of drivers in Household b Enter a. Dependent Variable: Total number of Trips made by HH b. All requested variables entered. Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .558 a .311 .306 4.630 a. Predictors: (Constant), Housing unit owned or rented, Households whose residents live in the region more than one month, but less than six months per year, Count of HHMs less than 18 years old, Monday, Med income households $30,000 through $80,0 00, Count of adult HHMs at least 18 years old, Number of workers in HH, High income households more than $80,000, Number of drivers in Household ANOVA a Model Sum of Squares df Mean Square F Sig. 1 Regression 13610.083 9 1512.231 70.559 .000 b Residual 30176.673 1408 21.432 Total 43786.756 1417 a. Dependent Variable: Total number of Trips made by HH b. Predictors: (Constant), Housing unit owned or rented, Households whose residents live in the region more than one month, but less than six month s per year, Count of HHMs less than 18 years old, Monday, Med income households $30,000 through $80,000, Count of adult HHMs at least 18 years old, Number of workers in HH, High income households more than $80,000, Number of drivers in Household

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185 Coeffici ents a Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 1.549 .658 2.355 .019 Count of adult HHMs at least 18 years old .860 .295 .106 2.920 .004 Count of HHMs less than 18 years old 1.974 .151 .30 9 13.099 .000 Number of workers in HH .697 .175 .108 3.974 .000 Number of drivers in Household 1.012 .288 .139 3.514 .000 Med income households $30,000 through $80,000 .624 .314 .056 1.984 .047 High income households more than $80,000 2.052 .379 .1 61 5.410 .000 Monday .091 .332 .006 .275 .783 Households whose residents live in the region more than one month, but less than six months per year 2.030 1.294 .035 1.568 .117 Housing unit owned or rented .295 .438 .015 .674 .500 a. Dependent V ariable: Total number of Trips made by HH Model 2 Variables Entered/Removed a Model Variables Entered Variables Removed Method 1 Derived total HH income, Count of HHMs less than 18 years old, Count of adult HHMs at least 18 years old b Enter a. Depend ent Variable: Total number of Trips made by HH b. All requested variables entered. Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .545 a .297 .295 4.667 a. Predictors: Derived total HH income, Count of HHMs l ess than 18 years old, Count of adult HHMs at least 18 years old ANOVA a Model Sum of Squares df Mean Square F Sig. 1 Regression 12987.789 3 4329.263 198.759 .000 b Residual 30798.967 1414 21.781 Total 43786.756 1417 a. Dependent Variable: Tota l number of Trips made by HH b. Predictors: (Constant), Derived total HH income, Count of HHMs less than 18 years old, Count of adult HHMs at least 18 years old

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186 Coefficients a Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. E rror Beta 1 (Constant) .246 .394 .623 .533 Count of adult HHMs at least 18 years old 1.870 .192 .230 9.740 .000 Count of HHMs less than 18 years old 2.172 .146 .340 14.873 .000 Derived total HH income .210 .024 .211 8.900 .000 a. Dependent Varia ble: Total number of Trips made by HH Model 3 Variables Entered/Removed a Model Variables Entered Variables Removed Method 1 Weekend, Number of drivers in Household, Med income households $30,000 through $80,000, Count of HHMs less than 18 years old, Lo w income households less than $30,000 b Enter a. Dependent Variable: Total number of Trips made by HH b. All requested variables entered. Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .549 a .301 .299 4.655 a. Predict ors: (Constant), Weekend, Number of drivers in Household, Med income households $30,000 through $80,000, Count of HHMs less than 18 years old, Low income households less than $30,000 ANOVA a Model Sum of Squares df Mean Square F Sig. 1 Regression 13191. 967 5 2638.393 121.766 .000 b Residual 30594.789 1412 21.668 Total 43786.756 1417 a. Dependent Variable: Total number of Trips made by HH b. Predictors: (Constant), Weekend, Number of drivers in Household, Med income households $30,000 through $8 0,000, Count of HHMs less than 18 years old, Low income households less than $30,000

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187 Coefficients a Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 4.216 .469 8.998 .000 Number of drivers in House hold 1.963 .184 .269 10.682 .000 Count of HHMs less than 18 years old 1.951 .149 .306 13.074 .000 Low income households less than $30,000 2.423 .361 .202 6.712 .000 Med income households $30,000 through $80,000 1.588 .314 .141 5.061 .000 Week end .836 .276 .067 3.025 .003 a. Dependent Variable: Total number of Trips made by HH Model 4 Variables Entered/Removed a Model Variables Entered Variables Removed Method 1 Number of drivers in Household, Weekend, Med income households $30,000 throu gh $80,000, Count of HHMs less than 18 years old, Low income households less than $30,000, Count of adult HHMs at least 18 years old b Enter a. Dependent Variable: Total number of Trips made by HH b. All requested variables entered. Model Summary Mod el R R Square Adjusted R Square Std. Error of the Estimate 1 .554 a .306 .303 4.639 a. Predictors: (Constant), Number of drivers in Household, Weekend, Med income households $30,000 through $80,000, Count of HHMs less than 18 years old, Low income househo lds less than $30,000, Count of adult HHMs at least 18 years old

