Citation
A decision support system for dynamic scheduling

Material Information

Title:
A decision support system for dynamic scheduling practice and theory
Creator:
Aytug, Haldun
Publication Date:
Language:
English
Physical Description:
vii, 213 leaves : ill. ; 29 cm.

Subjects

Subjects / Keywords:
Atoms ( jstor )
Crossovers ( jstor )
Dispatching ( jstor )
Expert systems ( jstor )
Heuristics ( jstor )
Knowledge bases ( jstor )
Learning ( jstor )
Machine learning ( jstor )
Scheduling ( jstor )
Simulations ( jstor )
Decision support systems ( lcsh )
Production scheduling ( lcsh )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1993.
Bibliography:
Includes bibliographical references (leaves 199-212).
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Haldun Aytug.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
001917386 ( ALEPH )
AJZ2925 ( NOTIS )
30381669 ( OCLC )

Downloads

This item has the following downloads:


Full Text










A DECISION SUPPORT SYSTEM
FOR DYNAMIC SCHEDULING:
PRACTICE AND THEORY













By

HALDUN AYTUG


DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

1993














ACKNOWLEDGEMENTS


would


to thank my


advisor


Professor Gary


J. Koehler for


his constant


support and


assistance during


dissertation,


during


moments


frustration.


I am thankful to the other members of my committee, Professor Chung Yee


Lee, Professor Anthal Majthay, and Professor Richard A. Elnicki, for their input.


I would


like to thank Professor Selcuk Erenguc for his guidance as a graduate coordinator during


my studies at the University of Florida.


am grateful to friends who helped make life


enjoyable during my stay in Gainesville.


Finally,


am most grateful to my family for


their constant love and encouragement.

Last thanks go to International Business Machines Corporation for their support

on part of this dissertation.















TABLE OF CONTENTS


ACKNOWLEDGEMENTS


ABSTRACT


CHAPTERS


INTRODUCTION


Scheduling and Operations Research
Artificial Intelligence and Scheduling
Scheduling and Genetic Algorithms
Contents of This Dissertation .


* S S S S S S S S
* S S S S S S S S S S S S S S S


5 5 4 5 S S S S S S S S S 5 7


SCHEDULING, DISPATCHING AND ARTIFICIAL INTELLIGENCE


Overview of Scheduling and Operations Research
2.1.1 Definition of the Scheduling Problem
Environment .


S S S 5 lI


S. 10
,e Production
. 11


Notation and Parametric Description of Scheduling Problems


Scheduling Problem as it Appears in Industry
Last Word on OR Approaches


Dispatching ..
2.2.1 Some Dispatching Rules Discussed in Literature


2.2.2


A List of Dispatching Rules


Overview of Artificial Intelligence .
2.3.1 Expert Systems and Scheduling


2.3.1.1
2.3.1.2


. 17
19


21
. 23
. 28
. 34
. 35


Cases against and for Expert Systems in Scheduling


Some Reported ES Applications


Constrained Heuristic Search
Hybrid Artificial Intelligence Mt
Machine Learning Approaches
A Listing of Systems......


. 38


. .. . 50
.* .5 57


LEARNING


S. 68
2-1


6


page


A, _rln_.l. I r









GENETIC ALGORITHMS AND CLASSIFIER SYSTEMS


Overview of Genetic Algorithms


4.1.1


The Fundamental Theory of GAs and Implicit Parallelism


4.1.3


An Exact Representation of a GAs Search Behavior
Current Research on GAs


4 44 49z4


4.1.4 GA Applications on Scheduling .. .
GA Based Learning Systems and Classifier Systems


ISSUES ON FINITE GAs .


An Issue on Stopping Criteria
Stopping Criteria for GAs


5.2.1


5.2.2


First Passage Times: Preliminaries .. .
An Upper Bound on the Number of Iterations


* S 4 4 4 4 9 4
. 4 0 0 4 4


Extensions and Some Properties


LEARNING
SIMULATION


Overview


DISPATCHING


9 4 9 4 9 9 9 9 9
4 4 4 4 5 4 4 4


RULES


FOR


SCHEDULING


USING


* 9 9 4 9 9 9 9 4 9 9 4 4 9 4 9 9 9 9 4 4 9 4 9 4 9 9 9 4 9
* 4 4 4 4 4 4 4 4 4 4 9 4 4 9 4 4 9 9 4 4 4 4 S 4 4 4 4 4


Conceptual Model


Genetic Learning and Inference .. .. .. .. .
Simulation Environment .. . .
Exp eriment and Results . .
Discussion of Results . . .


Related Issues


1


GENERALIZATION OF THE GENETIC LEARNING SYSTEM


Overview


The Flowshop Extension
Knowledge Representation


* I 9 4 4
* S 9 4t 4


* 4 9 9 9 4
. .4 4


* 4 4 9 4 4 4 4 9 4 4 4 4 4 4
*. .4 4 4 .4 9 .4 .


7.3.1


7.3.3
7.3.4
7.3.5


BNF Form of The Rule Language
Rule-level Recombination Operators


Conjunct-level Operati
Inference Strategies .
Credit Assignment


Simulation Experiments


7.4.1
7.4.2
7.4.3


Experiment Set One
Experiment Set Two
Experiment Set Three


7.5 Interpretation of the Simulation Results


CONCLUSIONS AND FUTURE RESEARCH


f\ ',


. 1


89
89
92


* 4 9 9 4 4 4 4 4
* 4 S 4 9 4 4 4 9 .


ors 4 9 9 6 9 9 4 4 4 9 4 9 4 4 9 4 4 4 4 4


* 4 4 9 9 9 9 9 9 4 9 4 9 4 4 4 9 9 4 4 9 4 9 4 4

* 4 9 4 4 4 4 4 4 4 9 4 4 4 9 4 4 4 9 9 4


* 4 4 9 4 9 4 4 9 9 9 9 9 9 9 4


* 4 9 9 9 4 9 4 4 4 9 4 9 4 9 5 4








8.3.1


Conclusions


Future Research and Modifications to the System


REFERENCES


BIOGRAPHICAL SKETCH














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

A DECISION SUPPORT SYSTEM FOR DYNAMIC SCHEDULING:
PRACTICE AND THEORY

By

Haldun Aytug


August 1993


Chairman:


Professor Gary J. Koehler


Major Department:


Decision and Information Sciences


Knowledge acquisition


major


bottleneck


in successfully


implementing


Expert System in a production environment.


domain expert exists in


Moreover, it is very questionable that a


this domain, due to the dynamic and complex nature of the


environment.


Knowledge


base


update


is another


problem


Expert


System


approaches for the scheduling domain since some production environments are subject to


frequent


changes


making


existing


knowledge


obsolete.


remedy


to the


knowledge acquisition and update problems is using


"Machine Learning"


approaches.


This reduces the dependence on a human expert and automates the knowledge acquisition

and update processes.

In this research we motivate the need for using machine learning techniques for


S Sl -- S S S S S ,1








knowledge base. Due to their continuous feedback control mechanisms, classifier systems

are very appropriate for updating knowledge bases when the environment is changing.

We have developed a learning system that is integrated with a simulation environment


(developed in C++) which supports inference. A rule language supportive of the genetic

search operators used by the system has been developed. Two subsystems the "learning


subsystem"


and the


"task subsystem" interact throughout the


"knowledge construction"


process.


The learning subsystem evaluates the performance of the task subsystem after


every learning episode and generates an expectedly better knowledge base for the task


subsystem to use in the next learning episode.


This procedure stops after a reasonable


knowledge base is constructed.

The theoretical part of this research involves developing a worst case bound on the


number of learning episodes


the system has to


perform before stopping


with a


performing knowledge base.


This is equivalent to developing a stopping criteria for


genetic algorithms since classifier systems use genetic algorithms to search for new rules.


To date


there


been


no series attempt to develop a stopping


criteria


for Genetic


Algorithms.


We have developed an upper bound on the number of iterations a GA has


to execute to assure seeing an optimal solution with a specified confidence level by using


the concept of first passage times of a Markov Chain.


For a given string length, we have


also found the optimal number of iterations necessary before stopping.














CHAPTER


INTRODUCTION


Scheduling has long been an interest of


theoretical point of view.


researchers both from a practical and a


Scheduling is a problem encountered in every type of business.


Examples are project scheduling, flight scheduling, scheduling classes at a university,


production scheduling, etc.


Whatever the application is, scheduling involves assigning


scarce


resources


to operations.


this dissertation


we will


restrict our attention


production scheduling problems.

In a production environment, schedules take the form of assigning operations to

resources such as machines, and labor in a sequence that will optimize some performance

criteria.


It is possible to define the scheduling problem at different levels.


At the highest


level scheduling is more of a long term deployment of resources to production types at

an aggregate level, whereas at the lowest level, scheduling involves the actual assignment


of each individual resource for each individual operation.


In this study we will focus on


the lowest level, the actual allocation of resources to operations.


There has been an extensive amount of work in this area.


Traditional optimization


techniques offer high quality and elegant solutions to a very restricted subset of these


problems.


Due to their restrictive nature, models solved this way


have very


limited










Recently,


there has been a


trend towards increasing the generalizability of the


scheduling models.


These approaches can model very complex environments, but due to


the complexity of the problem they offer lower quality solutions with a very high degree


of applicability.


Artificial Intelligence (AI) techniques have been very promising for


solving


scheduling


problems.


This


can be


attributed


to their


ability


incorporate domain specific knowledge into the search process and their flexibility in

modeling different aspects of the scheduling environment.


In the following sections we will


briefly introduce different approaches to the


scheduling problem.


1.1 Scheduling and Operations Research


Scheduling


as a sequencing


problem


attracted


much


attention


from


Operations Research community.


(Baker,


Starting with Johnson's work on flow shop problems


1974), and Jackson's on single machine problems (Lawler et al., 1985) in 1954,


research has progressed to more challenging problems.


As the problem types evolved to


more complex forms and became more representative of the scheduling environment, the

algorithms developed by researchers started to fail to achieve the optimal solutions within


reasonable time frames.


It was not until the foundation of the complexity theory that


researchers realized they were dealing with inherently very hard problems.


Starting with


this new knowledge, research on sequencing shifted to developing heuristic algorithms










Most


problems


tackled


optimization


methods


consider


very


simplistic


environments.


Typical problems attacked involve a few


machines, infinite resources and


deterministic


attributes.


stochastic


nature


problem


usually


completely ignored.


Performance


measures


considered


are not


more


realistic


model


assumptions.


Usually simple criteria such as flow time, lateness, etc. have been used to


measure


performance


algorithms


developed.


These


measures


have


been


selected since they are functions that are relatively easy to work with.


However, there


has been almost no effort to investigate cost or quality related measures.

There has been some work on the stochastic scheduling problems, but due to their


complexity,


analytical


models


involve


restrictive


assumptions


about


probability


distributions.

When complete solution methods do not exist, it has been common practice to


apply rules of thumb to solve the problem.


Dispatching rules are simple heuristics that


are found to work well in stochastic environments.

Simulation has almost never been used for optimization on scheduling problems

due to the fact that the approach itself does not suggest a way of solving the problem.

It has almost exclusively been used to test how good an algorithm performs when certain


assumptions of the algorithm are relaxed.


Simulation has been extensively utilized to


compare the performances of heuristic rules in non-deterministic environments.








4

In a relatively recent survey by Lageweg et al. (1981), it has been reported that

problems that are optimally solvable are less than ten percent of the total number of

problems tackled by optimization methods.

Even though thirty years of research has compiled a large database of algorithms


for scheduling problems.


Most of these are not directly applicable for real time control


of scheduling operations.


It is only


during the last decade that the researchers have


focused on methods that can connect this background knowledge to real environments.



1.2 Artificial Intelligence and Scheduling


During


twenty


years


there


have


been


enormous


improvements


computing technology.


Current personal computers are almost as powerful as yesterday's


mainframes and


are easily


accessible.


Most production


environments


are computer


integrated.


Applications of computing are more ubiquitous.


Indeed, most production


environments are now computerized.

An early endeavor of computer scientists was to endow computers with the ability


to perform intelligently.


This area of research is called Artificial Intelligence (AI).


tremendous advances in computers have made AI a more tractable area.


Today it is


possible to write software that outperforms humans.


Al techniques


have


been


successfully


implemented


many


domains.


example, Expert Systems (ESs) have found large application domains from banking to








5

During the last decade there has been an enormous number of AI applications on


scheduling.


Researchers developed


ESs for many different production environments,


(Alpar and Srikanth 1989a), (Chang 1985), (Kerr and Ebsary, 1988), (O'Keefe 1986).


was discovered that knowledge base construction was the main bottleneck to building


such systems.


ESs were not easy to maintain, and their simple inference mechanisms


proved


to be


insufficient for


most


problems.


Yet ESs


were able


to solve


a lot


problems and help achieve some of the management objectives (Miller, Lufg and Walker

1988).


Other


AI applications focus on search heuristics and knowledge representation.


Knowledge representation is important because the system should be able to represent


domain specific knowledge.


Search heuristics are important because most AI applications


focus on real


time scheduling


where


is a critical constraint.


Search


heuristics,


sometimes referred to as meta knowledge, should efficiently search for the solution and


must exploit knowledge representation language characteristics.


Search schemes such as


Constrained


Heuristic Search,


(CHS)


(Arff


Hasle


1990),


(Fox,


1983),


(Fox and


Sycara,


1990),


blackboard style control, (Ow, Smith and Thriez 1988), (Smith, Ow and


Potvin,


1990),


planning algorithms (Shaw,


1988c) have been successfully applied.


Even though these systems are able to successfully utilize AI techniques, they lack


one important


aspect


intelligence:


"learning."


There


been


little


work


developing scheduling systems that can learn.


Even though the learning problem has








6

Recently, there has been work on heuristic discovery using learning algorithms.


Such systems use a learning algorithm to


generate a knowledge base and utilize this


knowledge for problem solving (Piramuthu et al., 1991), (Yih 1990).


to their ability to represent complex domains and apply


knowledge, AI approaches are most promising for scheduling.


domain specific


They not only provide


powerful


problem


solving


mechanisms


blend


today's


computer


integrated manufacturing environment.



1.3 Scheduling and Genetic Algorithms


Genetic Algorithms (GAs) are general purpose, stochastic search algorithms.


They


conduct the search by manipulating bit strings and employ stochastic operators such as


reproduction, crossover and mutation.


At each iteration a GA moves from one population


of strings to another until a set of useful strings are found.


Until


recently,


little


work


been


done


on the


search


behavior


GAs.


Holland's schemata theory is of little help to explain the convergence behavior of GAs.

Recently there has been significant work on analyzing GAs as Markov Chains (Nix and


Vose,


1992).


Results are still far from applicability but the model introduces powerful


analytical tools for investigating GA search characteristics and


worst case analyses.


Genetic operators have been employed for


sequencing problems.


There has been


research on developing new operators that are suitable for sequencing problems (Whitley,










Classifier


Systems


(CSs)


are adaptive


learning


systems


use GAs as


discovery algorithms.


Their application to scheduling has been limited due to their weak


knowledge representation language.


Nevertheless, it has been suggested that they are


robust learning systems in dynamic domains (Goldberg 1990).


First attempts to use them


to learn sequencing heuristics rather than sequences have proven promising (Hilliard et


al., 1987), (Hilliard et al.,


1989).


1.4 Contents of This Dissertation


Most optimization approaches to scheduling suffer from their overly simplistic


assumptions,


their


inability


incorporate


domain


specific


knowledge


their


inflexibility


adjusting


to environment changes.


Even


though


such


techniques are


capable of producing high quality solutions with respect to their presumed environment,

solutions generated by such methods are not directly applicable for real time scheduling.


The solutions generated


may even


be infeasible


because of


their overly simplifying


assumptions.


power.


Among all OR techniques, only simulation offers adequate representational


It is also very useful in performing "what if" analysis.


Almost


approaches


employ


enough


expressive


power


for representing


domain characteristics.


Expert Systems lack the adequate search power necessary to


search the rule space efficiently enough.


Among the Al approaches to the scheduling


problem, most of the recent


work


been


towards


using domain


specific


heuristic








8

these methods are successful in solving specific problems, they are unable to adapt their


search mechanisms as the environment changes.


They lack the ability to learn.


Applications of Machine Learning (ML) in scheduling problems are at an early


stage.


Even though some encouraging results exist, pure ML approaches are too general


for a complex domain like scheduling.


In this dissertation we concentrate on a hybrid


approach which combines the knowledge generated by OR research over the last thirty


years and the knowledge representation techniques enabled by AI research.


A GA search


mechanism is employed to discover cases where certain heuristics are applicable.


We test


the plausibility of


a GA based learning approach.


We focus our attention on a flowshop


environment which is complex enough to test the usefulness of


such an approach.


object oriented simulation environment that is capable of handling inference is utilized.


We also study the behavior of

on the computational complexity of (


GAs as search algorithms.


jAs.


We present a bound


We prove some properties of this bound and


demonstrate


optimal


search


parameters


can be


obtained


to minimize


computational complexity of GA under certain conditions.


Chapter


we present


literature


survey


approaches


scheduling.


Emphasis is on dispatching rules and AI applications in scheduling.


In this


chapter we discuss limitations and advantages of both AI and OR approaches.


We also


motivate the need for learning in real time scheduling systems.


Chapter 3 mainly focuses on learning.


Part of the chapter is dedicated to Machine










results


some earlier


work


on ML.


Finally,


we analyze


the existing


research


scheduling from a ML perspective.


We review the literature on


GAs and CSs in Chapter 4.


We start with earlier


theoretical findings on GAs.


Next,


we present a discussion


of several applications of


GAs and CSs in other domains as well as in the scheduling domain.


A large part of this


chapter will be devoted to the results of Vose and Liepins, (1991), and Nix and Vose,

(1992) which will provide building blocks for Chapter 5.


In Chapter 5,


we develop a bound on run time complexity of a GA.


We derive


the bound through a series of theorems and lemmas.


Part of the analytical results we


need are borrowed from the research on spectral analysis of non-negative matrices.


Chapter 6 summarizes our first attempt to build a learning system using GAs.


first analyze a simple, hypothetical production environment and compare the performance


of the


learning system against systems using single heuristics


with no learning.


further investigate the possibility of learning optimal rules by simulating an environment

where an optimal rule is known to exist.


Chapter 7 extends the idea described in Chapter 6 to a flowshop environment.


rule language that is able to capture the knowledge related to a flowshop environment is


described.


Results of simulation experiments are presented and discussed by comparing


to some known dispatching heuristics.


Finally, in Chapter 8, conclusions and directions for


future research for both














CHAPTER


SCHEDULING, DISPATCHING AND ARTIFICIAL INTELLIGENCE

2.1 Overview of Scheduling and Operations Research


Research


on scheduling problems


has a long history,


dating


back


to the


nineteen fifties and early nineteen sixties.


Most of the optimal rules and algorithms for


certain classes of problems were found during these initial stages.


As production systems


evolved and became more complex, mathematical models representing these real systems


have


become


more


complex.


After


Stephen


Cook


introduced


theory


completeness in


(Gary and Johnson


1979), researchers realized that most of the


scheduling

namely N]


problems


P-complete


belonged

problems.


to the

This


class


triggered


computationally


research


intractable


on heuristic


problems,


algorithms


scheduling that do


not guarantee optimal solutions but do


guarantee a good solution


within some error limits of the optimal solution.


It was also shown that these models


could deal with comparatively realistic problem types and appeared to be more robust


optimization


based


methods (Rodammer and


White


1988).


Recent results have


shown that even these heuristic algorithms have their limitations.


It was believed that for


NP-complete


problem and


given


error tolerance


there existed


an approximation


algorithm that could solve the problem within the specified


error bounds, but it was


a,_. *- Tfl--. 1_ ~.. 11.. .... r










section


we review


production


scheduling


problems


discuss


advantages and disadvantages of


traditional Operations Research (OR) methods used for


their solution.



2.1.1 Definition of the Scheduling Problem and the Production Environment


From an OR point of view, the scheduling problem can be defined as finding a

sequence of operations on a given set of jobs that will give an optimal solution with


respect to the prespecified performance criterion.


There may be more than one measure


of interest for a given problem formulation.


Each may result in different solutions.


Also,


a slight change in the problem may drastically change its mathematical modelling.


often the case that there may exist a polynomial time algorithm for a model but a slight

change may yield a problem without exact solution methods in polynomial time.


production environment is defined by the number of machines, the type of


machines, and the nature of the flow on the shop floor.

machines are assumed to have infinite buffer sizes. All m


All queues feeding into the


machines are assumed to be able


to process only one operation at one time.

When a production environment has a work flow that is unidirectional where each


job visits each


contrary,


machine


if the


installed


have routes


series,


specified


we refer to


a prior,


it as a


flowshop.


but the routes do


not enforce a


unidirectional flow, such an environment is called a job-shop.










operation is known before the operation is preformed.


The release time of a job is the


time the


job enters the shop floor and is available for processing.


These are usually


assumed to be zero or, if not zero, are assumed to be known a priori.


It is implicitly


assumed that the scheduler has perfect information as to when the job is going to be


available.


Due dates are the times when the jobs are supposed to leave the shop floor and


be ready for shipment to the customer.


Machines are assumed to be the only type of scarce resource.


Labor and raw


materials


are assumed


to be


available


infinite


amounts.


some


production


environments with different types of job families, there may be sequence dependent setup


times between two jobs coming from different families.


There may also be technological


constraints


imposing


precedence


relationships


between


operations


a job.


example, assume a job has five operations performed on it before being completed, and


operation


two has


to be


performed


before


operation


five.


This is


referred


as a


precedence relationship.


In a flowshop environment such a relationship is implicit.


2.1.2 Notation and Parametric Description of Scheduling Problems


be the number of machines;

be the number of jobs;

be the processing time of job j on machine i;










be the release time of job j;


be the completion time of job j;

be the flowtime of job j;

be the lateness of job j; and

be the tardiness of job j.


completion


time


time


when


a job


ready


to leave


system.


Flowtime,


lateness


tardiness


are defined


non-decreasing


functions


completion time as follows:

F.=C -r.,
J J J

L. = C. -d.,
J J J


A function of completion time is called a


completion time if it is non-decreasing in completion time.


"regular measure" with respect to the


Hence flowtime, lateness and


tardiness are regular measures with respect to completion time.


Scheduling problems are defined by three parameters a/3/y (Lawler et al.


1985).


The first parameter, a, is the description of the shop floor and can be any of the

following:


The shop floor consists of only one machine.


max(OLj)








14

mJ: The shop floor is a job-shop with m machines.

The second parameter, I3, is the description of the constraints or the attributes of


the problem.


If f3 is null then the problem has no constraints and the attributes are in


their most general form.


Some typical specifications are the following.


Release time of job (which is not necessarily zero.)


prec:

pmtn:


There are precedence relationships between the jobs.

Preemption is allowed.


Setup time of sij


is required if job j is processed after job i when


There is no setup required if j=i.


All processing times are equal to p.


third


parameter,


is the


description


objective


function


to be


minimized. Usually these functions are regular measures with respect to the completion


time of the job.

Cmax:


C,:
il=


F*:
Fmax"





F


Some typical performance measures are the following.

Maximum completion time, often referred to as "makespan".


Total completion time.



Maximum flowtime.


Total flowtime.


Aflov~mim ltnm Qpn>


Pj =p










Tmax


Maximum tardiness.


Total tardiness.



Total weighted tardiness.


In an excellent survey by Lawler et al., (1985) many scheduling problems are


listed and


solution


methods are discussed.


Similarly


Lageweg et al.,


(1981) present


complexity results for 4,536 problems and some references.


It is not surprising to see that


only 9% of these problems are listed as easy problems with 81% as NP-complete.


remaining 10%


are open problems.


Some of these problems and their solution methods,


if any, are given in


Table 2-1.


Table 2-1


clearly


demonstrates that,


other than single machine problems


simple performance measures, scheduling problems are mostly intractable by classical OR

techniques.

Most of the OR approaches look at oversimplified versions of the real problem,

such as assuming deterministic processing times, known release times and well behaved


quantifiable objective functions.


Even with such oversimplifying assumptions most of


these


problems


class


of NP-complete


problems.


Furthermore,


solution


methods suggested can not incorporate qualitative management objectives and heuristic

Irnnuwleao. intn thp nrnhls-n











Table 2-1.


Some scheduling problems


PROBLEM COMPLEXITY ALGORITHM
1/prec/fmax P Lawler, (Lawler et al. 1985).
1/pmtn,rj,prec/fm, P Baker,Lawler,Lenstra and Rinnooy
Kan, (Lawler et. al 1985).
1//Lmax,Tmax P Earliest Due Date, (Baker 1974).
1/rjLmax NP Special cases are solvable by extended
Jackson's algorithm, (Lawler et al.
1985)
1//iC P Shortest Processing Time, (Baker
1974)
l//IwjCj P Weighted SPT, (Baker 1974).
1/ri/XC, NP Pseudopolynomial algorithm by
Lawler, (Lawler et al. 1985).
1//ITj NP Generalized SPT, (Lawler et al. 1985).
mP//iCj P (Lawler et al. 1985).
mP//XTj NP (Lawler et al. 1985).
mP//Cmax NP There are approximation algorithms,
(Lawler et al. 1985).
2F//Cmax, 2/pmtn/Cmax P Johnson's algorithm, (Baker 1974).
2F/ri/Cm,x NP (Lawler et al. 1985).
2F//Lmn NP (Lawler et al. 1985).
2F//iC, NP (Lawler et al. 1985).
3F//Cmax NP (Lawler et al. 1985).
3F/pmtn/Cmax NP (Lawler et al. 1985).
3F/pmtn/XCC% NP (Lawler et al. 1985).










2.1.3 Scheduling Problem as it Appears in Industry


Even the simplistic mathematical models of the scheduling environment are hard,


but as may be expected, real life problems are even harder.


Smith explains the reasons


as follows:

The sources of difficulty identified included (1) the need to adhere to a
typically idiosyncratic set of restrictions relating to production processes,
resource capabilities, and resource availability, (2) the need to balance a


large


conflicting


set of


objectives


unpredictability of factory operation.


(Smith


preferences,
1988b, p. 382)


To make life more complicated, the performance measures are not usually as simple as


those listed earlier.


Management usually sets multiple objectives which not only interact


but also conflict with each other.


Sadeh and Fox explain this very clearly.


Real-life scheduling problems are subject to a variety of preferences such
as meeting due dates, reducing the number of machine set-ups, reducing


inventory costs,


using


accurate and/or fast machines,


some jobs are performed within a single work-shift,


making sure that
. Although these


preferences are usually set independently to one another, they interact. For
instance selection of a good start time for an activity (e.g. to meet a due
date) may prevent the selection of an accurate machine for another


operation or may prevent meeting another job'


due date.


For this reason,


selecting operation start times or allocating resources based solely on local


a prionr


preferences


is likely to result in


poor schedules.


Preference


propagation is meant to allow for the construction of measures that reflect
preference interactions. These measures can then serve to guide the
construction of a good overall schedule rather than a schedule that locally


optimizes a subset of preferences.


(Sadeh and Fox 1989, p.


What happens in a real time situation is even more drastic than explained above.


The operator responsible for all this has other worries, too.


The tools the


nneratnr ic rePnnsnihle can't all nmn the amrne kind nf nrndncNt and heRause










fabrication steps.


Each wafer must go


through, say, a photo process


or 15 times, each process building a layer resulting in a three dimensional


complexity--you can't build


level


B before you


build


level


complexity is compounded by other difficulties such as all boxes which
store a lot of wafers look alike and often an important customer comes in


with a


special request.


Modern


Times at its


worst.


For operator and


manager alike, the whole manufacturing process is like a giant chess game


--except


unpredictabilit


complica
v make


demanding of games.


ntea sequencing, corn
it harder to think th
(Sullivan and Fordyce


ibinatorial


Rough than e
1990, p. 53')


complexity,


;ven


and
most


Kerr and Ebsary state the reasons for choosing heuristic approaches to scheduling

rather than an optimal OR method as follows:

*..


The first type of approach


{ the OR approach)


was rejected on the basis


that: { 1 } known future requirements and probable events will influence the
short term schedule in an aggregate way, but it would be unreasonable to
incorporate these into a short term optimization approach because of the
uncertainty associated with them.
{ 2 } the environment is unlikely to remain static even over a period as


short as 12 hours. (Kerr and Ebsary


1988, pp.


19-20)


A real life production environment is subject to changing constraints, fluctuating


resource availabilities and even conflicts among the management objectives.


As such, the


problem


is more of


rescheduling


scheduling


to the dynamic


nature of


problem (Rodammer and White


1988).


OR models are not capable of capturing the


important qualitative aspects of the problem


as actually


occurnng


on the shop-floor.


Furthermore, most of the assumptions are never observed--almost no attribute of the


system is deterministic--or are irrelevant to the real problem. Finally, real life scheduling

problems have almost always no feasible solutions (Fox and Sadeh 1990).


This


I










Since production must still continue, some constraints--we will


them soft


constraints--must be relaxed in an intelligent manner so as to minimize both the cost of


re-solving


problem and


possible cost


associated


relaxing


that particular


constraint.


For example,


relaxing the due date constraint of


a less important job or


relaxing the constraint on labor availability by using


action.


overtime are common courses of


One feasible way of achieving this is to have a dedicated knowledge base that can


guide the relaxation process so as to minimize the associated costs.



2.1.4 Last Word on OR Approaches


Bel et al. summarize the above observations.


Optimization


combinatorial


methods.


This


approach


is mainly


concerned with a static point of view, and focuses on global objectives


satisfaction.


Nevertheless, due


to algorithm complexity, it does not deal


with realistic situations.


As a result, the model and criteria represent only


a very limited part of the real-live problems, which reduces the optimality


and even the feasibility of the solutions generated.
209)


(Bel et al.


1989, p.


There


are successful


approaches


in some


industries,


as the


flight


scheduling


system


American


Airlines


(Parker


1989),


it hardly


resembles


production


scheduling


problem as far as constraints and


the importance of real


decisions are concerned.


Even while dealing with the "nice" problems, there is another


inevitable problem OR modelling approaches suffer, Baker bluntly declares:

The traditional OR syndrome covering the application development cycle


has five steps:


modeler sets up application, 2) model is demonstrated


/










many industries which have long relied on mathematical programming,
these experts are taking early retirement. (Baker 1990, p. 108)


It is now clear that there is no easy way to solve all scheduling problems


most of them are NP-complete.


since


Those that can be solved in polynomial time can not


fully nor closely represent the real life problem, and thus we can not draw conclusions


from their results.


What is the most promising approach then?


If solving this problem


is so hard,


what is the remedy found in real manufacturing applications?


Researchers and manufacturers have found a few solutions for the computational


burden associated with solving the scheduling problem.


Instead of looking for a globally


optimal


solution,


a good


feasible


solution


reflects


important


management


objectives


can be


accepted.


There


are several


ways


finding


such


solutions:


simulation, by dispatching rule heuristics or by artificial intelligence approaches.


Optimization by simulation is preferred over optimization by analytical


methods


when the function can not be represented analytically, or an analytical solution is not


possible.


There are different approaches to optimization by simulation such as response


surface methodology or perturbation analysis.

Response Surface Methodology (RSM) is used to define the relationship between


input


variables


performance


criteria.


Usually


it is assumed


performance criteria can be represented as a kt degree


variable,

values.


polynomial function of the input


The technique requires repetitive simulation runs with varying input variable


Once the response surface is estimated the optimal can be found bhv some search


S,








21
The Perturbation Analysis Methodology (PAM) uses an estimate of the gradient


of the function of interest to direct its search.


The input variables are perturbed slightly


throughout the simulation run to get an idea of the gradient function.


Depending on the


new gradient estimate, more perturbation is done. Finally the simulation stops when the

output of the simulation converges to an acceptable value. One advantage of this method


over RSM


is that optimization is done within


the simulation, however,


like all


other


gradient search techniques it suffers from convergence to local optima.


For scheduling


problems, simulation is used to


test the performance of certain


dispatching heuristics, such as in Vepsalainen and Morton (1987).


Usually the problem


is fixed and a number of runs is performed to compare two or more heuristics in the same


setting.


There is no effort to discover under which parameter values the heuristic being


tested is superior to the others.

In the following sections, we will discuss dispatching rule heuristics and artificial

intelligence approaches.


Dispatching


A popular alternative to optimization methods is the use of dispatching rules to


select the next job to be processed on a machine.


This appears to be the actual practice


used in many shop floors where the dispatcher uses a simple rule of thumb to select the


next job.


The dispatching problem can be defined as follows:


given a processor and a








22
Dispatching rules have been found to be easy to use and thus very convenient for


real time decision making.


However,


"a noticeable shortcoming is the inherent myopic


nature of dispatching" (Bhaskaran and Pinedo


1992), pp.


The greedy nature of the


rules causes suboptimal, low quality solutions for certain problems.


They are useful for


short term scheduling in an environment where exogenous events are highly likely to


occur.


Research on dispatching rules have shown that there is no dispatching rule that


dominates the others on all types of problems or even on the variations of the same


problem. For

and solves the


example, the SPT


rule selects the job having the shortest processing time


1//EF problem optimally.


However, for the same problem, the EDD rule


selects the job having the earliest due date and is superior if the objective function is Lmx.


When


production


environment


is highly


dynamic


when


random


events


common, dispatching rules perform better than they do in a deterministic environment.

This observation is stated in Bhaskaran and Pinedo:


In contrast, when the processing times of all jobs are deterministic and the
machine is subject to an arbitrary breakdown process, the WSPT rule does
not necessarily minimize the weighted sum of completion times. {On the
contrary, in a stochastic, one machine environment where processing times


are randomly distributed WSEPT


rule minimizes the sum of the expected


completion times. }


are more


robust


Such a phenomenon,


in a


random


environme


where simple dispatching rules
:nt than in a fully predictable


deterministic


environment,


is fairly


common.


(Bhaskaran


Pinedo


1992, pp.


1-12)


On top of being robust, dispatching rules have some other nice properties.


It has


ljkno F-n hm nrI knlerl n a^ nn^ Lt .nl. a4- 11 --,-.- .-- A l 1r -_-._-_-_----P-- I1 1








23

and tardiness measures, related dispatching rules are somewhat sensitive to the due date

assignment rules (Blackstone, Phillips and Hogg 1982).

In the following subsections we discuss several dispatching rules and present a

large list of rules compiled from articles appearing in the literature.



2.2.1. Some Dispatching Rules Discussed in Literature


In this section some dispatching rules and the cases where they have been found


useful will be listed.


It also has to be noted that most of these rules are tested in a job-


shop environment, but there is no inherent disadvantage in using them in a flowshop


environment.


We will not


consider dispatching rules used for processes with precedence


constraints since they do not have direct implementation for a flowshop environment.

Rules referred to as static do not change the priority of the job as time passes.

On the contrary, dynamic rules change the priorities of jobs as time advances.

Even though some authors make a distinction between dispatching and sequencing


rules, in this research they are considered the same.


times to a queue


If the dispatching rule is applied


of size N, by removing the highest priority job each time, it acts as


a sequencing rule.

Below we summarize many common dispatching rules.

The Select In Random Order (SIRO) rule is simplistic in that it does not use any


information about the shop floor.


As expected, it has not been found useful for any








24
The First Come First Served (FCFS) rule assigns the highest priority to the first


job in the queue.


It has been found useful for minimizing the variance of the average


waiting time if pj


- f, for all j.


It also minimizes the expected average waiting time in


the queue if pj is independent and identically distributed (i.i.d).

The First At Shop First Served (FASFS) rule, a variation of FCFS used in job-

shops gives the highest priority to the job that entered the shop the earliest, breaking ties


arbitrarily or by FCFS.


It has been useful for reducing the variance of the average total


time spent in the shop by all jobs.

The Earliest Due Date (EDD) rule assigns the highest priority to the job with the


earliest due date.


the case of


The EDD rule minimizes maximum lateness, maximum tardiness and


non-deterministic processing times, minimizes the expected maximum


lateness but not the expected maximum tardiness if the environment is a single machine


or a proportionate flowshop.


Another version of EDD, referred to as Modified earliest


Due Date (MDD) rule, tends to produce good tardiness results.


The modified due date


is computed as


*=max(d.,t +pj)


where t is the current time (Baker and Bertrand 1982)


like SPT


MDD has a tendency to perform


when due dates are tight and like EDD when due dates are loose.


Longest


Processing


Time


(LPT)


selects


longest


processing time.


Even though it is not optimal it is useful in mP//C_. problems.


Another









Processing


Time (LERPT) rule is optimal


P//E[Cmax].


LEPT


and LERPT behave


identical for a large family of problems.

The Most Work Remaining (MWKR) rule allocates the highest priority for the job


with the most work remaining on it,


where work is defined as


Pigj
in S


and S is the index


set of the remaining operations.


MWKR tends to minimize the makespan for a job shop


environment.


The Shortest Processing


literature.


Time (SPT) rule is


perhaps the most discussed rule in


selects the job with the shortest processing time.


SPT is optimal for


where machines are proportionate, and


and mF//J(t), where J(t) is the number of jobs in the shop at time t.


1//J and mP//J


1//J(t), mP//J(t)


It is also optimal for


, mF//J where J is the average number of jobs in the system (Bhaskaran


and Pinedo


1992).


also minimizes mean lateness in a single server environment.


Even though SPT performs well in minimizing the number of tardy jobs when due dates

are established exogenously (Blackstone, Phillips and Hogg 1982), one of the problems

with SPT is that it causes high variance in lateness related measures (Day and Hottenstein


1970).


It is also found to be irrelevant to cost-related measures, suggesting that cost is


not related to flow-time (Blackstone, Phillips and Hogg 1982).


In the case of stochastic


processing times, and under fairly general conditions the Shortest Expected Processing


Time (SEPT) is optimal for the above problems.


The Shortest Remaining Processing


'NC Cj~ mP//I= cj mF~C c










machine problems,


when


jobs have different release times and preemption is allowed


(Bhaskaran and Pinedo 1992.)

The Slack per Operation (SLACK/OPN) rule selects the job with the smallest slack


time per operation ratio. The Minimum Slack (SLACK) rule selects the job with the

minimum slack time remaining. SLACK/OPN, SLACK and EDD rules are known to


perform better in minimizing the variance in lateness related measures compared to SPT


FCFS.


SLACK/OPN


performs


better


in minimizing


number


tardy


compared to EDD and the SLACK rules (Blackstone, Phillips and Hogg

One other due date related rule is the Critical Ratio (CR) rule, w


the job with the smallest critical ratio.


1982).


which selects the


The critical ratio CR is calculated by


CR=


d,-t


and L is the waiting time remaining in the queue for job j (Blackstone, Phillips and Hogg


1982).


CR rule is known to work well for mean tardiness (Park, Raman and Shaw 1989).


Least


Work Remaining


(LWKR) rule selects the


job with


the least work


remaining,


where work is defined as before.


LWKR tends to minimize the flowtime in


job-shops.

The Weighted Shortest Processing Time (WSPT) rule, assigns the highest priority


to the job that has the highest


ratio,


where wj is the weight--or importance--given to









for parallel


machines and proportionate flowshops.


WSEPT


rule is optimal for


l//Ew.E[C.] in a stochastic environment even in the presence of machine breakdowns.


The Shortest Setup


Time First (SST) rule assigns the highest priority to the job


that requires the shortest setup time, possibly zero time units if the previous job was from


the same family.


SST tries to minimize the total time spent in setups.


SST has not


proven very useful.

The following two rules try to capture the power of individual rules by taking a

combination of them.

The Dynamic Composite Rule (DCR), attempts to minimize the total tardiness in


a job-shop environment.


DCR selects the job with the highest priority index l(t) which


is calculated as


I1(t)= k1 (d 1


-pi ) +k2 i(t) p, +


kW(t)
m3
f w,(t)
I1I


where


m is the number of machines in the shop, and Wi(t) and W,(t) are the current


workload of the current machine and the next machine respectively.


The performance of


the rule is comparable to SPT in total lateness and the number of tardy jobs, and is better


tardiness.


It also


produces


variance


flowtimes


compared


to SPT


(Bhaskaran and Pinedo 1992).










Perhaps one of the most useful rules in a job-shop environment is the COVERT


The Cost OVER Time rule aims at minimizing the total tardiness.


The priority


index I(t) is calculated by


max(kp -u.,O)


pjkp


where


is the


sum of


processing


times


jobs divided


by the


number


machines.


The job with the lowest index is given the highest priority.


As can be seen from the above discussions no single dispatching rule dominates


the others in all environments.


the contrary, most are very


specific to a limited


number of environments.


Given the vast variety of scheduling environments and the


changing nature of the job shop, it is not practical to find a feasible enumeration method

to find out which dispatching methods to use under which circumstances.

Our research will try to overcome this problem by using a system responsive to


changes.


Our theoretical and applied method will adaptively update the set of current


dispatching rules as the environment changes.


2.2.2


A List of Dispatching Rules


Before we present a list of dispatching rules we will introduce


additional notation


that is adapted from Blackstone, Phillips and Hogg, (1982). Let


ha lb1 arnn ,i '~rrn .









be the time job j is scheduled to be completed at station i;


be the remaining processing time of job j on machine i at time t;

be the expected waiting time of job j in station (queue) i, given that there

are a jobs waiting in line; and


be the dollar value of job j.


Definition 2.1:


A proportionate flowshop is one where p..


=ap j, a>0,Vj.


Table 2-2 consists of a long list of dispatching rules.


name, abbreviation, the calculation of


For each rule we give its


its priority index set, and conditions where it has


been found useful.











0 o -



dU Q )
01 a)E'

o S a.
s w 4-


S W c


0W a0 Cd ~ t're
vrj H0k






a.),OI-

C:ED r
U cl3
H Bk+ImCEl e a
p4 E








C-

CI -, M
I Pr


F- ~
Cr V
04 Vt-\ \1V
_
zP
07.?'
p c


C-





C) C)
I- V


$ o C) bJ
U, 4)
O Cr CraoE












































































-s4


0 C
4-





-0iE



4)


4)


-a ?


1
~F-~










_3 2





C
0
C)

i~i ~0




o



cnt~








I-;

.6 .r SVI


C) H >) U, U, C

I" -e j%J V
-~ VI~ VIv j
Clj VI

-r -

E> IIY~

U V

4)M -





pa z
ON1
0











_ _3 3





S

U,




U~OS




II









o -
F- -







I VI




o 0g
0.

.s z
uC







rr.l










2.3 Overview of Artificial Intelligence


Artificial Intelligence (AI) emerged as a symbolic computation paradigm during


early 1960s.

intelligent.


It was the aim of AI research to generate systems that could be considered

Even though intelligence in humans takes many forms, such as judgement,


creativity, plausible reasoning etc.,


AI research restricts its attention to


"computational


techniques for performing tasks that apparently require intelligence when performed by


humans" (Tanimoto


1990).


research


mainly


focuses


on knowledge


representation,


developing


search


techniques, perception and inference (Tanimoto


1990).


To date many applications have


been developed and used that are products of AI research.


Expert Systems, robotics,


character recognition, natural language understanding, planning, learning applications are


examples of the results of


AI research.


Mathematical Programming methods in OR use optimization techniques to solve


complex


problems


domains.


Mathematical


Programming


methods


have


objective function to be optimized and a constraint set that restricts the search space. On


the contrary, Al methods depend heavily on heuristic knowledge to direct a search.


relationships in the problem do not need to be represented by mathematical equations.

Constraints and objective function(s)--usually referred to as goals--can be ill defined and


all may be non-quantifiable (Simon 1987).


Most importantly, AI methods can incorporate


experience and expertise into the solution of the problem.









Al approaches look promising for problems of higher complexity.


A solution form an AI


method


not be


optimal


hence,


inferior


to the


solutions


found


optimization algorithms.


However, the flexibility of modelling and the ability to yield


reactive solutions is greatly enhanced.


In dynamic production environments, the biggest


problem a scheduler is usually faced with is how to handle exceptions such as rush jobs,


machine breakdowns, resource unavailabilities, etc.


Clearly mathematical models of the


scheduling problems are seldom capable of handling such cases whereas most of the


implemented AI systems, such as OPIS (Fox


1990), (Ow


1988), are able to handle these


cases using heuristic knowledge.

In the following subsections, four different families of AI approaches to solving


the scheduling problem will be presented.


The distinction between any two families is


not well defined


since all methods borrow ideas from each other.


Nonetheless each


family captures the prevalent theme of its members.


The four categories are:


1. Expert Systems (ES) approaches,


Constrained Heuristic Search (CHS),


3. Hybrid methods, and

4. Machine Learning (ML) approaches.



2.3.1. Expert Systems and Scheduling


Expert Systems (ES) attempt to mimic the decision making behavior of the domain










an inference engine, and


3. an explanation subsystem, coupled with a user interface.


the scheduling context,


a knowledge-base has rules of thumb or facts that


represent the


knowledge about the


scheduling problem,


the factory


environment, job


descriptions, etc.


Any inference strategy, such as backward chaining or forward chaining,


can be used depending on the structure of the knowledge base.


An explanation subsystem


will give the line of reasoning behind the decisions made by the system.

Even though the ES approaches have been successful in many domains, like loan

approval, medical diagnosis, fault detection, etc., the same has not always been true for


the scheduling domain.


A close look at the medical diagnosis domain, for example, will


reveal


there


indeed


exists


domain


experts


from


whom


necessary


knowledge can be extracted.


This however is not so clear for the scheduling domain.


The next subsection will present views concerning this issue.


2.3.1.1


Cases against and for Expert Systems in Scheduling


Building a knowledge base for scheduling is a clear bottleneck for an expert


scheduling system.


In addition, there is considerable controversy about the existence of


scheduling experts.


However, Mc


Kay et al.


(1992) report that there are scheduling


experts.


They


state:


In conclusion, it is suggested that human expertise in scheduling exists and
is a valuable component of any realistic scheduling nlanninp environment








37


Still, most researchers have beliefs against the suitability of ES approaches to


scheduling.


Fox reports the following difficulties.


... taking an expert systems approach to scheduling appeared inappropriate.
There are two problems with the expert systems approach:
(1) Problems like factory scheduling tend to be so complex that they


are beyond
Therefore,


cognitive
schedules


capabilities
produced b'


human


scheduler


scheduler.
are poor;


nobody wants to emulate their performance.
expert scheduler exists.


{There indeed no


(2) Even it the problem is of relatively low complexity, factory
environments change often enough that any expertise built up over
time becomes obsolete.
Expert systems appear to be appropriate only when the problem is both


small and stable.


(Fox


1990, p. 81)


Basically


expert


systems


are not suitable


scheduling


domain


for the


following reasons,


(Fox


1990),


(Rodammer and


White


1988),


(Blessing and Watford


1987), (Savell, Perez


and Koh 1989) and (Steffen and Greene


1986).


Most


scheduling


experts are


not real


experts.


Their


decision


making


process is more akin to reacting to crises or management dictates rather


than that of analyzing the underlying problem.


Thus, they can not give


general recipes for cost-effective solutions.


The scheduling problem is inherently very complex.


Hence large-scale


problems are


to solve


within


a reasonable amount of


using


inference strategies such as froward or backward chaining.

The scheduling environment is highly dynamic, so any rule of thumb valid


rr I


.








38
Contrary to the above results Miller, Lufg and Walker report a successful ES

implementation.


The large potential savings achievable through Expert Systems Scheduling,
as proven by the $10 million annual pay back at a Westinghouse plant,
will attract significant industrial interest in the next few year, making this
one of the hottest areas for expert systems applications (Miller, Lufg and


Walker 1988, p.


176-177)


Even


though


are generally


believed


to be


unsuitable


for the


scheduling


environment, there is still a big advantage for expert systems ideas.


Their ability to


represent ill structured, ill defined, qualitative aspects of the problem is valuable.


inherent ability of ESs to represent such characteristics can be incorporated into a hybrid

approach which will be discussed in the following sections.



2.3.1.2 Some Reported ES Applications


Most of the ES applications reported in this review are actually implemented or


are in a prototyping stage.


As expected, the authors report the standard bottleneck of


building


such


systems--the


knowledge


acquisition


stage.


Even


most


applications


are fairly successful with regard to acceptance by the staff and are being put


to actual use on the shop-floor.


Clancy and


Mohan (1990) describe


an expert


system, RBD, designed to help


make real-time dispatching decisions by using sequencing rules representing company


knowledge.


To enable real-time decision making, the system is fed with real-time data










. Order type,

. Equipment status,

. Work station characteristics, and

. Job characteristics.


Using the above criteria the system produces a priority list of jobs.


priority job is then selected.


The highest


The system has no learning capabilities.


RBD has


been implemented and used in the semiconductor industry.


The results


obtained


so far show a decrease in Work in Progress (WIP) and an increase in critical


equipment utilization.


Kerr and


problem


Ebsary (1988)


company


describe an


producing


expert s

"specialist


system


approach


products


to the scheduling


to customer


specified


configurations from approximately 3,000 different types of subassemblies, machine


parts


raw materials."


Due to the complexity of the task, the authors were unable to elicit knowledge


from the domain expert.


When the classical knowledge acquisition techniques proved


useless, the authors constructed the knowledge base by analyzing the actual schedules


prepared by the schedulers.


The resulting knowledge-base is composed of


six different


sets of rules categorized as follows:

Priority rules,

Job precedence rules,








40
Contingency rules, and

Time conversion rules.

The system was able to access real-time data about the shop-floor status via a

relational database system, and make real time dispatching decisions.


The authors


report two problems with the project.