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188 ANOVA a Model Sum of Squares df Mean Square F Sig. 1 Regression 13417.489 6 2236.248 103.899 .000 b Residual 30369.267 1411 21.523 Total 43786.756 1417 a. Dependent Variable: T otal number of Trips made by HH b. Predictors: (Constant), Number of drivers in Household, Weekend, Med income households $30,000 through $80,000, Count of HHMs less than 18 years old, Low income households less than $30,000, Count of adult HHMs at least 18 years old Coefficients a Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 3.657 .498 7.344 .000 Count of HHMs less than 18 years old 1.999 .149 .313 13.375 .000 Low income households less th an $30,000 2.473 .360 .207 6.865 .000 Med income households $30,000 through $80,000 1.586 .313 .141 5.073 .000 Weekend .817 .275 .066 2.965 .003 Count of adult HHMs at least 18 years old .948 .293 .116 3.237 .001 Number of drivers in House hold 1.269 .282 .174 4.499 .000 a. Dependent Variable: Total number of Trips made by HH Model Validation Details For the purpose of simplicity, only the first 20 rows are extracted from the spreadsheet, which shows the calculation process.

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189 True rates Pred. rates from local model Pred. Rates from transferred model Absolute difference local vs. true Abs. % diff. local vs. true Absolute difference tran s fer vs. true Abs. % diff. transfer vs. true 15 5.749 6.635 9.251 0.617 8.365 0.558 16 9.686 9.479 6.3 14 0.395 6.521 0.408 12 12.938 13.363 0.938 0.078 1.363 0.114 9 8.956 10.496 0.044 0.005 1.496 0.166 9 8.722 8.549 0.278 0.031 0.451 0.050 18 8.722 4.927 9.278 0.515 13.073 0.726 12 5.688 4.583 6.312 0.526 7.417 0.618 6 3.471 4.210 2.529 0.422 1.790 0.298 2 3.401 4.142 1.401 0.701 2.142 1.071 4 2.132 3.141 1.868 0.467 0.859 0.215 6 6.505 4.927 0.505 0.084 1.073 0.179 8 8.091 9.177 0.091 0.011 1.177 0.147 20 10.939 10.360 9.061 0.453 9.640 0.482 11 6.505 5.869 4.495 0.409 5.131 0.466 0 8.091 9.3 34 8.091 9.334 4 4.801 3.484 0.801 0.200 0.516 0.129 8 6.822 6.654 1.178 0.147 1.346 0.168 0 5.236 5.398 5.236 5.398 18 8.799 11.217 9.201 0.511 6.783 0.377 0 3.401 4.456 3.401 4.456

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190 APPENDIX B PROJECT DATA FOR CAS E STUDY I Project # 20800 1 1 Project Summary Project Map

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191 Crash Data Environmental Impact

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192 Other Information The proposed project is consistent with the 2060 Florida Transportation Plan long range goals and objectives. Funding for this project is identified in the current D istrict 2 SIS Plan. 9 The project is also consistent with local County and City comprehensive plans. Capacity and Level of Service. With the No Build Alternative the level of service conditions are anticipated to be LOS F. The proposed Rural Alternat ive will achieve 2040 design year LOS B on the bypass route and result in a LOS B on the existing route. The Rural Alternative will meet the SIS level of service criteria. In the design year, 2040, there will be a 57 percent reduction of traffic on exist ing U.S. 301 between S.R. 100 and S.R. 16, a 31 percent reduction in traffic on S.R. 16 west of U.S. 301, and a 16 percent reduction of traffic on S.R.100 west of U.S. 301. 10 This project is located on the facility of SR 200 (US 301) from CR 227 to CR 233. The improvement involves project development and environment (PD&E) study. The project is to result in the construction of a four lane limited access bypass on a new alignment, located on the west side of the City of Starke urban area. The project plan is consistent with Bradford County Comprehensive Plan, City of Starke Five Year Work Program. 9 U.S. 301 (State Road 200) Record of Decision, February 4, 2014 10 Draft Environmental Impact Statement Starke U.S. 301 Corridor Study

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193 Project # 209301 3 Project Summary