. Capturing expert knowledge comprehensive enough to cover all the cases one

may face in such an environment was impossible.

. The highly dynamic nature of the scheduling environment caused the knowledge

base to be invalid very rapidly.


(1988)


describe


an expert


system,


PAMS,


hybrid


knowledge-base composed of rules,


frames and some heuristic knowledge which


specific


to the domain of scheduling parallel machines.


The knowledge base can be


broken down into four sets of rules, dealing with:

Job status,

Machine status,

Labor status, and

Material status.


PAMS has a two stage control


strategy where a feasible schedule is generated in


the first phase and


is evaluated


and updated


in the second phase, if desired.


system is capable of producing schedules at different levels of detail.


The authors report


was










Savell,


Perez and


(1989)


describe a classical


Expert System application,


implemented for a semiconductor production plant.


Due to the modular nature of the


environment the knowledge base could be constructed separately reflecting knowledge


about each cell rather than the whole factory.

through interviews with the domain experts.


The knowledge acquisition was carried out

The resulting knowledge base had two types


of rules:

Rules to assign priorities, and


Rules


to assign


production


cells


to the


equipment


(Equipment


Scheduler).

Priority rules are used throughout the whole system but each cell has its own

knowledge-base independent of the others for equipment assignment.

Even though the system helped to organize the current scheduling practice, the

authors report the problems with run-time performance and the assessment of the system.



2.3.2. Constrained Heuristic Search


Constrained Heuristic Search, CHS, can be viewed as constraint satisfaction, where

a search to find the feasible solution is guided by heuristic knowledge.

The constraint satisfaction problem, CSP, can be formulated by using a constraint


graph,


where nodes are variables and arcs are n-ary constraints among the values the


variables may be assigned.


Problem solving is performed by sequentially choosing a









constraints are satisfied and all variable assignments are made.


If a node is found that


can not be expanded yet no feasible solution is reached, the algorithm backtracks to the


closest unexplored node and continues the search from there.


In a scheduling problem


this can be viewed as generating sub-schedules and backtracking when the current sub-

schedule violates the constraints.

CHS utilizes the techniques used for CSP but, in addition uses heuristic knowledge


to guide the search, so that costly backtracking is minimized.


Perhaps the most crucial


difference between CSP and CHS is that CHS also makes use of an objective function

to evaluate the assignments, rather than a blind search that will result in poor solutions


with respect to the performance criteria.

information that they found useful for


Fox, Sadeh and Baykan (1989) present heuristic


the scheduling problem which they refer to as


problem textures:

1. Value Goodness,


Constraint tightness,

Variable tightness with respect to a set of constraints,


4. Constraint reliance,


Variable tightness,

Variable contention, and

Constraint arity.


When


viewed


as an AI


search


algorithm,


CHS


methodology


consists









1. Define an initial state,


where no variable is assigned a value.


while the goal state is not reached do {


Match the best operator that applies to the given state.


3. Apply the operator.

}

The matching performed in Step (2) is the most difficult part of the algorithm.


For a successful match the algorithm not only needs to satisfy the preconditions of the

relevant operators, but also needs to find the best operator to apply in order to reduce the

search complexity of the problem.

Note that Step (3) will result in either adding a structure to the graph, further

restricting the domain of the variable, or reformulating the problem, such as relaxing

some of the constraints.


In the rest of this section,


search algorithm.


we will present papers that use CHS as their main


Even though most systems presented here use unique strategies to


guide


their


search,


main


search


strategy


CHS.


Most


systems


use additional


heuristics other than CHS, to limit the search space and reduce the computational burden.


Hasle


(1990)


discuss


constraint-guided


heuristic


search


knowledge used to implement this metho

implementation that uses the above ideas.

that generates routing and processing inf(


A system called PLATO-PS is under


The system has a process generation subsystem

)rmation. The sequencing subsystem "utilizes










sequence using heuristic, constraint-guided state space search".


The sequencer utilizes


heuristics for pruning the search space, such as:

ordering heuristics and

grouping heuristics.

The constraint-guided search uses heuristics for pruning the state-space search, such as:

constraint violation and

state selection.


Bensana


et al.


(1986),


Erschler


Esquirol


(1986),


et al.


(1989)


introduce two systems called MASCOT and OPAL. The systems are designed to use three

types of knowledge during the process of deriving feasible schedules:

The theoretical knowledge on scheduling problems,

Empirical knowledge about priority rules, and

Practical knowledge about technological constraints.


The so called Constrained Based Analysis (CBA) approach aims


at generating


restrictions on local scheduling decisions by only considering limit times and resource


availability constraints.


As soon as a new precedence constraint is found, a limit time


updating is searched. If such an update can be accomplished, the new value is propagated

as far as possible, along the technological and other precedence constraints which have


already been accounted for.


When no more updating is possible, a search for a new


precedence constraint is undertaken.









support module is used to


provide advice on


the sequencing of


operations based on


practical


or heuristic


knowledge.


Finally


supervisor


coordinates


mteraction


between the two modules by calling each in order as needed.


If no feasible schedule is


found the supervisor calls a failure recovery module that selectively relaxes some of the

constraints such as due dates.


Erschler and


Roubellat (1989) introduce a system called OARABAID which uses


constraint-based


analysis


as described above.


Constrained heuristic search has been extensively utilized for the implementation


ISIS and CORTES systems.


The general design of these systems are geared


towards:

constructing a representation language adequate enough to capture the nature of

the problem and


. developing a search architecture capable of


exploiting the search space both


effectively and efficiently.

ISIS-1 is an order-centered scheduler which tries to construct schedules by considering


jobs rather than


available


resources.


system


identifies


next


schedule through the use of CHS and tries to schedule each order and selectively relax


any causal


constraint found


to be unsatisfactory


(Fox


1984).


ISIS-2


is an enhanced


version of ISIS-1, where instead of solving the problem at one level, the system attacks


it in a hierarchical manner.


The systems first selects an order, then analyzes the available








46
of resource versus order scheduling which is referred to as "multiperspective scheduling"


by the author (Fox 1990).


First, bottleneck machines are identified by a rough draft of


the final schedule and these machines are tried to be assigned operations.


Then the


system considers an order based scheduling.

CORTES is a distributed system for production planning, scheduling and control


(Fox and Sycara


1990).


The CORTES system, compared to the ISIS family, considers


jobs and resources as aggregate variables (Fox


1990).


The approach used in activity


scheduling is very similar to the least commitment strategy used in planning systems.

The problem solving method of the CORTES system can be summarized as follows.

1. An initial state is generated.


The constraints imposed by the current state is propagated.


Texture measures (Fox, Sadeh and Baykan


'89), are computed.


4. Based on (3), a state is selected.


A rule is matched to the current state, and an assignment is made.


If the goal


state is not reached, steps (2) through (4) are repeated.


Research on both ISIS and CORTES has reported promising results.


texture measures has


The use of


resulted in a reduction of the search complexity.


Steffen


Greene


(1987)


introduce


an approach


named


"dedicated-shared


decomposition," where, after the production planning level, they assign certain jobs to


dedicated


machines,


in each


subproblem


perform


dedicated


loading,








47
Usually selection of the dedicated machine is done according to the customer


preference.


The scheduling is handled by a heuristic algorithm that will minimize the


conflicts for competing jobs. Loading and sequencing of the shared resources are done

by "Constraint Directed Search." Based on adherence to the constraints included in the


prototype, the authors conclude that the approach is applicable.



2.3.3. Hybrid Artificial Intelligence Methods


The OPIS


family is different from the


ISIS/CORTES family in that it uses a


blackboard style control.


The blackboard contains the necessary information about the


factory and is capable of managing the temporal constraints.


actual


scheduling


decision


are made


an analysis


decision


knowledge sources (KSs).


The former one is used to analyze the available capacity


whereas the latter two are used for resource or order based scheduling decisions.


At each cycle, after propagating the results of


any unexpected events such as


capacity conflicts, machine breakdowns, etc., the search manager priorities and stores


them on the "agenda."


The task with the highest priority is executed as a subtask (Fox


1990).


OPIS


is a reactive scheduling system which is designed to deal with exogenous


events.


When


such


an event


is encountered,


consequences


effects


propagated onto the existing schedules.


Conflict arising from this change are stored in










decision tree to decide which KS(s) to


use for exception handling.


The OPIS systems


family extends the multi-perspective scheduling view of the ISIS 3 system and allows

alternative solution methods within each view.

Ow, Smith and Howie (1988) describe a distributed scheduling system called CSS

which uses two types of knowledge bases:


. the work order manager,


WOM,


. the resource broker.


The idea of CSS is similar to the one described in (Shaw 1986).


The system uses


a bidding


methodology.


WOM


estimates


completion


time


a work


order


examining its operations graph and initiates a bid among the nodes which could perform


the job.


After evaluating the bids submitted, the job is sent to the selected node.


resource brokers evaluate the availability of their resources and bid according to this


information.


The search method used in the system is called a two-pass best-first search.


Shaw (1986) uses a network-wide bidding scheme, where each cell bids for a job

to schedule, and the one that has the best bid gets the job to process.

Decisions to be made by the system are:

which cell to assign the job and

the sequencing and scheduling within the each cell.

Performance measures used are:










job lateness and tardiness statistics, and

average in-process waiting time.

The author uses a planning algorithm for scheduling within the cell.


Shaw


manufacturing


(1988b)


describes


environment


a decentralized,


has been


divided


cooperative


cells


system


composed


where


a number


machines.


The cells can communicate with each other through a Local Area Network.


The scheduling problem is addressed in two levels.


In level one a cell that wants to


submit a job calls for "bids" from the other cells which believe that they can process the


Whichever gives the best bid with respect to the performance criteria wins the bid


and the job is transferred to that cell.

At the cell level, a planning algorithm is used which is driven by pattern matching


and state transformation operators.


Basically the operators that match the current state


are applied until a goal state is reached or a failure is reported--i.e. there is no infeasible


solution.


Cell levels also contain manufacturing modules (operators), decision rules, and


scheduling heuristics.

The author reports that the system, on the average, performs better than myopic

SPT, bidding SPT, and bidding EFT.

Shaw (1988c) describes a system that employs:


pattern-directed


inference


to capture


dynamic


nature


scheduling


environment,










.the A*


search algorithm (Tanimoto 1990),


to expedite the searching procedure.


The author employs a strategy that generates a schedule for each job and then uses


the planning methodology to resolve the conflicts that arises


resources at the same time intervals.


due to sharing the same


To solve the conflicts the author suggests two


approaches:


Critic


Mechanism:


This method


uses a table called


"Table of Multiple


Effects (TOME)"


where for each element in that table they have to check


the delator lists and adder lists--which is very costly.


Another drawback


problem


is that


can not identify


alternative


resources


operators.


Reasoning


about


Resources:


This


works


identifying


conflicting


interactions and then, using a plan revision procedure tries to improve the

makespan as much as possible.


In all three papers by Shaw,


the author analyzes the feasibility of the bidding


scheme used in connection with a planning algorithm at the cell level.


The real schedule


construction done at the cell level is a good example of heuristic search where cumulative


processing


time


estimated


remaining


processing


time


is used


as heuristic


knowledge to guide the search.



2.3.4 Machine Learning Approaches










as new decisions were made.

as executable instructions. L


The intelligence (the heuristics) was coded into the source


Unless the code changes, they will remain the same and will


react exactly the same way they had done previously even if those actions resulted in a

bad decision.

In this section we will present papers that use at least one Machine Learning (ML)


approach


to construct their


knowledge


bases.


classify


them


as knowledge


discovery systems.

are not updated.


Note however that, once the knowledge bases are constructed, they

So even these systems can not improve their performances through


"experience"


possible exception


system


SCHEDULE by


Lamatsch


et al.


(1988).


Their contribution is however their ability to construct knowledge that often helps


the performance system to achieve better results than those accomplished by non-learning

systems.

Blessing and Watford (1987) describe a FMS scheduling system, INFMSS, where


the knowledge is represented by frames.


They structure the knowledge base in three


dimensions namely;

FMS description on one axis,

part mix on another,


schedule proposed on the third axis.


If any point in that three dimensional space is already defined, the expert system uses










The schedule that gives the best result is chosen as the answer.


Those points are saved


for further reference.


This mechanism is referred to as rote learning.


Even though the system saves old


decisions that gave good results, it has no means of generalizing them and we suspect that

in such a complex environment the chances of observing the same state is very low.


interesting


approach


to the


scheduling


problem


been


discussed


Chryssolouris, Lee and Domroese (1990).


The objective of the study is to be able to find


the weights of the criteria for the decision-making process at the workcenter level based


on some performance measure.


A Neural Net has been used for this purpose.


Examples


for training are generated by simulation by fixing the operational policy and workload of


the workcenter.


The outputs of the simulation are the performance measures.


The input


to the


neural


network


is the


workload


workcenter and


desired


levels


performance.


The outputs of the network are the weights necessary to achieve the desired


level of performances.


The weights can be considered as follows: Given a scheduling


heuristic, what must be the relative importance of local criteria with respect to each other


so as to achieve the desired


level


of performance.


The authors


use a system


called


MADEMA to carry out the actual scheduling decisions within the simulation.


Hilliard et al. (1987), (1989) describe a series of experiments

rules for simple job shop scheduling tasks by using classifier systems.


to leam general


The system knows


different predicates, dispatching rules, which it can use for sorting the jobs in the queue.









can discover the optimal rule, SPT


for a single machine minimum lateness problem (we


assume this is total lateness), and good solutions for minimum weighted tardiness problem


Another emerging approach to scheduling problems is case based reasoning.


learning system stores each case seen so far as a piece of knowledge, in what is referred


to as a


"Case Base."


During problem solving, if a match is found for any of the cases


stored in the case base, the solution method or the results stored with the case is applied


to the problem.


The match does not need to be exact.


Koton (1989), describe a system


called


SMARTplan


is used


resource


allocation


scheduling


airlift


operations.


Due to the size of the search space only a partial match of the cases are


required for successful instantiation of a stored case.


Only those cases that are successful


are stored for future use.


Lamatsch et


al. (1988) describe an expert system named SCHEDULE that uses


reduction digraphs to match the given problem as an instance of a scheduling problem


solvable by the stored heuristics.


All the heuristics are polynomial time algorithms that


can produce optimal or near optimal results published in various journals.


If no match


is found, the system first tries to find a problem that is close to the original problem with


respect to a metric they define.


If that fails, a relaxation of the problem is solved.


system has a learning capability by adaptively adjusting the distances between two nodes


of the graph.


As the user prefers a problem to solve as a substitute for the original










problem is a better approximation for a certain type of problem.


Note that each node is


a type of problem that can be reduced to each other if there is a path between them.


Nakasuka


Yoshida


(1992)


describe


another


inductive


learning


method


discover rules for a scheduling environment.


At any given decision point the system is


simulated forward by using all possible dispatching rules separately.


Once the best rule


is found,


that state and


rule applied


is saved


as an


example and


the simulation


continues until the next dispatching decision point.


After enough examples are generated


a binary decision tree is constructed by a specialized induction algorithms.


also describe the details of the induction algorithm.


The authors


The system is used to find good


solutions for the tardiness and makespan performances, i.e. one measure is given as a


constraint and the other is optimized.


The system performs better than single dispatching


rules.


Piramuthu et


al. (1991) describe a


hybrid method for scheduling that


employs


an experimental


environment,


using


simulation,


a learning


component.


New


knowledge is incorporated into a pattern-directed scheduling system.


For a given state


defined by eight control parameters, the system is simulated by using each dispatching


rule they have considered as useful.


The dispatching rule that yields the best result with


respect to the performance measure is specified as a positive example for the learning


subsystem.


In this way a training set is constructed.


decision tree is constructed using Quinlan's


ID3 algorithm


From the training examples a

n. Each path from the root to










is done, the system is ready to


make schedules by matching the state of the system to


one of the rules created and by using the dispatching heuristic at the leaf node to choose

the operation to be performed.


Shaw,


Raman


Park


(1991)


discuss


adding


a learning


capability


knowledge-based scheduling system.


The authors discuss how rule induction can be used


in conjunction with dispatching rules (i.e., rule induction can be used to determine


important attributes of the system and then to choose the dispatching rule to


use).


This


is called Pattern Directed Scheduling (PDS) by the authors.


In an experiment, the authors


use four such rules that are derived by taking into consideration eight attributes of the

system.

Even though the overall performance of PDS is reported to be better than using

a single dispatching rule, this approach is very costly since examples have to be created

by simulation runs except for a few known cases when an optimal rule is known to exist.

Except for a few trivial scheduling problems, it is not possible nor feasible to construct


or simulate an

Thesen ai


"oracle" that is required by most inductive learning algorithms.


(1986) describe a knowledge-based robot scheduling system.


Knowledge is not acquired from a domain expert, but rather created using simulation


expenments.


The authors simulate the system by using dispatching rules and then, based


on the specified performance measures, they decide on which dispatching


rule to use


given the system state which is defined by the robot position, number of electroplating


nd









Yih (1990) describes an approach to the knowledge acquisition task to schedule


the operations of a material handling robot.


processing tank to another.


The robot has to carry each part from one


This has to be scheduled so that the part do not get spoiled


in the tanks.


The authors develop the


Trace Driven Knowledge Acquisition (TDKA)


methodology to acquire rules. The methodology requires simulation experiments with

scheduling experts, in this case students. The records collected from the simulation,


traces, are used to define the classes and to select a rule applicable for each class.


author describes an algorithm for the class formation and rule assignment.

TDKA is suitable for knowledge extraction the method is limited by th

expert schedulers and their consistency during decision making. The methi


Even though


e existence of


od also suffers


from heavy involvement with manual procedures.

Yih and Thesen (1991) describe the same experimental setting discussed in (Yih


1990).


This time using the traces of the decisions a set of states


and state transition


probabilities are defined.


Based on this information the decision process is analyzed as


a Markov decision process behaving according to the calculated transition probabilities.


The optimal policy of the model is used for rule formation.


same problem described in Yih (1990).


The idea is applied to the


The method produces a good set of optimal rules,


but they are not sufficient to cover the entire rule space and also they are limited with the


existence of real scheduling experts.


This shortcoming has been fixed in


Yih (1992).


After the optimal


policies are discovered,


the author uses a


modified version


of the










base.


rules


formed


perform


much


better


identified


human


schedulers.

Yih, Liang and Moskowitz (1992) use the same problem to describe an OR/NN


hybrid approach. This time an NN is used to generalize from the optimal policy of the

semi-Markov process. That is, each state,optimal policy pair is given as an example to


a NN.


After training the NN is able to make predictions that are of better quality than


human schedulers.



2.3.5 A Listing of Systems


In Table 2-3 we summarize the research done in knowledge based scheduling.


Below


we describe the ideas behind the columns in the table.


Knowledge Representation refers to the type of knowledge representation scheme

used in the system.

For a feasible running performance most systems employ an intelligent search


heuristic.


Given the complexity of the scheduling domain this appears to be the key


aspect of the system.


As noted earlier, most ES applications presented here have run-time


performance problems, due to using backward or forward chaining, without making use


of other available information.


However, using heuristics like CHS,


often improve their


performance.

The manufacturing environment for which the system is developed will be listed








58

Since almost all of the systems presented here have knowledge bases, it is also


important to discriminate how their knowledge base is organized.


This often reflects the


problem


solving philosophy of the system.


For example,


ISIS-2


uses a hierarchical


problem solving architecture hoping that this will reduce the size of the search space.


Some others facilitate a distributed problem solving architecture.


The "Structure" column


captures this information.


The ability of the system to learn is mentioned in the "Learning" column. If the

system has a learning capability the nature of the learning algorithm used is listed.


Finally, the "External Module"


other external systems.


column tells if the system is interacting with any


The interaction may be in the form of feeding information to an


external module, communicating with a simulation program, getting data from a data base,

etc.


Some columns of Table 2-3 are adapted from Kusiak and Chen (1988).












59




0 U2 .9 :
4)r -
$4 9 E
'tl 8, z
Y r-IY
Ca ol a





Otoo




-J cc-


-o p

U, (A -l





I to



U, C
00 04) U I Iv
UU U,
Ca~~ U c U
U to
or~ C~oaa
C"" .0S
So C:



E ~ n ccl= l8U




Oo to *0
S~ 0 .
I- -~



U _


C)


U, (A V)aasv
4) -S 4 )j
4) ~0 -1
-~ U, c


LL1

'a'
0 '6 *~ 'a
""o 'a I.
tocr Q J a 0






























































































4)


d)3


V)
ho
.f;


w K
Irl


,,


f-










61




saC. 0L
EEV

WV) C). C#

toWvb)S











C)
C.) >>, ~


C. -a- U~t





Cu -C

C ton M~




C. ) C Co
o Ca C) C) c



a C)5 g

b. bM .5'3.


'us %.'t 0C
C.) ..

V1 V1




00. .1 -I I
LI.I- LL L


'-- C)


-= *I fl'h I;c!I











62




V, 0~ 'a
Vn
-




bL) C~E




ou I-


0=


Caa 0.S







E V
(a8 C C5 m c


E a o
o~ a E
U Cl 0 S C

(N-
4)I)B.



C Co


~ci
Q) o )
LI, O .
E O d) C



as Ca Ca o

C) *5
C) 0
'S 4)


'C .. or-
C ~~~ 00 C'-- n










63


Y 4.)
~C) '0 U, C)
0 aCf4 G) P4
agz0.0





U, -4'uP1 1 OKP

*-C ou3 r








C) o


o' 0



C) U'i
Sc 4=bl .
'S~~E -u 6.C)
.~e '0C)4 -
U 6., 0~ S c


C) '0a )
z S
$0


Pa c-I



o~c 'Uc 0a,
Ua

'0s
S C-, o
Vj V1 u C)
U, -
o a)E
4= -P I-',9,





PS 33 0

'a 03 -al
-z "9(
P7% YO dfC ,











64



C)o C
0P C 00
3 0
0zcn
p~ $ 00>




oh 0

E!s'3Q











nYoo



33 0

-a, C
-d U

U W sv
o a 0


Ca 0 E


C) 0
S 'C)


I- V2-Bv
1U> 0a Cs




o Vso






m Ca
-~B _
ii-.rr









65

a)
C' 0 Ca
o$ o

-J~ C- cnv ,v



al)
-J


a)a
o ~G) V4)
Si ra. .00 .00 00



a) )

Ca Ca 4) l a. PY~ ~ j.

C5 .0.0. '
o~a -' .C .
C0 C0uo c
rfl~~ C) "
C) CL) e



o V 0
M S C 6
C) V) 'S 2



4) 0
0E o a a

Ca Ca Ca
C) C)
&, 0' 0
"~LLS &
B .5 C
4)j ~4) 0~
__ ~ V C
CP ~gCp 3 U )

r.r t












66



r0
zC 0
p~0 0
E~ a
ozt~
Sm
0

B vl rC
w O 0

W III I I o







C. o U


Ct

CC

C
0l o4-c




0Q 0

4- 0- CtC C.)
C 0- 0c oa Ct

s:o 8
C) &,

rci c vl
Pc W0



-a 0






Ca U
o 0lv

Cfl U, -~Be8



C~ C
4) 08


0. 00










67



0 0
Ea a
-
wE v I -
-0h
Cd C- v








EE








C.)


0O O




Ca
U 0. u





C))






.0
F-a d








C I I-~














CHAPTER 3
LEARNING

3.1 An Overview of Machine Learning


Learning is a very broad term that denotes the way in which people increase their


knowledge and skills.


Machine Learning (ML) concentrates on generating systems that


can learn and thus acquire new "declarative knowledge", improve their performances for


problem


solving


through


instruction


or practice,


organize


generalize


new


knowledge (Carbonell, Michalski and Mitchell 1983).


For example, the knowledge base


required by an expert system can be generated by using learning algorithms and then

refined by the learning sub-system so that the expert system performs better than the "no-

learn" case.


Research on ML dates back to the early


1960's (Cohen and Feigenbaum 1982).


Most of the ideas used today were initiated during the earlier years of ML research.


example, adaptive systems depending on random mutation and selection were created


hoping


that these


processes


would


result in


intelligent systems.


Various analogs of


neurons were developed and tested.


During the mid


1960's and early


1970'


s, it became apparent that learning was a


hard task and that it was virtually impossible to learn without any prior knowledge of the


domain or meta knowledge about the task.


This led to research concentrated on systems








69

Finally, within the last decade, ML research centered around the theory of learning


as well as its applications to specific domains.


Even though the theoretical approaches


consider the most general form of the learning problem, most of the applied ML research


focuses on problems specific to the domain for which it is being developed.


Carbonell,


Michalski


Mitchell


describe the


trend


that started


1970's


as The


Modern


Knowledge-Intensive Paradigm."


Before


discussing


details


research,


it is useful


to consider


dimensions of ML approaches.


to their assumptions.


That is, we will characterize the approaches with respect


We use four dimensions of learning: definition, methodology, nature


mode.


discuss


the research


done


within


dimensional


framework.


dimension,


definition


learning,


describes


research


perceives learning.


What do researchers mean when they use the word "learning"?


all applications, share the same view of learning.


Let us see how learning is defined.


Cohen and Feigenbaum define learning from four different perspectives.


Herbert Simon (in press) defines learning as any process by which a


system


improves


its performance...


more


constrained


view


learning, adopted by many people who work on expert systems, is that


learning is acquisition of explicit knowledge...


learning


is skill


acquisition...


a forth


view


3} A third view is that
of learning is that it is


theory formation, hypothesis formation and inductive inference.
and Feigenbaum 1982, pp. 326-327)


(Cohen


Most AI applications, regardless of whether they are learning applications or not,










The acquisition of explicit knowledge is the main focus of ES applications.


Even


though ESs are not learning systems themselves, the problem of knowledge acquisition


initiated


a substantial


amount of research


on issues about


learning.


It is useful to


consider


evolution


approaches


to knowledge


acquisition


since


we believe


demonstrates in which direction ML research is going.


is not an


exaggeration


to say that ESs enjoyed


success


domains


where


expertise existed and where knowledge did not become obsolete in time.


This is exactly


one of


reasons


were


not successful


scheduling


domain.


scheduling domain is so complex and dynamic that it is almost impossible for humans to


understand the existing causal relationships. However, eliciting expert knowledge is the

bottleneck of ES development (Cohen and Feigenbaum 1982), indeed in any knowledge


intensive systems.


After realizing this, the trend in knowledge acquisition shifted from


classical techniques like protocol analysis, or interviews to interactive techniques where


the knowledge acquisition task was given to the learning system.


The learning system


guided


search


concept formation


asking


questions


to the expert and


refining its current hypothesis based on the answer given by the expert.


One such system


is TEIRESIAS by Davis (1982) which is used for medical diagnosis.

During the course of development of ESs, researchers realized, to their dismay,


that for some domains even interactive systems proved infeasible.


There were no experts


or the experts were not able to dedicate time to the knowledge acquisition process.


This










help.


As a result, ML research concentrated on developing learning algorithms that are


in turn used for developing systems that can learn.


Learning requires an extensive amount of inference.


Inference can be deductive,


or inductive, and sometimes both.

needs to explore the hypothesis space


During the inference process,

e, which is usually very large.


the learning system

This necessitates a


powerful inference mechanism.


There are different approaches to implementing this


mechanism which are summarized within the second dimension.


The second dimension of learning is the philosophy employed for learning.


other words, it is the methodology utilized by the system to learn.

Most learning methodologies considered in ML literature can be classified into

four groups: rote learning, learning by being told, learning from examples and learning

by analogy (Cohen and Feigenbaum 1982).


Rote learning can be viewed as memorization of problem instances.


system does not try to generalize.


The learning


An instance encountered is stored as knowledge.


main issue here is organizing the instances in storage and accessing them as needed.


example, assume the system is trying to learn the prices of different cars.


Assume the


system conceptualizes a car by using attributes such as color, A/C, number of doors,


engine size, transmission type, etc.


When the system is presented with the specifications


of the car it checks to see if it has seen that instance before.


the price of the car and stores the example.


If not, the system calculates


If so, the system responds without executing








72
(assuming that is the case) and tries to calculate the price if presented a yellow colored

car even if it has information about a red colored car of the same type.


Cohen


Feigenbaum


explain


learning


being


told,


or advice


taking,


follows: "Learning by being told, in which the information provided by the environment

is too abstract or general and, thus the learning element must hypothesize the missing


details" (Cohen and Feigenbaum 1982), pp. 328.


The system should have the knowledge


to be able to interpret high level information, make it operational for itself, and then


integrate it to


knowledge


(Cohen


Feigenbaum


1982).


scheduling


environment where the system


is learning


how schedules are evaluated,


system


should have the capability of understanding what "avoid creating high WIP inventories"


means and take the correct action to achieve this goal.


This advice is then integrated into


the existing


knowledge


system


decides


if this is a


useful


advice


after


evaluating its performance.


Note that such a system has very demanding assumptions like


prior


knowledge


domain,


consistency


initial


knowledge


base,


existence of a performance evaluation entity.

Cohen and Feigenbaum (1982), describe learning by analogy as follows:

Learning by analogy, in which the information provided by


environment


relevant


only


analogous


performance


thus,


learning


system


must


discover the analogy and hypothesize analogous rules for its
present performance task. (Cohen and Feigenbaum 1982,
p. 328)

A & i A J r ^ .i -








73
gives vague information about how a particular instance is an instance of another concept.

AM tries to utilize this information together with the information supplied in the VIEWS

slot to map existing examples into examples of the concept under construction (Cohen

and Feigenbaum 1982).

Perhaps the most extensively analyzed learning strategy is learning from examples.


There are very


different approaches


to learning from examples, such as


learning


induction,


explanation


based


generalization,


Neural


Networks


(NNs)


Genetic


Algorithm (GA) based learning systems.


We will focus on induction and learning from


examples in


this section


only


briefly mention


neural


networks.


The GA


based


systems will be covered in Chapter 4.

Inductive learning is a data intensive approach (Quinlan 1986), where the learning


task is to generate a knowledge base after seeing a set of examples. An example is an

n-ary tuple representing n-1 attributes of the object of interest and its class. The resulting


knowledge


base should classify all


of the


training


examples correctly.


Most of


learning systems such as CLS, ID3, ACLS, ASSISTANT use decision trees for knowledge

representation and others like AQR, CN2 try to learn production rules (Clark and Niblett


1989).


A more general knowledge representation is decision lists (Rivest 1987).


Omitting the technical details, a decision tree construction algorithm can be stated

as follows:


1. If all


the instances are from exactly one class,


the current node is the









74

a. select the attribute that is best for classifying the current examples.

b. us the attribute to partition the current examples adding a branch to the


tree for each partition.


Construct the decision tree recursively from each


these branches.


For example, assume a customer is represented


occupation and credit history.

customers for loan purposes.


by four attributes: age, salary,


The learning task is to differentiate the good and bad

A decision tree may look like in Figure 3-1:


Figure 3-1 A Decision Tree


Rules are conjunctions of attributes from the node to a leaf.


For example, one rule


S ~ ~~~~ r-, S S .. .I I I I


I rrr I r


^^^^ nrr t-* ^










Since


the method


is data driven,


the resulting


tree can


different for


different data sets.


Also,


the trees generated


the same example set may


differ


depending on the method used to choose attributes on which to split.


Even though the


accuracy of the tree is not sensitive to the split criteria used, the depth of the tree is very


sensitive to this measure (Mingers


1989a).


In noisy domains,


where there is a lot of


measurement errors, pruning the decision tree often improves the accuracy of the tree.

Again the shape of the tree after pruning depends on the pruning method and there is no


known optimal way of pruning


(Mingers 1989b).


Decision trees have been applied to domains like medicine, agriculture, banking,


production, etc.


Specific applications can be found in (Messier and Hansen 1988), (Braun


and Chandler 1987), (Carter and Cotlett 1987) and (Piramuthu et al.


1991).


Explanation Based Learning (EBL)--or Explanation Based Generalization (EBG)--


is a knowledge intensive process.


The bias required for the search is the domain theory


as opposed


to the


inductive


imposed


attributes


considered


concept


formation by the inductive learning algorithm. In other words, the learning element has


some


knowledge


about the domain


as opposed


to having


no information


about


environment.


The task is generalization rather than acquiring new knowledge.


mechanics


of EBL


are quite


simple.


learning


element


some


knowledge about the domain it is operating in.


set of small cardinality.


It is given a set of examples, usually a


The first task is to explain why this example is an instance of










For example, assume the target concept is


by using integration by parts.


indefinite integrals that can be taken


The system has the knowledge of how to take integrals of


polynomial functions, trigonometric functions, logarithmic functions, etc.


The system also


knowledge


integration


techniques


integration


parts,


trigonometric


substitution, etc.


Assume the example is


x. The learning system must be able to


explain why this is an example of

from this example that /x "e x ne.


integration by parts and then be able to generalize


N, is solvable by integration by parts.


methodology


EBL


is very


close


to the


humans


learn


through


experience.


For example, assume a student is learning how to take derivatives.


At first,


he is inexperienced, a novice. After learning the rules of taking derivatives he is able to

solve problems of similar nature. However, he is still very slow and follows the steps his


teacher had told him. After solving enough examples he is able skip steps, and finally he

is able to find the solution without evaluating each step but rather checking a few crucial


steps.


At that point his knowledge is said to be tacit.


Similarly, before the examples are


presented the learning system is a novice,

generalize and draw conclusions. In other


that it is more general and in a more operational form.


but after a few examples it is expected to


words the existing knowledge is compiled so


By this way the system not only


generalizes its knowledge but also reaches to conclusions very efficiently.


that this is how experts operate.


Many believe


Since the knowledge they have is tacit, already in the


'I I C ,, II I 0 I I .1 .aI










Logic


Theorist (O'rorke


1989) is a system that uses EBL methods.


EBL is also


used in natural language understanding (Dejong and Mooney


1986), concept discovery


and learning simple tasks (Mitchell, Keller and Kedar-Cabelli


1986).


Research on EBL


focuses on alternate strategies to improve the efficiency of learning


(Flann, Dietterich


1989)


believe


most


intelligent


systems


have


to employ


EBL


methodology for performance improvement.


Most research on EBL is restricted to


very simple problems which are easily


solvable by


humans,


like understanding a plain English paragraph


or recognizing an


object such as a coffee cup.


Research on applying different methodologies for search and


inference is still on progress.


NNs are composed of


individual computing entities linked together as a network.


Research on neurocomputing dates back to the 1940's and was first analyzed by Warren


McCulloch and Walter Pitts (Hecht-Nielsen


1990).


After an interruption for about ten


years, research in this area concentrated on network architectures, and learning algorithms

for NNs.


The general model of NNs has of

between nodes and input and output conn


processing elements (nodes), connections (arcs)

elections. Each node has a transfer function and


a local memory that consists of weights and necessary variables. Most NNs have at least

three layers: an input layer, an output layer and a processing layer. The nodes in the


input and output layers do not process the signals.


They simply transmit it.


The transfer










which then may activate the nodes output connection--the node fires.


In this manner an


input signal is transferred to the output.


Learning in NNs is accomplished by training.


Training can be in supervised, or


graded mode or the network can be self organizing (Hecht-Nielsen 1990).


on the first two modes.


We will focus


In supervised training, a network is given a set of examples


consisting of the pair (XkYk),


where Yk is the true function value.


In graded mode, the


network receives a grade of how well it has done on each example.


In both cases each


node is expected to update its local memory and to adjust its weight vector with respect

to the feedback, so as to be able to discover the true function.


NNs


have


successfully


been


applied


to pattern


recognition,


such as character


recognition and many other domains ranging form credit approval to image compression


(Hecht-Nielsen


1990).


The third dimension of ML research is the "nature

as static, incremental and adaptive learning. In static lea


" of learning which we classify


ring, the learning system does


not consider new information after the learning task has been completed.


ready for decision making.

new information comes in.


learned is static.


The system is


With incremental learning, the knowledge base is revised as

This type of learning still assumes that the concept being


Adaptive learning can be described as a continuous cycle of generate,


test and refine.


The system constructs knowledge with the available information.


As new


information arrives, the system tests the validity of the current knowledge and refines it










The fourth and


last dimension we will consider is the "mode"


refers to the existence or absence of supervision during learning.

levels: supervised, semi-supervised and unsupervised modes. For ex


of learning.


This


We consider three


sample, ID3 works in


supervised


mode


since


there


an ORACLE


classifies


examples


whereas


organizing NNs work in unsupervised mode.

Learning from Observation and Discovery, or so called "unsupervised learning",

is a very general form of inductive learning where the system is not tutored by a teacher.

Carbonell, Michalski and Mitchell classify systems that employ unsupervised learning by

the degree of interaction with the external environment.

The extreme points in this dimension are:


passive


observation


where


learner


classifies


taxonomizes


observations of multiple aspects of the environment.


Active experimentation,


where the learner perturbs the environment to


observe
involves


results of its


gener


acquired concepts.
EURISKO svsten


.1


nr


perturbation.


... often


this form


of learning


action of examples to test hypothesized or partially
This type of learning is exemplified in Lenat's AM and
s (Lenat 1976, 1983.) (Carbonell, Michalski and


Mitchell 1983, p. 73)

In the following section we will discuss theoretical issues on learning algorithms,


present some results of research conducted in this area.


In Section 3.3


we will


analyze the scheduling domain from a learning perspective and discuss the research within

the four dimensional framework we have described in this section.




3.2 Theory of Learning


r










there are domains where developing a learning system is impossible.

decade there has been an enormous amount of research on the learn


During the last


ability of certain


concepts, on the complexity of learning and on characterizing the learning task, especially


after the pioneering work of Valiant


(1984).


Research has shown that some concepts are


learnable by at least one learning algorithm and some are not learnable in polynomial

time or require an exponentially large set of examples.

We start our discussion of these results with some definitions and notation.

Valiant proposed the idea of learning a concept with low error and doing this with


high probability instead of learning a concept with complete accuracy.


Later this was


referred to as Probably


Approximately Correct


(PAC)-learning (Haussler


1987).


A learning algorithm calls a routine named EXAMPLES which selects examples

with respect to a probability distribution P and labels them correctly, possibly by the help


of an ORACLE.


The error between the hypothesized concept and a target concept is


defined as the symmetric difference between two concepts.


A learning algorithm tries to


generate a concept g such that the probability that the error between g and the target


concept f is less than e, i.e.


and f.


P(fAg)

where A is the symmetric difference between g


A PAC-learning algorithm can formally be defined as follows (Natarajan


1991):


An algorithm A is a PAC learning algorithm for a class of concepts F if;


A takes inputs e


e (0,1], 8


(0,1] and n


N where e and 8 are the error


and confidence parameters respectively, and n is the length parameter.










For all concepts f


eF and all


probability distributions P, A


outputs a


concept g e


F, such that with probability at least (1-8), P(fAg)


Research in this area focuses on bounds on the number of examples and the time


required to learn a concept in terms of the parameters 6 and E.


Most of the work done


has focused on learning boolean concepts such as pure conjunctive, pure disjunctive,


internal disjunctive, k-CNF and


k-DNF concepts.


Assume a concept can be defined by n attributes, a1,..,a..


A pure conjunctive form


is defined as the conjunction of a subset of these variables.


A pure disjunctive


form is


defined as the disjunction of a subset of the variables.


A concept is a k-CNF concept if


it is represented by the conjunction of arbitrary number of clauses where a clause is a


pure disjunction of at most k variables.


represented by


Similarly a formula is in


the disjunction of an arbitrary number of terms,


conjunction of at most k variables.


k-DNF form if it is

where each term is a


An internal disjunctive concept is the same


as pure


conjunctive where each conjunct can be a compound atom.


a value is called an atom.


An attribute that is assigned


If an atom is a disjunction of more than one atoms of the same


attribute, it is called a compound atom.


In his pioneering work on PAC-learning,


classes of learnable concepts.


Valiant (Valiant


He shows that certain classes


1984) discusses the


boolean concepts like


k-CNF concepts, monotone DNF concepts, or arbitrary concepts with a variable appearing


only once are learnable.


But his findings are not generalizable to less restrictive arbitrary










He also


gives


the necessary


conditions


for a


class of


concepts to


learnable


polynomial


sample complexity.


He reports that all pure conjunctive, disjunctive and


internal disjunctive concepts are PAC-learnable.


k-CNF and k-DNF concepts are also


PAC-learnable with the exception that when k is large, computational efficiency is not

guaranteed.


Angluin


Liard


(1988)


demonstrate


PAC-identifiability


CNF(k,n)


concepts in noisy domains given that the noise rate is bounded above by


S


where


CNF(k,n) denotes the class of concepts in conjunctive normal form defined on n variables


with at most k literals per clause, and M is the number of clauses.

bounds on the number of examples needed for PAC-learnability. T


They also provide


hey conclude that in


the presence of noise, PAC-learnability may not be computationally feasible for many

domains.

So far we have assumed that the learning element had access to an ORACLE that


labels the examples correctly.


What if such an ORACLE does not exist, which is usually


the case.


Board and Pitt


(1989) suggest such a scenario where the system tries to learn


multiple concepts inductively when there is only


partial information about the labels of


the examples.


They refer to this as semi-supervised learning.


The learning element is


trained with example pairs and the labeling tells if they belong to the same class or not.

The authors show that most classes that are PAC-learnable such as k-CNF and k-DNF.








83
Most of the work done in this area is of only theoretical interest and most of the


bounds on sample complexity are loose bounds with little practical value. In practice,

most of the algorithms developed for learnable classes perform much better. But still


there are a few open issues most of the authors mention (Valiant 1984),


(Haussler 1988).


Most of the algorithms assume that there is neither classification nor measurement errors


on the examples.


domains.


The concepts where PAC-learnability is proven are very restrictive


It is assumed that the attributes considered for describing the domain,


inductive bias, are enough for learning.


That is,


we assume there is no error due to


omitting certain useful attributes.


It is clear that many domains do not have these nice


properties.

In the following section we will discuss the projection of these issues discussed

here onto the scheduling domain.



3.3 Scheduling as a Machine Learning Problem


In Chapter 2 we characterized the scheduling problem and its domain structure.


From a ML perspective,


what concepts need to be learned in this domain?


How could


we characterize the target concept?


What are the relevant attributes of the domain and


the concept?


Looking


at the


dimensions of ML,


which choices are suitable


learning in the scheduling domain?

Before we answer these questions let us briefly recall aspects of the scheduling










attributes


required


to describe


system


status,


which


include


characteristics,


machine characteristics,


process characteristics,


work flow characteristics etc., is very


high.


There is no known optimal way of doing certain tasks and thus no dependable


ORACLE exists.


A high ratio of classification error may be present due to lack of perfect


information.

The task is learning a strategy or a set of strategies that produce good schedules.


How are these strategies characterized?

The answer is we do not know yet. Bu


Are they k-DNF, k-CNF or arbitrary concepts?


it it is clear that we can not learn good strategies


that can cover all


possible scheduling


environments.


Scheduling


environments have


different characteristics and


usually the concept of


a good


schedule varies from one


environment to the other.


For example,


for the


problems


1//Cmax and 2F//Cmax, it is


known that


and Johnson's rule, respectively, are optimal.


Hence, we have to focus


on individual environments.


Even so, it is highly unlikely that one rule will be enough


classifying


good


schedules


within


an environment.


Thus


we need


to learn


disjunctive rules that are not necessarily in any normal form.


If we can characterize all


relevant states of the system in a small finite number of cases, then we can learn rules

that apply to each case.


Hence, learning in a scheduling environment is discovering a set of


disjunctive


rules that can use an arbitrary combination of the system attributes. Our purpose is to be

able to discover good scheduling strategies rather than good schedules. Those strategies










how we characterize these conditions.


Fitting this view to the first dimension,


we want


to acquire explicit knowledge about the domain.

Analyzing the scheduling problem with respect to the second dimension requires


finding the best methodology to use.


This is the hardest one to justify.


We will narrow


our choices by explaining why we do not use certain methodologies.


is eliminated due to its inability to generalize.


First, rote learning


Learning by analogy seems unsuitable


because we can not find any domain that we can draw analogies from.


Learning by being


told requires an extensive use of domain knowledge which we do not have.


choice we have is learning from examples.


The last


We will support this view because we have


a large portfolio of examples, or we can generate them by simulation runs.


be able to characterize the relevant attributes of the system.


We will also


This methodology does not


require an


initial


domain knowledge that is expressive enough


to explain


the causal


relationships among entities.


Next is the question of which algorithm to use.


Inductive learning algorithms


require the existence of an


ORACLE and are highly sensitive to noise.


Case based


reasoning


is not suitable


because


in such


a dynamic


environment seldom


case


common


enough


to make


it worth


storing.


today's


competitive


manufacturing


environment the manufacturers are able to compete by introducing new products.


This


in return


changes their processes and scheduling characteristics.


believe that a


system will need a method that is suitable for working with imperfect information and










Static


learning


algorithms are


not suitable due


to the


dynamic


nature of the


domain.


In this environment, the only system that can survive is the one that can monitor


the environment and use new information to change its knowledge adaptively.


Also, we


not only want to acquire explicit knowledge but also improve the systems performance

or at least keep it at an acceptable level in time.

Finally, due to the lack of perfect information, we believe a semi-supervised mode


of learning will


have to


be carried


The system


will only be able to


get partial


information about its decisions so it must have a way of making full use of the available


information.


That is information given in the past and at present.


Part of the research discussed in section 2.3.4 such as Piramuthu et al. (1991),


Thesen


and Lei


(1986) and Yih (1990), concentrate on knowledge acquisition but they


do not consider rule refinement.


The knowledge produced is explicit, meaning that the


resulting knowledge base can explain why a certain rule applies.


Lamatsch et al. (1988)


skip the knowledge acquisition step and assume the existence of an initial knowledge base


employ


simple


learning


algorithm


to further


improve


performance


existing learning system.


On the other extreme,


Chryssolouris (1990) use neural nets,


which


produce


implicit


knowledge.


Koton's


case


based


reasoning


approach


incremental process where the case base is generated as new examples are seen Hilliard

et al. (1987), (1989) employs classifier systems to discover optimal or good rules for a


known class of problems.


Classifiers systems use GAs.


GAs are inherently adaptive and










A survey of GAs and classifier systems will be presented in the next chapter.


will also discuss how they can be used as learning algorithms for rule discovery and rule

refinement.

All of the papers focusing on ML applications in scheduling make simplifying


assumptions which limits their generalizability.


Nevertheless, their results have been most


encouraging.


In Table 3-1


we summarize machine learning in scheduling with respect to our


four dimensional framework.





























































O/u
Co
-Cs
Ukr


COG.
CF


Cti

Ct


Uk e


Ct
Cl
cPc


C -

Uk


Ct
(C


9 U)


U)
ba.)a
Ct

cPC


vl
eo3~
.S=1 n


X
W















CHAPTER 4
GENETIC ALGORITHMS AND CLASSIFIER SYSTEMS

4.1 Overview of Genetic Algorithms


Genetic Algorithms (GAs), first studied by Holland, are general purpose search

algorithms based on an analogy to natural selection or, survival of the fittest (Goldberg


1989).


Population


members


are represented


artificial


strings,


corresponding


chromosomes.


The search starts with a population of randomly selected strings, and from


these


next


generation


is created


using


genetic


operators.


each


iteration


individual


strings


are evaluated


respect to


performance criteria and


return


assigned a fitness value, or strength.


Based on their fitness values, strings are selected


to construct the next generation by applying genetic operators.


Even though the GA


moves from one population to another stochastically, it has been shown that the algorithm


"converges" (Vose and Liepens


1991a).


Compared to other optimization techniques, GAs have less restrictive assumptions.

The basic differences can be summarized as follows:


1.GAs


work


a coding


parameter


not the


parameters


themselves.
2. GAs search from a population of points, not a single point.
3. GAs use payoff (objective function) information, not derivatives or other
auxiliary knowledge.


4. GAs


ise probabilistic


transition


rules.


not deterministic


mules.










GAs are also inherently parallel algorithms.


Usually the strings are defined on the binary {0,1 } alphabet.


For a problem that


uses strings of length y,


(from


bit 0 to


bit y-1),


the possible number


of solutions to


consider is


. Yet, the GA is able to search this solution space very efficiently by using


these three operators.


There are three operators that guide the search.


As mentioned above these are


probabilistic


operators


not guarantee


an improvement from


one iteration


another, unlike for example, the simplex method.


The first operator is reproduction.


In reproduction, strings are probabilistically


chosen based on their fitness values and carried to the next generation without any further


modification.


Strings with high fitness values have better chances of survival--survival


of the


fittest.


operator is applied


to protect fit


individuals


from an accidental


extinction, and possibly to increase their number in the following generations.


The second operator is crossover.

strings based on their strength. After sele


is selected.


Crossover is a binary operator that selects two


;cting the strings a crossover site for both strings


Then the substrings to the right of the crossover site are exchanged.


example, assume S, = 10111 and S, = 11001.


Assume the crossover site is chosen to be


After crossover the resulting


strings,


called


offspring


or children, are


1000


1111.


Crossover helps to increase the number of similar strings in the next generation


by combining the substrings (genes), of strong individuals with the hope that this will










The third operator, a unary operator, is mutation.


values, and thus acts completely random.

the bit values of a selected string. Assum


Mutation is not based on fitness


Mutation is carried out by randomly changing


[e S, = 10111 is chosen for mutation and assume


bit 0 and 3 are probabilistically chosen for mutation.


After mutation S,


will be


11110.


Mutation helps to find solutions that are not reachable by applying only crossover and


reproduction.


That is the only mechanism that can move a GA from a local optima when


crossover does not result in radically different offspring.