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194 Project Map Crash Data

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195 Other Information Capacity The segment of I 295 from SR 9B to SR 202 (JTB Blvd.) currently experiences heavy peak period congestion with speeds well below the posted speed limits due to demand that exceeds capacity. In 2013, I 295 operated at Level of Service (LOS) F from SR 9B to SR 152 (Baymeadows Road) and at LOS D from SR 152 (Baymeadows Road) to SR 202 (JTB Blvd.). By 2040, the entire segment of I 295 within the study limits will operate at LOS F Travel Time Reliability Travel time reliability measures the extent of this unexpected delay and is defined as the consistency or dependability of travel times, as measured from day to day and/or across different times of day. The free flow travel time along I 295 (measured as part of the I 295 Planning Feasibil ity Study) between US 1 and Town Center Parkway is approximately 7.4 minutes. In the existing conditions, travel times in the peak hour vary between 8.4 and 13.5 minutes in the I 295 northbound direction (a.m. peak), and between 10.6 and 19.3 minutes in th e southbound direction (p.m. peak). The travel times from US 1 to Town Center Parkway vary from 14 to 160 percent above the free flow travel time during these peak hours. The variability in travel time is caused by several bottleneck locations within the s tudy area that cause stop and go conditions. Transportation Demand The North Florida Transportation Planning Organization (NFTPO) Envision 2035 Long Range Transportation Plan (LRTP) (revised March 14, 2013) identifies the need for additional capacity al ong I 295 within the project limits. This project is SR 9A (I 295) from SR 9B to SR 202 (JTB Blvd.) Managed Plan Fiscal Year 201 4/15 2018/19 (approved June 12, 2014).

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196 Project # 209537 4 Project Summary Project Map

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197 Crash Data Environmental Impact

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198 Project # 209658 4 Project Summary Project Map

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199 Crash Data

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200 Project # 209659 3 Project Summary

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201 Project Map Crash Data

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202 Project # 210711 2 Project Summary Project Map

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203 Crash Data

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204 Project # 213323 1 Project Summary Project Map

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205 Crash Data

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206 Project # 213345 7 Project Summary

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207 Project Map

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208 Crash Data Environmental Impact

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209 Project # 428865 1 Project Summary Project Map

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210 Crash Data Environmental Impact

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211 LIST OF REFERENCES Ackerman, F., & Heinzerling, L. (2002). Pricing the priceless: Cost benefit analysis of environmental protection. University of Pennsylvania Law Review 1553 1584. Afshar, A., & Fat hi, H. (2009). Fuzzy multi objective optimization of finance based scheduling for construction projects with uncertainties in cost. Engineering Optimization 41 (11), 1063 1080. Afshar, A., Kaveh, A., & Shoghli, O. R. (2007). Multi objective optimization of time cost quality using multi colony ant algorithm. Asian Journal of civil engineering (Building and Housing) 8 (2), 113 124. Afshar, A., Ziaraty, A. K., Kaveh, A., & Sharifi, F. (2009). Nondominated archiving multicolony ant algorithm in time cost trade off optimization. Journal of Construction Engineering and Management 135 (7), 668 674 Ali, M. M., & Elazouni, A. (2009). Finance based CPM/LOB scheduling of projects with repetitive non serial activities. Construction Management and Economics 27 (9), 839 856. Alonso, J. A., & Lamata, M. T. (2006). Consistency in the analytic hierarchy process: a new approach. International Journal of Uncertainty, Fuzziness and Knowledge Based Systems 14 (04), 445 459. American Society of Civil Engineers Florida Section. (2012). 2012 Report card for Florida's infrastructure. American Society of Civil Engineers. American Society of Civil Engineers. (2013). Report card for America's infrastructure. American Society of Civil Engineers. Amiri, M. P. (2010). Project selection for oil fields development by using the AHP and fuzzy TOPSIS methods. Expert Systems with Applications 37 (9), 6218 6224. Asgar i, M. S., & Afshar, A. (2008, August). Modeling subcontractors cooperation in time; cooperative game theory approach. In First International Conference on Construction in Developing Countries (ICCIDC I) (pp. 312 319). Association for Project Management. ( 2012). APM Body of Knowledge. Atkinson, R. (1999). Project management: cost, time and quality, two best guesses and a International journal of project management 17 (6), 337 342. Babu, A. J. G., & S uresh, N. (1996). Project management with time, cost, and quality considerations. European Journal of Operational Research 88 (2), 320 327. Baker, D., Bridges, D., Hunter, R., Johnson, G., Krupa, J., Murphy, J., & Sorenson, K. (2002). Guidebook to decision making methods. Developed for the U S Department of Energy

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221 BIOGRAPHICAL SKETCH Xi Zheng earned a bache degree in civil engineering from Tongji University, Shanghai in 2005. He worked for China Merchants Chongqing Communications Research & Design Institute Co. Ltd. and enjoyed being an engineer there during 2005 2009. He received a Master of Science de gree in civil engineering from University of Florida in May 2011 and then decided to continue with the PhD program in the same department. He was also admitted to the Master of Science program in f inance at University of Florida and graduated from the program in May 2014. He specialized in project financing, cash flow management, and construction project optimization. He received his Ph.D. in civil engineering in August 201 6 under the guidance of Dr. Ralph Ellis. He plans to find a career that can integrate his extensive knowledge in finance with real engineering and project management practice.