Even though it is possible to implement a GA in many different ways, the simplest

GA is stated as follows:


Given


string


population


crossover probability


mutation


probability (p), a


function (f) (f(x)


> 0, for all x) to be optimized and a stopping


criteria:

1. Set t = 0, and generate an initial population P, of size n.


While the stopping criteria is not satisfied


Find the fitness f(i) of each string


in P,. Let


C f(i)

f(i)
i-=I


While all the elements of next generation Pt., are not created


n n n










else carry S, and S2 to the next generation.


Select the children S


' and S2,'


(i =0 to y-1)


if U= U(0,1) < p,


flip the i'h bit


I



Set t = t + 1.


The resulting population is the solution.


Due to their stochastic nature GAs do not guarantee an optimal solution at their


termination.


However,


empirical


experience


has shown


converge


to good


quality, near optimal solutions very quickly.


In the next section we will explain this


behavior of GAs.



4.1.1 The Fundamental Theory of GAs and Implicit Parallelism


Schemata


concept


theory


are useful


(Goldberg


1989)


explaining


implicit


GAs


quickly


parallelism


converge


(Goldberg


a high


1989),


fitness


population of strings.


Consider a string of length y defined on the alphabet {0,1


and let S={ 0,1 }T. Then










same values at the same bit positions for some bit positions.


and assume we fix the values at the


H={0110,


For example, assume 7=4,


1st and 3rd bit position then


0010, 0111, 0011}.


H can also be represented as a string using the alphabet (0,1,*} where means either a


Oor 1.


In our example


H is 0*1*


The length of a schema H, 6(H), is the distance between the first and the last fixed


positions.

1989). Ii


The order of a schema


I our example, 6(H) =


, o(H), is the number of fixed positions (Goldberg


3-1 = 2 and o(H) =


The fundamental


theorem of GAs states


"short,


order above-average


schemata receive exponentially increasing trials in subsequent generations,"


1989), pp. 33.


(Goldberg


The expected number of members of H in the next generation, m(H,t+1)


is bounded by,


m(H,t+l)> m(H,t) f(H
f


1- (H) -o(H) p
y-1


The term f(H) is the average schema fitness, whereas f is the average population fitness.


Z and p are the crossover and mutation rates respectively.


The reproduction operator tries


to preserve the schema whereas the crossover and mutation operators disrupt the schema.


That is why short, low order schemata have better chances of survival. Such low order,

short schemata are called building blocks since they lead to better solutions. So, after a


4-.II, n-a c rr -nlrf ti'- ln nin.,'rar 'C oytrn no halnn'r, n n frntn cnh "i oa' ,l c'rk'a.., nftn ",;i11 ; n,'n,.,r onr'


'. (1)




Full Text

PAGE 1

$ '(&,6,21 6833257 6<67(0 )25 '<1$0,& 6&+('8/,1* 35$&7,&( $1' 7+(25< +$/'81 $<78* $ ',66(57$7,21 35(6(17(' 72 7+( *5$'8$7( 6&+22/ 2) 7+( 81,9(56,7< 2) )/25,'$ ,1 3$57,$/ )8/),//0(17 2) 7+( 5(48,5(0(176 )25 7+( '(*5(( 2) '2&725 2) 3+,/2623+< 81,9(56,7< 2) )/25,'$

PAGE 2

$&.12:/('*(0(176 ZRXOG OLNH WR WKDQN P\ DGYLVRU 3URIHVVRU *DU\ .RHKOHU IRU KLV FRQVWDQW VXSSRUW DQG DVVLVWDQFH GXULQJ WKLV GLVVHUWDWLRQ DQG IRU KLV KHOS GXULQJ PRPHQWV RI IUXVWUDWLRQ DP WKDQNIXO WR WKH RWKHU PHPEHUV RI P\ FRPPLWWHH 3URIHVVRU &KXQJ
PAGE 3

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f f f

PAGE 4

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

PAGE 5

&RQFOXVLRQV )XWXUH 5HVHDUFK DQG 0RGLILFDWLRQV WR WKH 6\VWHP 5()(5(1&(6 %,2*5$3+,&$/ 6.(7&+ Y

PAGE 6

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

PAGE 7

NQRZOHGJH EDVH 'XH WR WKHLU FRQWLQXRXV IHHGEDFN FRQWURO PHFKDQLVPV FODVVLILHU V\VWHPV DUH YHU\ DSSURSULDWH IRU XSGDWLQJ NQRZOHGJH EDVHV ZKHQ WKH HQYLURQPHQW LV FKDQJLQJ :H KDYH GHYHORSHG D OHDUQLQJ V\VWHP WKDW LV LQWHJUDWHG ZLWK D VLPXODWLRQ HQYLURQPHQW GHYHORSHG LQ &f ZKLFK VXSSRUWV LQIHUHQFH $ UXOH ODQJXDJH VXSSRUWLYH RI WKH JHQHWLF VHDUFK RSHUDWRUV XVHG E\ WKH V\VWHP KDV EHHQ GHYHORSHG 7ZR VXEV\VWHPV WKH OHDUQLQJ VXEV\VWHP DQG WKH WDVN VXEV\VWHP LQWHUDFW WKURXJKRXW WKH NQRZOHGJH FRQVWUXFWLRQ SURFHVV 7KH OHDUQLQJ VXEV\VWHP HYDOXDWHV WKH SHUIRUPDQFH RI WKH WDVN VXEV\VWHP DIWHU HYHU\ OHDUQLQJ HSLVRGH DQG JHQHUDWHV DQ H[SHFWHGO\ EHWWHU NQRZOHGJH EDVH IRU WKH WDVN VXEV\VWHP WR XVH LQ WKH QH[W OHDUQLQJ HSLVRGH 7KLV SURFHGXUH VWRSV DIWHU D UHDVRQDEOH NQRZOHGJH EDVH LV FRQVWUXFWHG 7KH WKHRUHWLFDO SDUW RI WKLV UHVHDUFK LQYROYHV GHYHORSLQJ D ZRUVW FDVH ERXQG RQ WKH QXPEHU RI OHDUQLQJ HSLVRGHV WKH V\VWHP KDV WR SHUIRUP EHIRUH VWRSSLQJ ZLWK D ZHOO SHUIRUPLQJ NQRZOHGJH EDVH 7KLV LV HTXLYDOHQW WR GHYHORSLQJ D VWRSSLQJ FULWHULD IRU JHQHWLF DOJRULWKPV VLQFH FODVVLILHU V\VWHPV XVH JHQHWLF DOJRULWKPV WR VHDUFK IRU QHZ UXOHV 7R GDWH WKHUH KDV EHHQ QR VHULHV DWWHPSW WR GHYHORS D VWRSSLQJ FULWHULD IRU *HQHWLF $OJRULWKPV :H KDYH GHYHORSHG DQ XSSHU ERXQG RQ WKH QXPEHU RI LWHUDWLRQV D *$ KDV WR H[HFXWH WR DVVXUH VHHLQJ DQ RSWLPDO VROXWLRQ ZLWK D VSHFLILHG FRQILGHQFH OHYHO E\ XVLQJ WKH FRQFHSW RI ILUVW SDVVDJH WLPHV RI D 0DUNRY &KDLQ )RU D JLYHQ VWULQJ OHQJWK ZH KDYH DOVR IRXQG WKH RSWLPDO QXPEHU RI LWHUDWLRQV QHFHVVDU\ EHIRUH VWRSSLQJ f f 9OO

PAGE 8

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

PAGE 9

5HFHQWO\ WKHUH KDV EHHQ D WUHQG WRZDUGV LQFUHDVLQJ WKH JHQHUDOL]DELOLW\ RI WKH VFKHGXOLQJ PRGHOV 7KHVH DSSURDFKHV FDQ PRGHO YHU\ FRPSOH[ HQYLURQPHQWV EXW GXH WR WKH FRPSOH[LW\ RI WKH SUREOHP WKH\ RIIHU ORZHU TXDOLW\ VROXWLRQV ZLWK D YHU\ KLJK GHJUHH RI DSSOLFDELOLW\ $UWLILFLDO ,QWHOOLJHQFH $Of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fV ZRUN RQ IORZ VKRS SUREOHPV %DNHU f DQG -DFNVRQfV RQ VLQJOH PDFKLQH SUREOHPV /DZOHU HW DO f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

PAGE 10

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

PAGE 11

,Q D UHODWLYHO\ UHFHQW VXUYH\ E\ /DJHZHJ HW DO ;f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fV PDLQIUDPHV DQG DUH HDVLO\ DFFHVVLEOH 0RVW SURGXFWLRQ HQYLURQPHQWV DUH FRPSXWHU LQWHJUDWHG $SSOLFDWLRQV RI FRPSXWLQJ DUH PRUH XELTXLWRXV ,QGHHG PRVW SURGXFWLRQ HQYLURQPHQWV DUH QRZ FRPSXWHUL]HG $Q HDUO\ HQGHDYRU RI FRPSXWHU VFLHQWLVWV ZDV WR HQGRZ FRPSXWHUV ZLWK WKH DELOLW\ WR SHUIRUP LQWHOOLJHQWO\ 7KLV DUHD RI UHVHDUFK LV FDOOHG $UWLILFLDO ,QWHOOLJHQFH $,f 7KH WUHPHQGRXV DGYDQFHV LQ FRPSXWHUV KDYH PDGH $, D PRUH WUDFWDEOH DUHD 7RGD\ LW LV SRVVLEOH WR ZULWH VRIWZDUH WKDW RXWSHUIRUPV KXPDQV $, WHFKQLTXHV KDYH EHHQ VXFFHVVIXOO\ LPSOHPHQWHG LQ PDQ\ GRPDLQV )RU H[DPSOH ([SHUW 6\VWHPV (6Vf KDYH IRXQG ODUJH DSSOLFDWLRQ GRPDLQV IURP EDQNLQJ WR PHGLFDO GLDJQRVLV DQG DUH YHU\ HIIHFWLYH IRU VROYLQJ VXFK SUREOHPV 3DWWHUQ UHFRJQLWLRQ DQG QDWXUDO ODQJXDJH SDFNDJHV DUH UHDG\ WR EH FRPPHUFLDOL]HG

PAGE 12

'XULQJ WKH ODVW GHFDGH WKHUH KDV EHHQ DQ HQRUPRXV QXPEHU RI $, DSSOLFDWLRQV RQ VFKHGXOLQJ 5HVHDUFKHUV GHYHORSHG (6V IRU PDQ\ GLIIHUHQW SURGXFWLRQ HQYLURQPHQWV $OSDU DQG 6ULNDQWK Df &KDQJ f .HUU DQG (EVDU\ f 2f.HHIH f ,W ZDV GLVFRYHUHG WKDW NQRZOHGJH EDVH FRQVWUXFWLRQ ZDV WKH PDLQ ERWWOHQHFN WR EXLOGLQJ VXFK V\VWHPV (6V ZHUH QRW HDV\ WR PDLQWDLQ DQG WKHLU VLPSOH LQIHUHQFH PHFKDQLVPV SURYHG WR EH LQVXIILFLHQW IRU PRVW SUREOHPV
PAGE 13

5HFHQWO\ WKHUH KDV EHHQ ZRUN RQ KHXULVWLF GLVFRYHU\ XVLQJ OHDUQLQJ DOJRULWKPV 6XFK V\VWHPV XVH D OHDUQLQJ DOJRULWKP WR JHQHUDWH D NQRZOHGJH EDVH DQG XWLOL]H WKLV NQRZOHGJH IRU SUREOHP VROYLQJ 3LUDPXWKX HW DO f
PAGE 14

&ODVVLILHU 6\VWHPV &6Vf DUH DGDSWLYH OHDUQLQJ V\VWHPV WKDW XVH *$V DV UXOH GLVFRYHU\ DOJRULWKPV 7KHLU DSSOLFDWLRQ WR VFKHGXOLQJ KDV EHHQ OLPLWHG GXH WR WKHLU ZHDN NQRZOHGJH UHSUHVHQWDWLRQ ODQJXDJH 1HYHUWKHOHVV LW KDV EHHQ VXJJHVWHG WKDW WKH\ DUH UREXVW OHDUQLQJ V\VWHPV LQ G\QDPLF GRPDLQV *ROGEHUJ f )LUVW DWWHPSWV WR XVH WKHP WR OHDUQ VHTXHQFLQJ KHXULVWLFV UDWKHU WKDQ VHTXHQFHV KDYH SURYHQ SURPLVLQJ +LOOLDUG HW DOf f +LOOLDUG HW DOf f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

PAGE 15

WKHVH PHWKRGV DUH VXFFHVVIXO LQ VROYLQJ VSHFLILF SUREOHPV WKH\ DUH XQDEOH WR DGDSW WKHLU VHDUFK PHFKDQLVPV DV WKH HQYLURQPHQW FKDQJHV 7KH\ ODFN WKH DELOLW\ WR OHDUQ $SSOLFDWLRQV RI 0DFKLQH /HDUQLQJ 0/f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f UHVHDUFK DQG VRPH WKHRUHWLFDO LVVXHV LQYROYHG :H DOVR VXPPDUL]H WKH

PAGE 16

UHVXOWV RI VRPH HDUOLHU ZRUN RQ 0/ )LQDOO\ ZH DQDO\]H WKH H[LVWLQJ UHVHDUFK RQ VFKHGXOLQJ IURP D 0/ SHUVSHFWLYH :H UHYLHZ WKH OLWHUDWXUH RQ *$V DQG &6V LQ &KDSWHU :H VWDUW ZLWK HDUOLHU WKHRUHWLFDO ILQGLQJV RQ *$V 1H[W ZH SUHVHQW D GLVFXVVLRQ RI VHYHUDO DSSOLFDWLRQV RI *$V DQG &6V LQ RWKHU GRPDLQV DV ZHOO DV LQ WKH VFKHGXOLQJ GRPDLQ $ ODUJH SDUW RI WKLV FKDSWHU ZLOO EH GHYRWHG WR WKH UHVXOWV RI 9RVH DQG /LHSLQV f DQG 1L[ DQG 9RVH f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

PAGE 17

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f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f 5HFHQW UHVXOWV KDYH VKRZQ WKDW HYHQ WKHVH KHXULVWLF DOJRULWKPV KDYH WKHLU OLPLWDWLRQV ,W ZDV EHOLHYHG WKDW IRU DQ\ 13FRPSOHWH SUREOHP DQG JLYHQ HUURU WROHUDQFH WKHUH H[LVWHG DQ DSSUR[LPDWLRQ DOJRULWKP WKDW FRXOG VROYH WKH SUREOHP ZLWKLQ WKH VSHFLILHG HUURU ERXQGV EXW LW ZDV VKRZQ WKDW IRU FHUWDLQ FODVV RI SUREOHPV HYHQ DSSUR[LPDWLRQ LV 13FRPSOHWH

PAGE 18

,Q WKLV VHFWLRQ ZH UHYLHZ SURGXFWLRQ VFKHGXOLQJ SUREOHPV DQG GLVFXVV WKH DGYDQWDJHV DQG GLVDGYDQWDJHV RI WUDGLWLRQDO 2SHUDWLRQV 5HVHDUFK 25f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

PAGE 19

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cM EH WKH SURFHVVLQJ WLPH RI MRE M RQ PDFKLQH L 3M EH WKH SURFHVVLQJ WLPH RI MRE M IRU RQH PDFKLQH SUREOHPVf EH WKH GXH GDWH RI MRE M

PAGE 20

LM EH WKH UHOHDVH WLPH RI MRE M &M EH WKH FRPSOHWLRQ WLPH RI MRE M )M EH WKH IORZWLPH RI MRE M /M EH WKH ODWHQHVV RI MRE M DQG 7M EH WKH WDUGLQHVV RI MRE M 7KH FRPSOHWLRQ WLPH LV WKH WLPH ZKHQ D MRE LV UHDG\ WR OHDYH WKH V\VWHP )ORZWLPH ODWHQHVV DQG WDUGLQHVV DUH GHILQHG DV QRQGHFUHDVLQJ IXQFWLRQV RI WKH FRPSOHWLRQ WLPH DV IROORZV ) & U f! M M M / & f§G} M M M DQG 7 PD[/f $ IXQFWLRQ RI FRPSOHWLRQ WLPH LV FDOOHG D UHJXODU PHDVXUH ZLWK UHVSHFW WR WKH FRPSOHWLRQ WLPH LI LW LV QRQGHFUHDVLQJ LQ FRPSOHWLRQ WLPH +HQFH IORZWLPH ODWHQHVV DQG WDUGLQHVV DUH UHJXODU PHDVXUHV ZLWK UHVSHFW WR FRPSOHWLRQ WLPH 6FKHGXOLQJ SUREOHPV DUH GHILQHG E\ WKUHH SDUDPHWHUV DS\ /DZOHU HW DO f 7KH ILUVW SDUDPHWHU D LV WKH GHVFULSWLRQ RI WKH VKRS IORRU DQG FDQ EH DQ\ RI WKH IROORZLQJ 7KH VKRS IORRU FRQVLVWV RI RQO\ RQH PDFKLQH P3 7KH VKRS IORRU FRQVLVWV RI P SDUDOOHO PDFKLQHV ZLWK LGHQWLFDO VSHHGV P) 7KH VKRS IORRU LV D IORZVKRS ZLWK P PDFKLQHV LQ VHTXHQFH

PAGE 21

P7KH VKRS IORRU LV D MREVKRS ZLWK P PDFKLQHV 7KH VHFRQG SDUDPHWHU LV WKH GHVFULSWLRQ RI WKH FRQVWUDLQWV RU WKH DWWULEXWHV RI WKH SUREOHP ,I LV QXOO WKHQ WKH SUREOHP KDV QR FRQVWUDLQWV DQG WKH DWWULEXWHV DUH LQ WKHLU PRVW JHQHUDO IRUP 6RPH W\SLFDO VSHFLILFDWLRQV DUH WKH IROORZLQJ Uc 5HOHDVH WLPH RI MRE ZKLFK LV QRW QHFHVVDULO\ ]HURf SUHF 7KHUH DUH SUHFHGHQFH UHODWLRQVKLSV EHWZHHQ WKH MREV SPWQ 3UHHPSWLRQ LV DOORZHG VcM 6HWXS WLPH RI Vc c LV UHTXLUHG LI MRE M LV SURFHVVHG DIWHU MRE L ZKHQ MAM 7KHUH LV QR VHWXS UHTXLUHG LI M L S S $OO SURFHVVLQJ WLPHV DUH HTXDO WR S 7KH WKLUG SDUDPHWHU \ LV WKH GHVFULSWLRQ RI WKH REMHFWLYH IXQFWLRQ WR EH PLQLPL]HG 8VXDOO\ WKHVH IXQFWLRQV DUH UHJXODU PHDVXUHV ZLWK UHVSHFW WR WKH FRPSOHWLRQ WLPH RI WKH MRE 6RPH W\SLFDO SHUIRUPDQFH PHDVXUHV DUH WKH IROORZLQJ &PD[ 0D[LPXP FRPSOHWLRQ WLPH RIWHQ UHIHUUHG WR DV PDNHVSDQ Q (& 7RWDO FRPSOHWLRQ WLPH L O ) f [ PD[r 0D[LPXP IORZWLPH ,, () L O 7RWDO IORZWLPH 0QD[ r 0D[LPXP ODWHQHVV Q (/ L O 7RWDO ODWHQHVV

PAGE 22

7 r PD[r 0D[LPXP WDUGLQHVV 7 L O 7RWDO WDUGLQHVV :7c L O 7RWDO ZHLJKWHG WDUGLQHVV ,Q DQ H[FHOOHQW VXUYH\ E\ /DZOHU HW DO f PDQ\ VFKHGXOLQJ SUREOHPV DUH OLVWHG DQG VROXWLRQ PHWKRGV DUH GLVFXVVHG 6LPLODUO\ /DJHZHJ HW DO f SUHVHQW FRPSOH[LW\ UHVXOWV IRU SUREOHPV DQG VRPH UHIHUHQFHV ,W LV QRW VXUSULVLQJ WR VHH WKDW RQO\ b RI WKHVH SUREOHPV DUH OLVWHG DV HDV\ SUREOHPV ZLWK b DV 13FRPSOHWH 7KH UHPDLQLQJ b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

PAGE 23

7DEOH 6RPH VFKHGXOLQJ SUREOHPV 352%/(0 &203/(;,7< $/*25,7+0 SUHFIPD[ 3 /DZOHU /DZOHU HW DO f SPWQUM SUHFIPD[ 3 %DNHU/DZOHU/HQVWUD DQG 5LQQRR\ .DQ /DZOHU HW DO f 7 [f PD[ 3 (DUOLHVW 'XH 'DWH %DNHU f IM/PD[ 13 6SHFLDO FDVHV DUH VROYDEOH E\ H[WHQGHG -DFNVRQfV DOJRULWKP /DZOHU HW DO f L LT 3 6KRUWHVW 3URFHVVLQJ 7LPH %DNHU f /,AT 3 :HLJKWHG 637 %DNHU f LUVT 13 3VHXGRSRO\QRPLDO DOJRULWKP E\ /DZOHU /DZOHU HW DO f ,7M 13 *HQHUDOL]HG 637 /DZOHU HW DO f P3LT 3 /DZOHU HW DO f P3;7M 13 /DZOHU HW DO f P3&PD[ 13 7KHUH DUH DSSUR[LPDWLRQ DOJRULWKPV /DZOHU HW DO f )&PD[ SPWQ&PD[ 3 -RKQVRQfV DOJRULWKP %DNHU f )U&PD[ 13 /DZOHU HW DO f )/PD[ 13 /DZOHU HW DO f )OT 13 /DZOHU HW DO f )&PD[ 13 /DZOHU HW DO f )SPWQ&PD[ 13 /DZOHU HW DO f )SPWQ6T 13 /DZOHU HW DO f

PAGE 24

6FKHGXOLQJ 3UREOHP DV LW $SSHDUV LQ ,QGXVWU\ (YHQ WKH VLPSOLVWLF PDWKHPDWLFDO PRGHOV RI WKH VFKHGXOLQJ HQYLURQPHQW DUH KDUG EXW DV PD\ EH H[SHFWHG UHDO OLIH SUREOHPV DUH HYHQ KDUGHU 6PLWK H[SODLQV WKH UHDVRQV DV IROORZV 7KH VRXUFHV RI GLIILFXOW\ LGHQWLILHG LQFOXGHG f WKH QHHG WR DGKHUH WR D W\SLFDOO\ LGLRV\QFUDWLF VHW RI UHVWULFWLRQV UHODWLQJ WR SURGXFWLRQ SURFHVVHV UHVRXUFH FDSDELOLWLHV DQG UHVRXUFH DYDLODELOLW\ f WKH QHHG WR EDODQFH D ODUJH DQG FRQIOLFWLQJ VHW RI REMHFWLYHV DQG SUHIHUHQFHV DQG f WKH XQSUHGLFWDELOLW\ RI IDFWRU\ RSHUDWLRQ 6PLWK E S f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f PD\ SUHYHQW WKH VHOHFWLRQ RI DQ DFFXUDWH PDFKLQH IRU DQRWKHU RSHUDWLRQ RU PD\ SUHYHQW PHHWLQJ DQRWKHU MREfV GXH GDWH )RU WKLV UHDVRQ VHOHFWLQJ RSHUDWLRQ VWDUW WLPHV RU DOORFDWLQJ UHVRXUFHV EDVHG VROHO\ RQ ORFDO D SULRUL SUHIHUHQFHV LV OLNHO\ WR UHVXOW LQ SRRU VFKHGXOHV 3UHIHUHQFH SURSDJDWLRQ LV PHDQW WR DOORZ IRU WKH FRQVWUXFWLRQ RI PHDVXUHV WKDW UHIOHFW SUHIHUHQFH LQWHUDFWLRQV 7KHVH PHDVXUHV FDQ WKHQ VHUYH WR JXLGH WKH FRQVWUXFWLRQ RI D JRRG RYHUDOO VFKHGXOH UDWKHU WKDQ D VFKHGXOH WKDW ORFDOO\ RSWLPL]HV D VXEVHW RI SUHIHUHQFHV 6DGHK DQG )R[ S f :KDW KDSSHQV LQ D UHDO WLPH VLWXDWLRQ LV HYHQ PRUH GUDVWLF WKDQ H[SODLQHG DERYH 7KH RSHUDWRU UHVSRQVLEOH IRU DOO WKLV KDV RWKHU ZRUULHV WRR 7KH WRROV WKH RSHUDWRU LV UHVSRQVLEOH FDQfW DOO UXQ WKH VDPH NLQG RI SURGXFWV DQG EHFDXVH WKH RSHUDWRU KDV D PL[HG VWUHDP RI SURGXFWV WKRXJKW PXVW EH JLYHQ WR ZKLFK SURGXFW LV JRLQJ ZKHUH )XUWKHUPRUH WRROV DUH LGLRV\QFUDWLF DERXW ZKHQ DQG KRZ WKH\ DJH DQG ZKDW HIIHFWV WKDW SURGXFHV 0HDQZKLOH RI FRXUVH KH KDV WR UHPHPEHU WKH SURFHVV VSHFLILFDWLRQV DQG VHTXHQFH RI

PAGE 25

IDEULFDWLRQ VWHSV (DFK ZDIHU PXVW JR WKURXJK VD\ D SKRWR SURFHVV RU WLPHV HDFK SURFHVV EXLOGLQJ D OD\HU UHVXOWLQJ LQ D WKUHH GLPHQVLRQDO FRPSOH[LW\f§\RX FDQfW EXLOG OHYHO % EHIRUH \RX EXLOG OHYHO $f§ 7KLV FRPSOH[LW\ LV FRPSRXQGHG E\ RWKHU GLIILFXOWLHV VXFK DV DOO ER[HV ZKLFK VWRUH D ORW RI ZDIHUV ORRN DOLNH DQG RIWHQ DQ LPSRUWDQW FXVWRPHU FRPHV LQ ZLWK D VSHFLDO UHTXHVW 0RGHUQ 7LPHV DW LWV ZRUVW )RU RSHUDWRU DQG PDQDJHU DOLNH WKH ZKROH PDQXIDFWXULQJ SURFHVV LV OLNH D JLDQW FKHVV JDPH f§H[FHSW WKH FRPSOLFDWHG VHTXHQFLQJ FRPELQDWRULDO FRPSOH[LW\ DQG XQSUHGLFWDELOLW\ PDNH LW KDUGHU WR WKLQN WKURXJK WKDQ HYHQ WKH PRVW GHPDQGLQJ RI JDPHV 6XOOLYDQ DQG )RUG\FH S f .HUU DQG (EVDU\ VWDWH WKH UHDVRQV IRU FKRRVLQJ KHXULVWLF DSSURDFKHV WR VFKHGXOLQJ UDWKHU WKDQ DQ RSWLPDO 25 PHWKRG DV IROORZV 7KH ILUVW W\SH RI DSSURDFK WKH 25 DSSURDFK` ZDV UHMHFWHG RQ WKH EDVLV WKDW ^` NQRZQ IXWXUH UHTXLUHPHQWV DQG SUREDEOH HYHQWV ZLOO LQIOXHQFH WKH VKRUW WHUP VFKHGXOH LQ DQ DJJUHJDWH ZD\ EXW LW ZRXOG EH XQUHDVRQDEOH WR LQFRUSRUDWH WKHVH LQWR D VKRUW WHUP RSWLPL]DWLRQ DSSURDFK EHFDXVH RI WKH XQFHUWDLQW\ DVVRFLDWHG ZLWK WKHP ^` WKH HQYLURQPHQW LV XQOLNHO\ WR UHPDLQ VWDWLF HYHQ RYHU D SHULRG DV VKRUW DV KRXUV .HUU DQG (EVDU\ SS f $ UHDO OLIH SURGXFWLRQ HQYLURQPHQW LV VXEMHFW WR FKDQJLQJ FRQVWUDLQWV IOXFWXDWLQJ UHVRXUFH DYDLODELOLWLHV DQG HYHQ FRQIOLFWV DPRQJ WKH PDQDJHPHQW REMHFWLYHV $V VXFK WKH SUREOHP LV PRUH RI UHVFKHGXOLQJ WKDQ VFKHGXOLQJ GXH WR WKH G\QDPLF QDWXUH RI WKH SUREOHP 5RGDWQPHU DQG :KLWH f 25 PRGHOV DUH QRW FDSDEOH RI FDSWXULQJ WKH LPSRUWDQW TXDOLWDWLYH DVSHFWV RI WKH SUREOHP DV DFWXDOO\ RFFXUULQJ RQ WKH VKRSIORRU )XUWKHUPRUH PRVW RI WKH DVVXPSWLRQV DUH QHYHU REVHUYHGDOPRVW QR DWWULEXWH RI WKH V\VWHP LV GHWHUPLQLVWLFf§RU DUH LUUHOHYDQW WR WKH UHDO SUREOHP )LQDOO\ UHDO OLIH VFKHGXOLQJ SUREOHPV KDYH DOPRVW DOZD\V QR IHDVLEOH VROXWLRQV )R[ DQG 6DGHK f n7KH RULJLQDO WH[W LV DGDSWHG IURP )HLJHQEDXP 0F&RUGXFN DQG 1LL f SS

PAGE 26

6LQFH SURGXFWLRQ PXVW VWLOO FRQWLQXH VRPH FRQVWUDLQWVf§ZH ZLOO FDOO WKHP VRIW FRQVWUDLQWVf§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f 7KHUH DUH VXFFHVVIXO 25 DSSURDFKHV LQ VRPH LQGXVWULHV VXFK DV WKH IOLJKW VFKHGXOLQJ V\VWHP RI $PHULFDQ $LUOLQHV 3DUNHU f EXW LW KDUGO\ UHVHPEOHV WKH SURGXFWLRQ VFKHGXOLQJ SUREOHP DV IDU DV FRQVWUDLQWV DQG WKH LPSRUWDQFH RI UHDO WLPH GHFLVLRQV DUH FRQFHUQHG (YHQ ZKLOH GHDOLQJ ZLWK WKH QLFH SUREOHPV WKHUH LV DQRWKHU LQHYLWDEOH SUREOHP 25 PRGHOOLQJ DSSURDFKHV VXIIHU %DNHU EOXQWO\ GHFODUHV 7KH WUDGLWLRQDO 25 V\QGURPH FRYHULQJ WKH DSSOLFDWLRQ GHYHORSPHQW F\FOH KDV ILYH VWHSV f PRGHOHU VHWV XS DSSOLFDWLRQ f PRGHO LV GHPRQVWUDWHG WR ZRUN f HQG XVHU LV WUDLQHG f PRGHOHU OHDYHV f DSSOLFDWLRQ GLHV 7KLV V\QGURPH LV HVSHFLDOO\ SUHYDOHQW ZLWK PDWKHPDWLFDO SURJUDPPLQJ DSSOLFDWLRQ ,Q IDFW ZH PLJKW VD\ WKDW WKH XVH RI PDWKHPDWLFDO SURJUDPPLQJ KDV EHHQ OLPLWHG E\ WKH DYDLODELOLW\ RI H[SHUWV 1RZ LQ

PAGE 27

PDQ\ LQGXVWULHV ZKLFK KDYH ORQJ UHOLHG RQ PDWKHPDWLFDO SURJUDPPLQJ WKHVH H[SHUWV DUH WDNLQJ HDUO\ UHWLUHPHQW %DNHU S f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f LV XVHG WR GHILQH WKH UHODWLRQVKLS EHWZHHQ WKH LQSXW YDULDEOHV DQG WKH SHUIRUPDQFH FULWHULD 8VXDOO\ LW LV DVVXPHG WKDW WKH SHUIRUPDQFH FULWHULD FDQ EH UHSUHVHQWHG DV D NWK GHJUHH SRO\QRPLDO IXQFWLRQ RI WKH LQSXW YDULDEOHV 7KH WHFKQLTXH UHTXLUHV UHSHWLWLYH VLPXODWLRQ UXQV ZLWK YDU\LQJ LQSXW YDULDEOH YDOXHV 2QFH WKH UHVSRQVH VXUIDFH LV HVWLPDWHG WKH RSWLPDO FDQ EH IRXQG E\ VRPH VHDUFK WHFKQLTXH

PAGE 28

7KH 3HUWXUEDWLRQ $QDO\VLV 0HWKRGRORJ\ 3$0f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f 8VXDOO\ WKH SUREOHP LV IL[HG DQG D QXPEHU RI UXQV LV SHUIRUPHG WR FRPSDUH WZR RU PRUH KHXULVWLFV LQ WKH VDPH VHWWLQJ 7KHUH LV QR HIIRUW WR GLVFRYHU XQGHU ZKLFK SDUDPHWHU YDOXHV WKH KHXULVWLF EHLQJ WHVWHG LV VXSHULRU WR WKH RWKHUV ,Q WKH IROORZLQJ VHFWLRQV ZH ZLOO GLVFXVV GLVSDWFKLQJ UXOH KHXULVWLFV DQG DUWLILFLDO LQWHOOLJHQFH DSSURDFKHV 'LVSDWFKLQX $ SRSXODU DOWHUQDWLYH WR RSWLPL]DWLRQ PHWKRGV LV WKH XVH RI GLVSDWFKLQJ UXOHV WR VHOHFW WKH QH[W MRE WR EH SURFHVVHG RQ D PDFKLQH 7KLV DSSHDUV WR EH WKH DFWXDO SUDFWLFH XVHG LQ PDQ\ VKRS IORRUV ZKHUH WKH GLVSDWFKHU XVHV D VLPSOH UXOH RI WKXPE WR VHOHFW WKH QH[W MRE 7KH GLVSDWFKLQJ SUREOHP FDQ EH GHILQHG DV IROORZV JLYHQ D SURFHVVRU DQG D TXHXH RI MREV ZDLWLQJ WR EH SURFHVVHG E\ WKDW SURFHVVRU ILQG D GLVSDWFKLQJ UXOH RU D VHW RI UXOHV WKDW ZLOO VDWLVI\ WKH PDQDJHPHQW REMHFWLYHV

PAGE 29

'LVSDWFKLQJ UXOHV KDYH EHHQ IRXQG WR EH HDV\ WR XVH DQG WKXV YHU\ FRQYHQLHQW IRU UHDO WLPH GHFLVLRQ PDNLQJ +RZHYHU D QRWLFHDEOH VKRUWFRPLQJ LV WKH LQKHUHQW P\RSLF QDWXUH RI GLVSDWFKLQJ %KDVNDUDQ DQG 3LQHGR f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f 6XFK D SKHQRPHQRQ ZKHUH VLPSOH GLVSDWFKLQJ UXOHV DUH PRUH UREXVW LQ D UDQGRP HQYLURQPHQW WKDQ LQ D IXOO\ SUHGLFWDEOH GHWHUPLQLVWLF HQYLURQPHQW LV IDLUO\ FRPPRQ %KDVNDUDQ DQG 3LQHGR SS f 2Q WRS RI EHLQJ UREXVW GLVSDWFKLQJ UXOHV KDYH VRPH RWKHU QLFH SURSHUWLHV ,W KDV EHHQ IRXQGf§EXW QRW DQDO\WLFDOO\ SURYHQf§WKDW WKH HIIHFWLYHQHVV RI PRVW GLVSDWFKLQJ UXOHV LV LQVHQVLWLYH WR WKH VKRS VL]H DQG WKH DUULYDO SDWWHUQ +RZHYHU LQ PLQLPL]LQJ ODWHQHVV

PAGE 30

DQG WDUGLQHVV PHDVXUHV UHODWHG GLVSDWFKLQJ UXOHV DUH VRPHZKDW VHQVLWLYH WR WKH GXH GDWH DVVLJQPHQW UXOHV %ODFNVWRQH 3KLOOLSV DQG +RJJ f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f UXOH LV VLPSOLVWLF LQ WKDW LW GRHV QRW XVH DQ\ LQIRUPDWLRQ DERXW WKH VKRS IORRU $V H[SHFWHG LW KDV QRW EHHQ IRXQG XVHIXO IRU DQ\ VHWWLQJ

PAGE 31

7KH )LUVW &RPH )LUVW 6HUYHG )&)6f UXOH DVVLJQV WKH KLJKHVW SULRULW\ WR WKH ILUVW MRE LQ WKH TXHXH ,W KDV EHHQ IRXQG XVHIXO IRU PLQLPL]LQJ WKH YDULDQFH RI WKH DYHUDJH ZDLWLQJ WLPH LI 3M a I IRU DOO M ,W DOVR PLQLPL]HV WKH H[SHFWHG DYHUDJH ZDLWLQJ WLPH LQ WKH TXHXH LI S LV LQGHSHQGHQW DQG LGHQWLFDOO\ GLVWULEXWHG LLGf 7KH )LUVW $W 6KRS )LUVW 6HUYHG )$6)6f UXOH D YDULDWLRQ RI )&)6 XVHG LQ MRE VKRSV JLYHV WKH KLJKHVW SULRULW\ WR WKH MRE WKDW HQWHUHG WKH VKRS WKH HDUOLHVW EUHDNLQJ WLHV DUELWUDULO\ RU E\ )&)6 ,W KDV EHHQ XVHIXO IRU UHGXFLQJ WKH YDULDQFH RI WKH DYHUDJH WRWDO WLPH VSHQW LQ WKH VKRS E\ DOO MREV 7KH (DUOLHVW 'XH 'DWH (''f UXOH DVVLJQV WKH KLJKHVW SULRULW\ WR WKH MRE ZLWK WKH HDUOLHVW GXH GDWH 7KH ('' UXOH PLQLPL]HV PD[LPXP ODWHQHVV PD[LPXP WDUGLQHVV DQG LQ WKH FDVH RI QRQGHWHUPLQLVWLF SURFHVVLQJ WLPHV PLQLPL]HV WKH H[SHFWHG PD[LPXP ODWHQHVV EXW QRW WKH H[SHFWHG PD[LPXP WDUGLQHVV LI WKH HQYLURQPHQW LV D VLQJOH PDFKLQH RU D SURSRUWLRQDWH IORZVKRS $QRWKHU YHUVLRQ RI ('' UHIHUUHG WR DV 0RGLILHG HDUOLHVW 'XH 'DWH 0''f UXOH WHQGV WR SURGXFH JRRG WDUGLQHVV UHVXOWV 7KH PRGLILHG GXH GDWH LV FRPSXWHG DV GI PD[GMW Sf ZKHUH W LV WKH FXUUHQW WLPH %DNHU DQG %HUWUDQG f 0'' KDV D WHQGHQF\ WR SHUIRUP OLNH 637 ZKHQ GXH GDWHV DUH WLJKW DQG OLNH ('' ZKHQ GXH GDWHV DUH ORRVH 7KH /RQJHVW 3URFHVVLQJ 7LPH /37f UXOH VHOHFWV WKH MRE ZLWK WKH ORQJHVW SURFHVVLQJ WLPH (YHQ WKRXJK LW LV QRW RSWLPDO LW LV XVHIXO LQ P3&PD[ SUREOHPV $QRWKHU YHUVLRQ RI /37 WKH /RQJHVW 5HPDLQLQJ 3URFHVVLQJ 7LPH /537f UXOH LV RSWLPDO IRU P3SUQWQ&PD[ ,I WKH SURFHVVLQJ WLPHV DUH VWRFKDVWLF WKH /RQJHVW ([SHFWHG 5HPDLQLQJ

PAGE 32

3URFHVVLQJ 7LPH /(537f UXOH LV RSWLPDO IRU 3(>&PD/(37 DQG /(537 EHKDYH LGHQWLFDO IRU D ODUJH IDPLO\ RI SUREOHPV 7KH 0RVW :RUN 5HPDLQLQJ 0:.5f UXOH DOORFDWHV WKH KLJKHVW SULRULW\ IRU WKH MRE ZLWK WKH PRVW ZRUN UHPDLQLQJ RQ LW ZKHUH ZRUN LV GHILQHG DV A S DQG 6 LV WKH LQGH[ LH6 VHW RI WKH UHPDLQLQJ RSHUDWLRQV 0:.5 WHQGV WR PLQLPL]H WKH PDNHVSDQ IRU D MRE VKRS HQYLURQPHQW 7KH 6KRUWHVW 3URFHVVLQJ 7LPH 637f UXOH LV SHUKDSV WKH PRVW GLVFXVVHG UXOH LQ OLWHUDWXUH 637 VHOHFWV WKH MRE ZLWK WKH VKRUWHVW SURFHVVLQJ WLPH 637 LV RSWLPDO IRU O\ & P3\A F P)\A 4 ZKHUH PDFKLQHV DUH SURSRUWLRQDWH DQG -Wf P3-Wf DQG P)-Wf ZKHUH -Wf LV WKH QXPEHU RI MREV LQ WKH VKRS DW WLPH W ,W LV DOVR RSWLPDO IRU DQG P3P)ZKHUH LV WKH DYHUDJH QXPEHU RI MREV LQ WKH V\VWHP %KDVNDUDQ DQG 3LQHGR f 637 DOVR PLQLPL]HV PHDQ ODWHQHVV LQ D VLQJOH VHUYHU HQYLURQPHQW (YHQ WKRXJK 637 SHUIRUPV ZHOO LQ PLQLPL]LQJ WKH QXPEHU RI WDUG\ MREV ZKHQ GXH GDWHV DUH HVWDEOLVKHG H[RJHQRXVO\ %ODFNVWRQH 3KLOOLSV DQG +RJJ ;f RQH RI WKH SUREOHPV ZLWK 637 LV WKDW LW FDXVHV KLJK YDULDQFH LQ ODWHQHVV UHODWHG PHDVXUHV 'D\ DQG +RWWHQVWHLQ f ,W LV DOVR IRXQG WR EH LUUHOHYDQW WR FRVWUHODWHG PHDVXUHV VXJJHVWLQJ WKDW FRVW LV QRW UHODWHG WR IORZWLPH %ODFNVWRQH 3KLOOLSV DQG +RJJ f ,Q WKH FDVH RI VWRFKDVWLF SURFHVVLQJ WLPHV DQG XQGHU IDLUO\ JHQHUDO FRQGLWLRQV WKH 6KRUWHVW ([SHFWHG 3URFHVVLQJ 7LPH 6(37f LV RSWLPDO IRU WKH DERYH SUREOHPV 7KH 6KRUWHVW 5HPDLQLQJ 3URFHVVLQJ 7LPH 6537f UXOH PLQLPL]HV WKH REMHFWLYH IXQFWLRQV RSWLPL]HG E\ 637 IRU WKH VLQJOH

PAGE 33

PDFKLQH SUREOHPV ZKHQ MREV KDYH GLIIHUHQW UHOHDVH WLPHV DQG SUHHPSWLRQ LV DOORZHG %KDVNDUDQ DQG 3LQHGR f 7KH 6ODFN SHU 2SHUDWLRQ 6/$&.231f UXOH VHOHFWV WKH MRE ZLWK WKH VPDOOHVW VODFN WLPH SHU RSHUDWLRQ UDWLR 7KH 0LQLPXP 6ODFN 6/$&.f UXOH VHOHFWV WKH MRE ZLWK WKH PLQLPXP VODFN WLPH UHPDLQLQJ 6/$&.231 6/$&. DQG ('' UXOHV DUH NQRZQ WR SHUIRUP EHWWHU LQ PLQLPL]LQJ WKH YDULDQFH LQ ODWHQHVV UHODWHG PHDVXUHV FRPSDUHG WR 637 6/$&.231 FRPSDUHG WR ('' DQG WKH 6/$&. UXOHV %ODFNVWRQH 3KLOOLSV DQG +RJJ f 2QH RWKHU GXH GDWH UHODWHG UXOH LV WKH &ULWLFDO 5DWLR &5f UXOH ZKLFK VHOHFWV WKH WKH MRE ZLWK WKH VPDOOHVW FULWLFDO UDWLR 7KH FULWLFDO UDWLR &5 LV FDOFXODWHG E\ G W BL / DQG / LV WKH ZDLWLQJ WLPH UHPDLQLQJ LQ WKH TXHXH IRU MRE M %ODFNVWRQH 3KLOOLSV DQG +RJJ f &5 UXOH LV NQRZQ WR ZRUN ZHOO IRU PHDQ WDUGLQHVV 3DUN 5DPDQ DQG 6KDZ f 7KH /HDVW :RUN 5HPDLQLQJ /:.5f UXOH VHOHFWV WKH MRE ZLWK WKH OHDVW ZRUN UHPDLQLQJ ZKHUH ZRUN LV GHILQHG DV EHIRUH /:.5 WHQGV WR PLQLPL]H WKH IORZWLPH LQ MREVKRSV 7KH :HLJKWHG 6KRUWHVW 3URFHVVLQJ 7LPH :637f UXOH DVVLJQV WKH KLJKHVW SULRULW\ WR WKH MRE WKDW KDV WKH KLJKHVW UDWLR ZKHUH Zc LV WKH ZHLJKWf§RU LPSRUWDQFHf§JLYHQ WR WKH MRE :637 LV NQRZQ WR RSWLPL]H WKH OeZ& SUREOHP DQG LV NQRZQ WR ZRUN ZHOO

PAGE 34

IRU SDUDOOHO PDFKLQHV DQG SURSRUWLRQDWH IORZVKRSV 7KH :6(37 UXOH LV RSWLPDO IRU OeZ(>&@ LQ D VWRFKDVWLF HQYLURQPHQW HYHQ LQ WKH SUHVHQFH RI PDFKLQH EUHDNGRZQV 7KH 6KRUWHVW 6HWXS 7LPH )LUVW 667f UXOH DVVLJQV WKH KLJKHVW SULRULW\ WR WKH MRE WKDW UHTXLUHV WKH VKRUWHVW VHWXS WLPH SRVVLEO\ ]HUR WLPH XQLWV LI WKH SUHYLRXV MRE ZDV IURP WKH VDPH IDPLO\ 667 WULHV WR PLQLPL]H WKH WRWDO WLPH VSHQW LQ VHWXSV 667 KDV QRW SURYHQ YHU\ XVHIXO 7KH IROORZLQJ WZR UXOHV WU\ WR FDSWXUH WKH SRZHU RI LQGLYLGXDO UXOHV E\ WDNLQJ D FRPELQDWLRQ RI WKHP 7KH '\QDPLF &RPSRVLWH 5XOH '&5f DWWHPSWV WR PLQLPL]H WKH WRWDO WDUGLQHVV LQ D MREVKRS HQYLURQPHQW '&5 VHOHFWV WKH MRE ZLWK WKH KLJKHVW SULRULW\ LQGH[ OMWf ZKLFK LV FDOFXODWHG DV ZKHUH P LV WKH QXPEHU RI PDFKLQHV LQ WKH VKRS DQG :cWf DQG :KWf DUH WKH FXUUHQW ZRUNORDG RI WKH FXUUHQW PDFKLQH DQG WKH QH[W PDFKLQH UHVSHFWLYHO\ 7KH SHUIRUPDQFH RI WKH UXOH LV FRPSDUDEOH WR 637 LQ WRWDO ODWHQHVV DQG WKH QXPEHU RI WDUG\ MREV DQG LV EHWWHU LQ WRWDO WDUGLQHVV ,W DOVR SURGXFHV ORZ YDULDQFH LQ IORZWLPHV FRPSDUHG WR 637 %KDVNDUDQ DQG 3LQHGR f

PAGE 35

3HUKDSV RQH RI WKH PRVW XVHIXO UXOHV LQ D MREVKRS HQYLURQPHQW LV WKH &29(57 UXOH 7KH &RVW 29(5 7LPH UXOH DLPV DW PLQLPL]LQJ WKH WRWDO WDUGLQHVV 7KH SULRULW\ LQGH[ ,MWf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f /HW W EH WKH FXUUHQW WLPH 6M EH WKH UHPDLQLQJ VHW RI ZRUN VWDWLRQV EHIRUH WKH MRE M LV FRPSOHWHG / EH DQ LQGLFDWRU YDULDEOH HTXDO WR LI MRE M LV SURFHVVHG DW VWDWLRQ L

PAGE 36

GcM EH WKH WLPH MRE M LV VFKHGXOHG WR EH FRPSOHWHG DW VWDWLRQ L 3LM EH WKH UHPDLQLQJ SURFHVVLQJ WLPH RI MRE M RQ PDFKLQH L DW WLPH W Zf EH WKH H[SHFWHG ZDLWLQJ WLPH RI MRE M LQ VWDWLRQ TXHXHf L JLYHQ WKDW WKHUH DUH D MREV ZDLWLQJ LQ OLQH DQG '9M EH WKH GROODU YDOXH RI MRE M 'HILQLWLRQ $ SURSRUWLRQDWH IORZVKRS LV RQH ZKHUH S DSN D!9M 7DEOH FRQVLVWV RI D ORQJ OLVW RI GLVSDWFKLQJ UXOHV )RU HDFK UXOH ZH JLYH LWV QDPH DEEUHYLDWLRQ WKH FDOFXODWLRQ RI LWV SULRULW\ LQGH[ VHW DQG FRQGLWLRQV ZKHUH LW KDV EHHQ IRXQG XVHIXO

PAGE 37

7DEOH 'LVSDWFKLQJ 5XOHV 1$0( $%%5(9,$7,21 35,25,7< ,1'(; 6(7 &200(176 6HOHFW ,Q 5DQGRP 2UGHU 6,52 8 1f 8VHV QR LQIRUPDWLRQ DERXW WKH VKRS )LUVW &RPH )LUVW 6HUYHG )&)6 5HGXFHV WKH YDULDQFH RI DYHUDJH ZDLWLQJ WLPH )LUVW $W 6KRS )LUVW 6HUYHG )$6)6 M_U-6UO9Nf (DUOLHVW 'XH 'DWH ('' ^M GMGN 9N` 0LQLPL]HV /A 7PD[ LQ D VLQJOH PDFKLQH RU SURSRUWLRQDWH IORZVKRS HQYLURQPHQW /RQJHVW 3URFHVVLQJ 7LPH /37 ^M 3LM3XFf9N` *RRG IRU PLQLPL]LQJ PDNHVSDQ )RU P3 & WKH UHODWLYH HUURU PD[ ,6 P /RQJHVW 5HPDLQLQJ 3URFHVVLQJ 7LPH /537 ^MO3L=3LNf9N` 2SWLPDO IRU 3SPWQ&PD[ 0RVW :RUN 5HPDLQLQJ 0:.5 LML ( 3\ A ( 3XFfY f 6L f 6N 7HQGV WR PLQLPL]H PDNHVSDQ LQ D MREVKRS 6KRUWHVW 3URFHVVLQJ 7LPH 637 M 3LM3LNf9N ` 0LQLPL]HV A & WKH QXPEHU RI MREV LQ WKH V\VWHP DW DQ\ WLPH DQG DYHUDJH QXPEHU RI MREV IRU VLQJOH PDFKLQH LGHQWLFDO SDUDOOHO PDFKLQHV DQG SURSRUWLRQDWH IORZVKRS VHWWLQJV

PAGE 38

7DEOH FRQWLQXHG 1$0( $%%5(9,$7,21 35,25,7< ,1'(; 6(7 &200(176 6KRUWHVW 5HPDLQLQJ 3URFHVVLQJ 7LPH 6537 ^M 3LMn3LNf9N` 2SWLPDO IRU UI ZKHUH I FDQ EH RQH RI & WKH QXPEHU RI MREV LQ WKH V\VWHP DW DQ\ WLPH DYHUDJH QXPEHU RI MREV LQ D VLQJOH PDFKLQH /HDVW :RUN 5HPDLQLQJ /:.5 -_ e3LMAe3LNf9NO Lf 6M Lf 6N $WWHPSWV WR PLQLPL]H WKH IORZWLPH LQ D MREVKRS :HLJKWHG 6KRUWHVW 3URFHVVLQJ 7LPH :637 OM 0 UV $O m7 2SWLPDO IRU A Z & :RUNV ZHOO IRU SDUDOOHO PDFKLQHV DQG SURSRUWLRQDWH IORZVKRSV IRU WKH VDPH REMHFWLYH IXQFWLRQ 6KRUWHVW 6HWXS 7LPH 667 ^M $ JUHHG\ UXOH ZKLFK WULHV WR PLQLPL]H WKH WLPH VSHQW LQ VHWXS :HLJKWHG VXP RI 637 DQG /:.5 ^M D3LM rfe 3\AD3LN Df e 3ON Lf 6 Lf 6IF DO9N` 5HPDLQLQJ 3URFHVVLQJ 7LPH ,PPLQHQW 3URFHVVLQJ 7LPH 537,37 M_ e 3\ eSXF LH6L LH6N 9N 3LM 3LN 637 WUXQFDWHG WR )&)6 637)&)6 8VH 637 ILUVW ,I WKHUH LV DQ\ LWHP ZDLWLQJ PRUH WKDQ VRPH VSHFLILHG DPRXQW RI WLPH VHOHFW E\ XVLQJ )&)6 )&6) WUXQFDWHG WR 637 )&)6637 8VH )&)6 ILUVW :KHQHYHU WKH TXHXH OHQJWK LV DERYH VZLWFK WR 637 XQWLO WKH TXHXH OHQJWK UHGXFHV WR

PAGE 39

7DEOH FRQWLQXHG 1$0( $%%5(9,$7,21 35,25,7< ,1'(; 6(7 &200(176 637; &DOFXODWH ) GW9n S8 M M P V 6HOHFW` M ) )N9N`nLI) XVH 637 RWKHUZLVH 6377 8VH 637 \ ZKHUH \ LV D FRQWURO SDUDPHWHU &RPSDUH LW WR 6/$&.231 DQG FKRRVH WKH PLQLPXP 0LQLPXP 6ODFN 7LPH 6/$&. X f 6 Lf 6N 6ODFN 2SHUDWLRQ 6/$&.231 f GMWB( 3MM GN W a( 3LN LH6M LH6N 9N ( 3LM ( Sr Lf 6 Lf 6N 0RGLILHG (DUOLHVW 'XH 'DWH 0'' ^-OG\AGA9N` 6RPHWLPHV FDOOHG WKH RSHUDWLRQ GXH GDWH 0RGLILHG 0LQLPXP 6ODFN 06/$&. IGM ( 3LM ( AGN ( 3LN ( Y f 6 f 6 f 6N f 6N -RE 6ODFN 5DWLR -65 f N GMW( 3LM GN a( 3LN Lf6L LH6N 9N GW G W N

PAGE 40

7DEOH FRQWLQXHG 1$0( $%%5(9,$7,21 35,25,7< ,1'(; 6(7 &200(176 0RGLILHG -RE 6ODFN 5DWLR 0-65 U f M GMW(3\( GNW(3LN( ZWNf f 6 f 6 f 6 f 6 \ n n N N 9NI GW GW N *UHDWHVW 'ROODU 9DOXH *'9 ^M _'9!'9N9N` &ULWLFDO 5DWLR &5 XL GW GW UVAYNn *LYHV JRRG UHVXOWV IRU PHDQ WDUGLQHVV

PAGE 41

2YHUYLHZ RI $UWLILFLDO ,QWHOOLJHQFH $UWLILFLDO ,QWHOOLJHQFH $,f HPHUJHG DV D V\PEROLF FRPSXWDWLRQ SDUDGLJP GXULQJ HDUO\ V ,W ZDV WKH DLP RI $, UHVHDUFK WR JHQHUDWH V\VWHPV WKDW FRXOG EH FRQVLGHUHG LQWHOOLJHQW (YHQ WKRXJK LQWHOOLJHQFH LQ KXPDQV WDNHV PDQ\ IRUPV VXFK DV MXGJHPHQW FUHDWLYLW\ SODXVLEOH UHDVRQLQJ HWF $, UHVHDUFK UHVWULFWV LWV DWWHQWLRQ WR FRPSXWDWLRQDO WHFKQLTXHV IRU SHUIRUPLQJ WDVNV WKDW DSSDUHQWO\ UHTXLUH LQWHOOLJHQFH ZKHQ SHUIRUPHG E\ KXPDQV 7DQLPRWR f $, UHVHDUFK PDLQO\ IRFXVHV RQ NQRZOHGJH UHSUHVHQWDWLRQ GHYHORSLQJ VHDUFK WHFKQLTXHV SHUFHSWLRQ DQG LQIHUHQFH 7DQLPRWR f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ff§XVXDOO\ UHIHUUHG WR DV JRDOVf§FDQ EH LOO GHILQHG DQG DOO PD\ EH QRQTXDQWLILDEOH 6LPRQ f 0RVW LPSRUWDQWO\ $, PHWKRGV FDQ LQFRUSRUDWH H[SHULHQFH DQG H[SHUWLVH LQWR WKH VROXWLRQ RI WKH SUREOHP 1HLWKHU WKH 0DWKHPDWLFDO 3URJUDPPLQJ DSSURDFKHV QRU WKH GLVSDWFKLQJ DSSURDFKHV WR VFKHGXOLQJ SUREOHP KDYH VXSHULRU SUREOHP VROYLQJ DELOLWLHV DV FRPSDUHG WR HDFK RWKHU

PAGE 42

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f 2Z ;f DUH DEOH WR KDQGOH WKHVH FDVHV XVLQJ KHXULVWLF NQRZOHGJH ,Q WKH IROORZLQJ VXEVHFWLRQV IRXU GLIIHUHQW IDPLOLHV RI $, DSSURDFKHV WR VROYLQJ WKH VFKHGXOLQJ SUREOHP ZLOO EH SUHVHQWHG 7KH GLVWLQFWLRQ EHWZHHQ DQ\ WZR IDPLOLHV LV QRW ZHOO GHILQHG VLQFH DOO PHWKRGV ERUURZ LGHDV IURP HDFK RWKHU 1RQHWKHOHVV HDFK IDPLO\ FDSWXUHV WKH SUHYDOHQW WKHPH RI LWV PHPEHUV 7KH IRXU FDWHJRULHV DUH ([SHUW 6\VWHPV (6f DSSURDFKHV &RQVWUDLQHG +HXULVWLF 6HDUFK &+6f +\EULG PHWKRGV DQG 0DFKLQH /HDUQLQJ 0/f DSSURDFKHV ([SHUW 6\VWHPV DQG 6FKHGXOLQJ ([SHUW 6\VWHPV (6f DWWHPSW WR PLPLF WKH GHFLVLRQ PDNLQJ EHKDYLRU RI WKH GRPDLQ H[SHUWV $Q (6 UHTXLUHV WKUHH EDVLF FRPSRQHQWV D NQRZOHGJH EDVH

PAGE 43

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f UHSRUW WKDW WKHUH DUH VFKHGXOLQJ H[SHUWV 7KH\ VWDWH ,Q FRQFOXVLRQ LW LV VXJJHVWHG WKDW KXPDQ H[SHUWLVH LQ VFKHGXOLQJ H[LVWV DQG LV D YDOXDEOH FRPSRQHQW RI DQ\ UHDOLVWLF VFKHGXOLQJ SODQQLQJ HQYLURQPHQW 7KLV H[SHUWLVH LV OLNH RWKHU H[SHUWLVH DQG LW LV EDVHG RQ WKH KXPDQfV OHDUQLQJ WR UHFRJQL]H XQGHUVWDQG DQG DGMXVW IRU EURNHQOHJ FXHV RU FRQILJXUDO LQIRUPDWLRQ IRXQG LQ WKH PDQXIDFWXULQJ HQYLURQPHQW 0H .D\ HW DO S f

PAGE 44

6WLOO PRVW UHVHDUFKHUV KDYH EHOLHIV DJDLQVW WKH VXLWDELOLW\ RI (6 DSSURDFKHV WR VFKHGXOLQJ )R[ UHSRUWV WKH IROORZLQJ GLIILFXOWLHV WDNLQJ DQ H[SHUW V\VWHPV DSSURDFK WR VFKHGXOLQJ DSSHDUHG LQDSSURSULDWH 7KHUH DUH WZR SUREOHPV ZLWK WKH H[SHUW V\VWHPV DSSURDFK f 3UREOHPV OLNH IDFWRU\ VFKHGXOLQJ WHQG WR EH VR FRPSOH[ WKDW WKH\ DUH EH\RQG WKH FRJQLWLYH FDSDELOLWLHV RI WKH KXPDQ VFKHGXOHU 7KHUHIRUH WKH VFKHGXOHV SURGXFHG E\ WKH VFKHGXOHU DUH SRRU QRERG\ ZDQWV WR HPXODWH WKHLU SHUIRUPDQFH ^7KHUH LQGHHG QR H[SHUW VFKHGXOHU H[LVWV` f (YHQ LI WKH SUREOHP LV RI UHODWLYHO\ ORZ FRPSOH[LW\ IDFWRU\ HQYLURQPHQWV FKDQJH RIWHQ HQRXJK WKDW DQ\ H[SHUWLVH EXLOW XS RYHU WLPH EHFRPHV REVROHWH ([SHUW V\VWHPV DSSHDU WR EH DSSURSULDWH RQO\ ZKHQ WKH SUREOHP LV ERWK VPDOO DQG VWDEOH )R[ S f %DVLFDOO\ H[SHUW V\VWHPV DUH QRW VXLWDEOH IRU WKH VFKHGXOLQJ GRPDLQ IRU WKH IROORZLQJ UHDVRQV )R[ f 5RGDPPHU DQG :KLWH f %OHVVLQJ DQG :DWIRUG f 6DYHOL 3HUH] DQG .RK f DQG 6WHIIHQ DQG *UHHQH f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

PAGE 45

&RQWUDU\ WR WKH DERYH UHVXOWV 0LOOHU /XIJ DQG :DONHU UHSRUW D VXFFHVVIXO (6 LPSOHPHQWDWLRQ 7KH ODUJH SRWHQWLDO VDYLQJV DFKLHYDEOH WKURXJK ([SHUW 6\VWHPV 6FKHGXOLQJ DV SURYHQ E\ WKH PLOOLRQ DQQXDO SD\ EDFN DW D :HVWLQJKRXVH SODQW ZLOO DWWUDFW VLJQLILFDQW LQGXVWULDO LQWHUHVW LQ WKH QH[W IHZ \HDU PDNLQJ WKLV RQH RI WKH KRWWHVW DUHDV IRU H[SHUW V\VWHPV DSSOLFDWLRQV 0LOOHU /XIJ DQG :DONHU S f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f§WKH NQRZOHGJH DFTXLVLWLRQ VWDJH (YHQ VR PRVW RI WKH DSSOLFDWLRQV DUH IDLUO\ VXFFHVVIXO ZLWK UHJDUG WR DFFHSWDQFH E\ WKH VWDII DQG DUH EHLQJ SXW WR DFWXDO XVH RQ WKH VKRSIORRU &ODQF\ DQG 0RKDQ f GHVFULEH DQ H[SHUW V\VWHP 5%' GHVLJQHG WR KHOS PDNH UHDOWLPH GLVSDWFKLQJ GHFLVLRQV E\ XVLQJ VHTXHQFLQJ UXOHV UHSUHVHQWLQJ FRPSDQ\ NQRZOHGJH 7R HQDEOH UHDOWLPH GHFLVLRQ PDNLQJ WKH V\VWHP LV IHG ZLWK UHDOWLPH GDWD DERXW WKH IDFWRU\ IORRU VWDWXV 5XOHV XVHG IRU SULRULWL]DWLRQ FRQVLGHU WKH IROORZLQJ FULWHULD &ULWLFDO UDWLR VWDUW GDWH H[SLUDWLRQ WLPH DQG ODWHQHVV

PAGE 46

2UGHU W\SH (TXLSPHQW VWDWXV :RUN VWDWLRQ FKDUDFWHULVWLFV DQG -RE FKDUDFWHULVWLFV 8VLQJ WKH DERYH FULWHULD WKH V\VWHP SURGXFHV D SULRULW\ OLVW RI MREV 7KH KLJKHVW SULRULW\ MRE LV WKHQ VHOHFWHG 7KH V\VWHP KDV QR OHDUQLQJ FDSDELOLWLHV 5%' KDV EHHQ LPSOHPHQWHG DQG XVHG LQ WKH VHPLFRQGXFWRU LQGXVWU\ 7KH UHVXOWV REWDLQHG VR IDU VKRZ D GHFUHDVH LQ :RUN LQ 3URJUHVV :,3f DQG DQ LQFUHDVH LQ FULWLFDO HTXLSPHQW XWLOL]DWLRQ .HUU DQG (EVDU\f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

PAGE 47

&RQWLQJHQF\ UXOHV DQG 7LPH FRQYHUVLRQ UXOHV 7KH V\VWHP ZDV DEOH WR DFFHVV UHDOWLPH GDWD DERXW WKH VKRSIORRU VWDWXV YLD D UHODWLRQDO GDWDEDVH V\VWHP DQG PDNH UHDO WLPH GLVSDWFKLQJ GHFLVLRQV 7KH DXWKRUV UHSRUW WZR SUREOHPV ZLWK WKH SURMHFW &DSWXULQJ H[SHUW NQRZOHGJH FRPSUHKHQVLYH HQRXJK WR FRYHU DOO WKH FDVHV RQH PD\ IDFH LQ VXFK DQ HQYLURQPHQW ZDV LPSRVVLEOH 7KH KLJKO\ G\QDPLF QDWXUH RI WKH VFKHGXOLQJ HQYLURQPHQW FDXVHG WKH NQRZOHGJH EDVH WR EH LQYDOLG YHU\ UDSLGO\ /HH DQG 6XK f GHVFULEH DQ H[SHUW V\VWHP 3$06 ZLWK D K\EULG NQRZOHGJHEDVH FRPSRVHG RI UXOHV IUDPHV DQG VRPH KHXULVWLF NQRZOHGJH ZKLFK ZDV VSHFLILF WR WKH GRPDLQ RI VFKHGXOLQJ SDUDOOHO PDFKLQHV 7KH NQRZOHGJH EDVH FDQ EH EURNHQ GRZQ LQWR IRXU VHWV RI UXOHV GHDOLQJ ZLWK -RE VWDWXV 0DFKLQH VWDWXV /DERU VWDWXV DQG 0DWHULDO VWDWXV 3$06 KDV D WZR VWDJH FRQWURO VWUDWHJ\ ZKHUH D IHDVLEOH VFKHGXOH LV JHQHUDWHG LQ WKH ILUVW SKDVH DQG LV HYDOXDWHG DQG XSGDWHG LQ WKH VHFRQG SKDVH LI GHVLUHG 7KH V\VWHP LV FDSDEOH RI SURGXFLQJ VFKHGXOHV DW GLIIHUHQW OHYHOV RI GHWDLO 7KH DXWKRUV UHSRUW LPSURYHPHQW RQ WDUGLQHVV PHDVXUHV

PAGE 48

6DYHOL 3HUH] DQG .RK f GHVFULEH D FODVVLFDO ([SHUW 6\VWHP DSSOLFDWLRQ LPSOHPHQWHG IRU D VHPLFRQGXFWRU SURGXFWLRQ SODQW 'XH WR WKH PRGXODU QDWXUH RI WKH HQYLURQPHQW WKH NQRZOHGJH EDVH FRXOG EH FRQVWUXFWHG VHSDUDWHO\ UHIOHFWLQJ NQRZOHGJH DERXW HDFK FHOO UDWKHU WKDQ WKH ZKROH IDFWRU\ 7KH NQRZOHGJH DFTXLVLWLRQ ZDV FDUULHG RXW WKURXJK LQWHUYLHZV ZLWK WKH GRPDLQ H[SHUWV 7KH UHVXOWLQJ NQRZOHGJH EDVH KDG WZR W\SHV RI UXOHV 5XOHV WR DVVLJQ SULRULWLHV DQG 5XOHV WR DVVLJQ WKH MREV LQ SURGXFWLRQ FHOOV WR WKH HTXLSPHQW (TXLSPHQW 6FKHGXOHUf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

PAGE 49

FRQVWUDLQWV DUH VDWLVILHG DQG DOO YDULDEOH DVVLJQPHQWV DUH PDGH ,I D QRGH LV IRXQG WKDW FDQ QRW EH H[SDQGHG \HW QR IHDVLEOH VROXWLRQ LV UHDFKHG WKH DOJRULWKP EDFNWUDFNV WR WKH FORVHVW XQH[SORUHG QRGH DQG FRQWLQXHV WKH VHDUFK IURP WKHUH ,Q D VFKHGXOLQJ SUREOHP WKLV FDQ EH YLHZHG DV JHQHUDWLQJ VXEVFKHGXOHV DQG EDFNWUDFNLQJ ZKHQ WKH FXUUHQW VXEn VFKHGXOH YLRODWHV WKH FRQVWUDLQWV &+6 XWLOL]HV WKH WHFKQLTXHV XVHG IRU &63 EXW LQ DGGLWLRQ XVHV KHXULVWLF NQRZOHGJH WR JXLGH WKH VHDUFK VR WKDW FRVWO\ EDFNWUDFNLQJ LV PLQLPL]HG 3HUKDSV WKH PRVW FUXFLDO GLIIHUHQFH EHWZHHQ &63 DQG &+6 LV WKDW &+6 DOVR PDNHV XVH RI DQ REMHFWLYH IXQFWLRQ WR HYDOXDWH WKH DVVLJQPHQWV UDWKHU WKDQ D EOLQG VHDUFK WKDW ZLOO UHVXOW LQ SRRU VROXWLRQV ZLWK UHVSHFW WR WKH SHUIRUPDQFH FULWHULD )R[ 6DGHK DQG %D\NDQ f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f

PAGE 50

'HILQH DQ LQLWLDO VWDWH ZKHUH QR YDULDEOH LV DVVLJQHG D YDOXH ZKLOH WKH JRDO VWDWH LV QRW UHDFKHG GR ^ 0DWFK WKH EHVW RSHUDWRU WKDW DSSOLHV WR WKH JLYHQ VWDWH $SSO\ WKH RSHUDWRU ` 7KH PDWFKLQJ SHUIRUPHG LQ 6WHS f LV WKH PRVW GLIILFXOW SDUW RI WKH DOJRULWKP )RU D VXFFHVVIXO PDWFK WKH DOJRULWKP QRW RQO\ QHHGV WR VDWLVI\ WKH SUHFRQGLWLRQV RI WKH UHOHYDQW RSHUDWRUV EXW DOVR QHHGV WR ILQG WKH EHVW RSHUDWRU WR DSSO\ LQ RUGHU WR UHGXFH WKH VHDUFK FRPSOH[LW\ RI WKH SUREOHP 1RWH WKDW 6WHS f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f GLVFXVV FRQVWUDLQWJXLGHG KHXULVWLF VHDUFK DQG WKH NQRZOHGJH XVHG WR LPSOHPHQW WKLV PHWKRGRORJ\ $ V\VWHP FDOOHG 3/$7236 LV XQGHU LPSOHPHQWDWLRQ WKDW XVHV WKH DERYH LGHDV 7KH V\VWHP KDV D SURFHVV JHQHUDWLRQ VXEV\VWHP WKDW JHQHUDWHV URXWLQJ DQG SURFHVVLQJ LQIRUPDWLRQ 7KH VHTXHQFLQJ VXEV\VWHP XWLOL]HV VHTXHQFLQJ KHXULVWLFV WR WUDQVIRUP WKH VHW RI RUGHUV IURP D IODW VWUXFWXUH WR D KLHUDUFKLFDO VWUXFWXUH RI JURXSV SRVVLEO\ RUGHUHG 7KH VFKHGXOHU WUDYHUVHV WKH SURGXFWLRQ RUGHU

PAGE 51

VHTXHQFH XVLQJ KHXULVWLF FRQVWUDLQWJXLGHG VWDWH VSDFH VHDUFK 7KH VHTXHQFHU XWLOL]HV KHXULVWLFV IRU SUXQLQJ WKH VHDUFK VSDFH VXFK DV RUGHULQJ KHXULVWLFV DQG JURXSLQJ KHXULVWLFV 7KH FRQVWUDLQWJXLGHG VHDUFK XVHV KHXULVWLFV IRU SUXQLQJ WKH VWDWHVSDFH VHDUFK VXFK DV FRQVWUDLQW YLRODWLRQ DQG VWDWH VHOHFWLRQ %HQVDQD HW DO f (UVFKOHU DQG (VTXLURO f DQG %HO HW DO f LQWURGXFH WZR V\VWHPV FDOOHG 0$6&27 DQG 23$/ 7KH V\VWHPV DUH GHVLJQHG WR XVH WKUHH W\SHV RI NQRZOHGJH GXULQJ WKH SURFHVV RI GHULYLQJ IHDVLEOH VFKHGXOHV 7KH WKHRUHWLFDO NQRZOHGJH RQ VFKHGXOLQJ SUREOHPV (PSLULFDO NQRZOHGJH DERXW SULRULW\ UXOHV DQG 3UDFWLFDO NQRZOHGJH DERXW WHFKQRORJLFDO FRQVWUDLQWV 7KH VR FDOOHG &RQVWUDLQHG %DVHG $QDO\VLV &%$f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

PAGE 52

VXSSRUW PRGXOH LV XVHG WR SURYLGH DGYLFH RQ WKH VHTXHQFLQJ RI RSHUDWLRQV EDVHG RQ SUDFWLFDO RU KHXULVWLF NQRZOHGJH )LQDOO\ WKH VXSHUYLVRU FRRUGLQDWHV WKH LQWHUDFWLRQ EHWZHHQ WKH WZR PRGXOHV E\ FDOOLQJ HDFK LQ RUGHU DV QHHGHG ,I QR IHDVLEOH VFKHGXOH LV IRXQG WKH VXSHUYLVRU FDOOV D IDLOXUH UHFRYHU\ PRGXOH WKDW VHOHFWLYHO\ UHOD[HV VRPH RI WKH FRQVWUDLQWV VXFK DV GXH GDWHV (UVFKOHU DQG 5RXEHOODW f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f ,6,6 LV DQ HQKDQFHG YHUVLRQ RI ,6,6 ZKHUH LQVWHDG RI VROYLQJ WKH SUREOHP DW RQH OHYHO WKH V\VWHP DWWDFNV LW LQ D KLHUDUFKLFDO PDQQHU 7KH V\VWHPV ILUVW VHOHFWV DQ RUGHU WKHQ DQDO\]HV WKH DYDLODEOH FDSDFLW\ FKHFNV WKH UHVRXUFH FRQVWUDLQWV DQG ILQDOO\ DVVLJQV WKH WLPH ERXQG RI HDFK UHVRXUFH UHTXLUHG IRU WKH RSHUDWLRQ )R[ DQG 6PLWK Ef ,6,6 LQWURGXFHV WKH LGHD

PAGE 53

RI UHVRXUFH YHUVXV RUGHU VFKHGXOLQJ ZKLFK LV UHIHUUHG WR DV PXOWLSHUVSHFWLYH VFKHGXOLQJ E\ WKH DXWKRU )R[ f )LUVW ERWWOHQHFN PDFKLQHV DUH LGHQWLILHG E\ D URXJK GUDIW RI WKH ILQDO VFKHGXOH DQG WKHVH PDFKLQHV DUH WULHG WR EH DVVLJQHG RSHUDWLRQV 7KHQ WKH V\VWHP FRQVLGHUV DQ RUGHU EDVHG VFKHGXOLQJ &257(6 LV D GLVWULEXWHG V\VWHP IRU SURGXFWLRQ SODQQLQJ VFKHGXOLQJ DQG FRQWURO )R[ DQG 6\FDUD f 7KH &257(6 V\VWHP FRPSDUHG WR WKH ,6,6 IDPLO\ FRQVLGHUV MREV DQG UHVRXUFHV DV DJJUHJDWH YDULDEOHV )R[ f 7KH DSSURDFK XVHG LQ DFWLYLW\ VFKHGXOLQJ LV YHU\ VLPLODU WR WKH OHDVW FRPPLWPHQW VWUDWHJ\ XVHG LQ SODQQLQJ V\VWHPV 7KH SUREOHP VROYLQJ PHWKRG RI WKH &257(6 V\VWHP FDQ EH VXPPDUL]HG DV IROORZV $Q LQLWLDO VWDWH LV JHQHUDWHG 7KH FRQVWUDLQWV LPSRVHG E\ WKH FXUUHQW VWDWH LV SURSDJDWHG 7H[WXUH PHDVXUHV )R[ 6DGHK DQG %D\NDQ ff DUH FRPSXWHG %DVHG RQ f D VWDWH LV VHOHFWHG $ UXOH LV PDWFKHG WR WKH FXUUHQW VWDWH DQG DQ DVVLJQPHQW LV PDGH ,I WKH JRDO VWDWH LV QRW UHDFKHG VWHSV f WKURXJK f DUH UHSHDWHG 5HVHDUFK RQ ERWK ,6,6 DQG &257(6 KDV UHSRUWHG SURPLVLQJ UHVXOWV 7KH XVH RI WH[WXUH PHDVXUHV KDV UHVXOWHG LQ D UHGXFWLRQ RI WKH VHDUFK FRPSOH[LW\ 6WHIIHQ DQG *UHHQH f LQWURGXFH DQ DSSURDFK QDPHG GHGLFDWHGVKDUHG GHFRPSRVLWLRQ ZKHUH DIWHU WKH SURGXFWLRQ SODQQLQJ OHYHO WKH\ DVVLJQ FHUWDLQ MREV WR GHGLFDWHG PDFKLQHV DQG WKHQ LQ HDFK VXESUREOHP WKH\ SHUIRUP GHGLFDWHG ORDGLQJ VHTXHQFLQJ DQG VKDUHG ORDGLQJ DQG VHTXHQFLQJ

PAGE 54

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f 7KH IRUPHU RQH LV XVHG WR DQDO\]H WKH DYDLODEOH FDSDFLW\ ZKHUHDV WKH ODWWHU WZR DUH XVHG IRU UHVRXUFH RU RUGHU EDVHG VFKHGXOLQJ GHFLVLRQV $W HDFK F\FOH DIWHU SURSDJDWLQJ WKH UHVXOWV RI DQ\ XQH[SHFWHG HYHQWV VXFK DV FDSDFLW\ FRQIOLFWV PDFKLQH EUHDNGRZQV HWF WKH VHDUFK PDQDJHU SULRULWL]HV DQG VWRUHV WKHP RQ WKH DJHQGD 7KH WDVN ZLWK WKH KLJKHVW SULRULW\ LV H[HFXWHG DV D VXEWDVN )R[ f 23,6 LV D UHDFWLYH VFKHGXOLQJ V\VWHP ZKLFK LV GHVLJQHG WR GHDO ZLWK H[RJHQRXV HYHQWV :KHQ VXFK DQ HYHQW LV HQFRXQWHUHG WKH FRQVHTXHQFHV RI WKH HIIHFWV DUH SURSDJDWHG RQWR WKH H[LVWLQJ VFKHGXOHV &RQIOLFW DULVLQJ IURP WKLV FKDQJH DUH VWRUHG LQ WKH DJHQGD DV LV WKH FDVH LQ 23,6 7ZR PRUH .6V DUH XVHG WR GHDO ZLWK WKH H[FHSWLRQV WKH RUGHU EDVHG ULJKW VKLIWHU DQG WKH GHPDQG VZDSSHU 7KH V\VWHP XVHV D

PAGE 55

GHFLVLRQ WUHH WR GHFLGH ZKLFK .6Vf WR XVH IRU H[FHSWLRQ KDQGOLQJ 7KH 236 V\VWHPV IDPLO\ H[WHQGV WKH PXOWLSHUVSHFWLYH VFKHGXOLQJ YLHZ RI WKH ,6,6 V\VWHP DQG DOORZV DOWHUQDWLYH VROXWLRQ PHWKRGV ZLWKLQ HDFK YLHZ 2Z 6PLWK DQG +RZLH f GHVFULEH D GLVWULEXWHG VFKHGXOLQJ V\VWHP FDOOHG &66 ZKLFK XVHV WZR W\SHV RI NQRZOHGJH EDVHV WKH ZRUN RUGHU PDQDJHU :20 DQG WKH UHVRXUFH EURNHU 7KH LGHD RI &66 LV VLPLODU WR WKH RQH GHVFULEHG LQ 6KDZ f 7KH V\VWHP XVHV D ELGGLQJ PHWKRGRORJ\ :20 HVWLPDWHV WKH FRPSOHWLRQ WLPH RI D ZRUN RUGHU E\ H[DPLQLQJ LWV RSHUDWLRQV JUDSK DQG LQLWLDWHV D ELG DPRQJ WKH QRGHV ZKLFK FRXOG SHUIRUP WKH MRE $IWHU HYDOXDWLQJ WKH ELGV VXEPLWWHG WKH MRE LV VHQW WR WKH VHOHFWHG QRGH 7KH UHVRXUFH EURNHUV HYDOXDWH WKH DYDLODELOLW\ RI WKHLU UHVRXUFHV DQG ELG DFFRUGLQJ WR WKLV LQIRUPDWLRQ 7KH VHDUFK PHWKRG XVHG LQ WKH V\VWHP LV FDOOHG D WZRSDVV EHVWILUVW VHDUFK 6KDZ f XVHV D QHWZRUNZLGH ELGGLQJ VFKHPH ZKHUH HDFK FHOO ELGV IRU D MRE WR VFKHGXOH DQG WKH RQH WKDW KDV WKH EHVW ELG JHWV WKH MRE WR SURFHVV 'HFLVLRQV WR EH PDGH E\ WKH V\VWHP DUH ZKLFK FHOO WR DVVLJQ WKH MRE DQG WKH VHTXHQFLQJ DQG VFKHGXOLQJ ZLWKLQ WKH HDFK FHOO 3HUIRUPDQFH PHDVXUHV XVHG DUH MRE IORZWLPH SURSRUWLRQ RI WKH MREV IDLOLQJ WR PHHW WKH GXH GDWH

PAGE 56

MRE ODWHQHVV DQG WDUGLQHVV VWDWLVWLFV DQG DYHUDJH LQSURFHVV ZDLWLQJ WLPH 7KH DXWKRU XVHV D SODQQLQJ DOJRULWKP IRU VFKHGXOLQJ ZLWKLQ WKH FHOO 6KDZ Ef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f§LH WKHUH LV QR LQIHDVLEOH VROXWLRQ &HOO OHYHOV DOVR FRQWDLQ PDQXIDFWXULQJ PRGXOHV RSHUDWRUVf GHFLVLRQ UXOHV DQG VFKHGXOLQJ KHXULVWLFV 7KH DXWKRU UHSRUWV WKDW WKH V\VWHP RQ WKH DYHUDJH SHUIRUPV EHWWHU WKDQ P\RSLF 637 ELGGLQJ 637 DQG ELGGLQJ ()7 6KDZ Ff GHVFULEHV D V\VWHP WKDW HPSOR\V SDWWHUQGLUHFWHG LQIHUHQFH WR FDSWXUH WKH G\QDPLF QDWXUH RI WKH VFKHGXOLQJ HQYLURQPHQW D SODQQLQJ WHFKQLTXH WR FRRUGLQDWH PDQXIDFWXULQJ SURFHVVHV DQG UHVRXUFH DVVLJQPHQWV DQG

PAGE 57

WKH $r VHDUFK DOJRULWKP 7DQLPRWR f WR H[SHGLWH WKH VHDUFKLQJ SURFHGXUH 7KH DXWKRU HPSOR\V D VWUDWHJ\ WKDW JHQHUDWHV D VFKHGXOH IRU HDFK MRE DQG WKHQ XVHV WKH SODQQLQJ PHWKRGRORJ\ WR UHVROYH WKH FRQIOLFWV WKDW DULVHV GXH WR VKDULQJ WKH VDPH UHVRXUFHV DW WKH VDPH WLPH LQWHUYDOV 7R VROYH WKH FRQIOLFWV WKH DXWKRU VXJJHVWV WZR DSSURDFKHV L &ULWLF 0HFKDQLVP 7KLV PHWKRG XVHV D WDEOH FDOOHG 7DEOH RI 0XOWLSOH (IIHFWV 720(f ZKHUH IRU HDFK HOHPHQW LQ WKDW WDEOH WKH\ KDYH WR FKHFN WKH GHODWRU OLVWV DQG DGGHU OLVWVf§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

PAGE 58

DV QHZ GHFLVLRQV ZHUH PDGH 7KH LQWHOOLJHQFH WKH KHXULVWLFVf ZDV FRGHG LQWR WKH VRXUFH DV H[HFXWDEOH LQVWUXFWLRQV 8QOHVV WKH FRGH FKDQJHV WKH\ ZLOO UHPDLQ WKH V DQG ZLOO UHDFW H[DFWO\ WKH VDPH ZD\ WKH\ KDG GRQH SUHYLRXVO\ HYHQ LI WKRVH DFWLRQV UHVXOWHG LQ D EDG GHFLVLRQ ,Q WKLV VHFWLRQ ZH ZLOO SUHVHQW SDSHUV WKDW XVH DW OHDVW RQH 0DFKLQH /HDUQLQJ 0/f DSSURDFK WR FRQVWUXFW WKHLU NQRZOHGJH EDVHV :H ZLOO FODVVLI\ WKHP DV NQRZOHGJH GLVFRYHU\ V\VWHPV 1RWH KRZHYHU WKDW RQFH WKH NQRZOHGJH EDVHV DUH FRQVWUXFWHG WKH\ DUH QRW XSGDWHG 6R HYHQ WKHVH V\VWHPV FDQ QRW LPSURYH WKHLU SHUIRUPDQFHV WKURXJK H[SHULHQFH ZLWK WKH SRVVLEOH H[FHSWLRQ RI V\VWHP 6&+('8/( E\ /DPDWVFK HW DO f 7KHLU FRQWULEXWLRQ LV KRZHYHU WKHLU DELOLW\ WR FRQVWUXFW NQRZOHGJH WKDW RIWHQ KHOSV WKH SHUIRUPDQFH V\VWHP WR DFKLHYH EHWWHU UHVXOWV WKDQ WKRVH DFFRPSOLVKHG E\ QRQOHDUQLQJ %OHVVLQJ DQG :DWIRUG f GHVFULEH D )06 VFKHGXOLQJ V\VWHP ,1)066 ZKHUH WKH NQRZOHGJH LV UHSUHVHQWHG E\ IUDPHV 7KH\ VWUXFWXUH WKH NQRZOHGJH EDVH LQ WKUHH GLPHQVLRQV QDPHO\ )06 GHVFULSWLRQ RQ RQH D[LV SDUW PL[ RQ DQRWKHU VFKHGXOH SURSRVHG RQ WKH WKLUG D[LV ,I DQ\ SRLQW LQ WKDW WKUHH GLPHQVLRQDO VSDFH LV DOUHDG\ GHILQHG WKH H[SHUW V\VWHP XVHV WKDW SRLQW DV WKH EHVW VFKHGXOH 2WKHUZLVH D VHDUFK IRU D IHZ VFKHGXOLQJ VWUDWHJLHV IRU WKH JLYHQ SDUW PL[ DQG )06 GHVFULSWLRQ LV FDUULHG RXW DQG HYDOXDWHG E\ D VLPXODWLRQ V\VWHP

PAGE 59

7KH VFKHGXOH WKDW JLYHV WKH EHVW UHVXOW LV FKRVHQ DV WKH DQVZHU 7KRVH SRLQWV DUH VDYHG IRU IXUWKHU UHIHUHQFH 7KLV PHFKDQLVP LV UHIHUUHG WR DV URWH OHDUQLQJ (YHQ WKRXJK WKH V\VWHP VDYHV ROG GHFLVLRQV WKDW JDYH JRRG UHVXOWV LW KDV QR PHDQV RI JHQHUDOL]LQJ WKHP DQG ZH VXVSHFW WKDW LQ VXFK D FRPSOH[ HQYLURQPHQW WKH FKDQFHV RI REVHUYLQJ WKH VDPH VWDWH LV YHU\ ORZ $Q LQWHUHVWLQJ DSSURDFK WR WKH VFKHGXOLQJ SUREOHP KDV EHHQ GLVFXVVHG E\ &KU\VVRORXULV /HH DQG 'RPURHVH f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f f GHVFULEH D VHULHV RI H[SHULPHQWV WR OHDUQ JHQHUDO UXOHV IRU VLPSOH MRE VKRS VFKHGXOLQJ WDVNV E\ XVLQJ FODVVLILHU V\VWHPV 7KH V\VWHP NQRZV GLIIHUHQW SUHGLFDWHV GLVSDWFKLQJ UXOHV ZKLFK LW FDQ XVH IRU VRUWLQJ WKH MREV LQ WKH TXHXH 7KH\ H[SHFW WKH FODVVLILHU V\VWHP WR ILQG WKH EHVW GLVSDWFKLQJ UXOH IRU UDQNLQJ WKH MREV LQ WKH TXHXH ZLWK UHVSHFW WR WKH SHUIRUPDQFH FULWHULD 7KH DXWKRUV UHSRUW WKDW WKH V\VWHP

PAGE 60

FDQ GLVFRYHU WKH RSWLPDO UXOH 637 IRU D VLQJOH PDFKLQH PLQLPXP ODWHQHVV SUREOHP ZH DVVXPH WKLV LV WRWDO ODWHQHVVf DQG JRRG VROXWLRQV IRU PLQLPXP ZHLJKWHG WDUGLQHVV SUREOHP $QRWKHU HPHUJLQJ DSSURDFK WR VFKHGXOLQJ SUREOHPV LV FDVH EDVHG UHDVRQLQJ 7KH OHDUQLQJ V\VWHP VWRUHV HDFK FDVH VHHQ VR IDU DV D SLHFH RI NQRZOHGJH LQ ZKDW LV UHIHUUHG WR DV D &DVH %DVH 'XULQJ SUREOHP VROYLQJ LI D PDWFK LV IRXQG IRU DQ\ RI WKH FDVHV VWRUHG LQ WKH FDVH EDVH WKH VROXWLRQ PHWKRG RU WKH UHVXOWV VWRUHG ZLWK WKH FDVH LV DSSOLHG WR WKH SUREOHP 7KH PDWFK GRHV QRW QHHG WR EH H[DFW .RWRQ ;f GHVFULEH D V\VWHP FDOOHG 60$57SODQ WKDW LV XVHG IRU UHVRXUFH DOORFDWLRQ DQG VFKHGXOLQJ IRU DLUOLIW RSHUDWLRQV 'XH WR WKH VL]H RI WKH VHDUFK VSDFH RQO\ D SDUWLDO PDWFK RI WKH FDVHV DUH UHTXLUHG IRU VXFFHVVIXO LQVWDQWLDWLRQ RI D VWRUHG FDVH 2QO\ WKRVH FDVHV WKDW DUH VXFFHVVIXO DUH VWRUHG IRU IXWXUH XVH /DPDWVFK HW DO f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

PAGE 61

SUREOHP LV D EHWWHU DSSUR[LPDWLRQ IRU D FHUWDLQ W\SH RI SUREOHP 1RWH WKDW HDFK QRGH LV D W\SH RI SUREOHP WKDW FDQ EH UHGXFHG WR HDFK RWKHU LI WKHUH LV D SDWK EHWZHHQ WKHP 1DNDVXND DQG
PAGE 62

LV GRQH WKH V\VWHP LV UHDG\ WR PDNH VFKHGXOHV E\ PDWFKLQJ WKH VWDWH RI WKH V\VWHP WR RQH RI WKH UXOHV FUHDWHG DQG E\ XVLQJ WKH GLVSDWFKLQJ KHXULVWLF DW WKH OHDI QRGH WR FKRRVH WKH RSHUDWLRQ WR EH SHUIRUPHG 6KDZ 5DPDQ DQG 3DUN f GLVFXVV DGGLQJ D OHDUQLQJ FDSDELOLW\ WR D NQRZOHGJHEDVHG VFKHGXOLQJ V\VWHP 7KH DXWKRUV GLVFXVV KRZ UXOH LQGXFWLRQ FDQ EH XVHG LQ FRQMXQFWLRQ ZLWK GLVSDWFKLQJ UXOHV LH UXOH LQGXFWLRQ FDQ EH XVHG WR GHWHUPLQH WKH LPSRUWDQW DWWULEXWHV RI WKH V\VWHP DQG WKHQ WR FKRRVH WKH GLVSDWFKLQJ UXOH WR XVHf 7KLV LV FDOOHG 3DWWHUQ 'LUHFWHG 6FKHGXOLQJ 3'6f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f GHVFULEH D NQRZOHGJHEDVHG URERW VFKHGXOLQJ V\VWHP .QRZOHGJH LV QRW DFTXLUHG IURP D GRPDLQ H[SHUW EXW UDWKHU FUHDWHG XVLQJ VLPXODWLRQ H[SHULPHQWV 7KH DXWKRUV VLPXODWH WKH V\VWHP E\ XVLQJ GLVSDWFKLQJ UXOHV DQG WKHQ EDVHG RQ WKH VSHFLILHG SHUIRUPDQFH PHDVXUHV WKH\ GHFLGH RQ ZKLFK GLVSDWFKLQJ UXOH WR XVH JLYHQ WKH V\VWHP VWDWH ZKLFK LV GHILQHG E\ WKH URERW SRVLWLRQ QXPEHU RI HOHFWURSODWLQJ WDQNV HWF

PAGE 63


PAGE 64

EDVH 7KH UXOHV IRUPHG WKLV ZD\ SHUIRUP PXFK EHWWHU WKDQ WKH LGHQWLILHG KXPDQ VFKHGXOHUV
PAGE 65

6LQFH DOPRVW DOO RI WKH V\VWHPV SUHVHQWHG KHUH KDYH NQRZOHGJH EDVHV LW LV DOVR LPSRUWDQW WR GLVFULPLQDWH KRZ WKHLU NQRZOHGJH EDVH LV RUJDQL]HG 7KLV RIWHQ UHIOHFWV WKH SUREOHP VROYLQJ SKLORVRSK\ RI WKH V\VWHP )RU H[DPSOH ,6,6 XVHV D KLHUDUFKLFDO SUREOHP VROYLQJ DUFKLWHFWXUH KRSLQJ WKDW WKLV ZLOO UHGXFH WKH VL]H RI WKH VHDUFK VSDFH 6RPH RWKHUV IDFLOLWDWH D GLVWULEXWHG SUREOHP VROYLQJ DUFKLWHFWXUH 7KH 6WUXFWXUH FROXPQ FDSWXUHV WKLV LQIRUPDWLRQ 7KH DELOLW\ RI WKH V\VWHP WR OHDUQ LV PHQWLRQHG LQ WKH /HDUQLQJ FROXPQ ,I WKH V\VWHP KDV D OHDUQLQJ FDSDELOLW\ WKH QDWXUH RI WKH OHDUQLQJ DOJRULWKP XVHG LV OLVWHG )LQDOO\ WKH ([WHUQDO 0RGXOH FROXPQ WHOOV LI WKH V\VWHP LV LQWHUDFWLQJ ZLWK DQ\ RWKHU H[WHUQDO V\VWHPV 7KH LQWHUDFWLRQ PD\ EH LQ WKH IRUP RI IHHGLQJ LQIRUPDWLRQ WR DQ H[WHUQDO PRGXOH FRPPXQLFDWLQJ ZLWK D VLPXODWLRQ SURJUDP JHWWLQJ GDWD IURP D GDWD EDVH HWF 6RPH FROXPQV RI 7DEOH DUH DGDSWHG IURP .XVLDN DQG &KHQ f

PAGE 66

7DEOH .QRZOHGJH %DVHG 6\VWHPV

PAGE 67

7DEOH FRQWLQXHG $XWKRU 6\VWHPf .QRZOHGJH 5HSUHVHQWDWLRQ &RQWURO 6WUDWHJ\ $SSOLFDWLRQ 6WUXFWXUH /HDUQLQJ ([WHUQDO 0RGXOH %URZQ f &$036f 5XOHV DQG IUDPHV &RQVWUDLQW JXLGHG 6FKHGXOLQJ '%06 &KDQJ f 5XOHV )RUZDUG 6HDUFK -RE 6KRS 6FKHGXOLQJ 6LPXODWLRQ &K\UVVRORXULV HW DO f f 0$'(0$6 '$7$ &RPSRQHQWf 5XOHV 3URGXFWLRQ 6FKHGXOLQJ +LHUDUFKLFDO &K\UVVRORXULV /HH DQG 'RPURHVH f 1HXUDO 1HWV :RUNFHQWHU 6FKHGXOLQJ /HDUQLQJ E\ ([DPSOHV 6LPXODWLRQ 0$'(0$ &ODQF\ DQG 0RKDQ f 5%'f 5XOHV -RE DQG )ORZ 6KRS 'LVSDWFKLQJ &RQVLVWHQF\ FKHFNLQJ PRGXOH &RQZD\ DQG 0D[ZHOO f //,66f 3DUWO\ E\ KXPDQ VFKHGXOHU PHQX GULYHQ ,QWHUDFWLYH VFKHGXOLQJ &DUQHJLH *URXS &257(6f )UDPHV UXOHV DQG KHXULVWLFV 0LFURRSSRUWXQLVWLF FRQVWUDLQW JXLGHG VHDUFK 6FKHGXOLQJ 'LVWULEXWHG DQG +LHUDUFKLFDO 6LPXODWLRQ &]LJOHU DQG :KLWDNHU f 6+236f 3UHGLFDWHV +HXULVWLFV DQG LQIHUHQFH HQJLQH 'H f 3UHGLFDWHV 3ODQQLQJ ZLWK EDFNZDUG GHGXFWLRQ 6FKHGXOLQJ LQ D )06 7ZR SKDVHG 'H f )UDPHV &3$ DQG ILOWHUHG EHDP VHDUFK 6FKHGXOLQJ LQ D )06 7KUHH VHWV RI NQRZOHGJH

PAGE 68

7DEOH FRQWLQXHG $XWKRU 6\VWHPf .QRZOHGJH 5HSUHVHQWDWLRQ &RQWURO 6WUDWHJ\ $SSOLFDWLRQ 6WUXFWXUH /HDUQLQJ ([WHUQDO 0RGXOH (UVFKOHU DQG (VTXLURO f 0$6&27f 5XOHV 0HWDUXOHV DQG FRQVWUDLQW EDVHG DQDO\VLV -REVKRS VFKHGXOLQJ (UVFKOHU DQG 5RXEHOODW f 25$%$,'f 5XOHV &RQVWUDLQWEDVHG -RE 6KRS 6FKHGXOLQJ )DUKRRGL f 2&6f )UDPHV DQG UXOHV $OJRULWKPV KHXULVWLFV 6FKHGXOLQJ 0RGXODU )R[ f )UDPHV &RQVWUDLQW GLUHFWHG VHDUFK /DUJH VFDOH MRE VKRS VFKHGXOLQJ 7KUHH OHYHO KLHUDUFK\ )R[ DQG .HPSI f &RQVWUDLQW EDVHG DQDO\VLV 6FKHGXOLQJ 7ZR SKDVHG *UDQW f )UDPHV DQG UXOHV +HXULVWLF UXOHV 5HSDLU MRE VFKHGXOLQJ 7KUHH OHYHO KLHUDUFK\ &DUQHJLH *URXS ,6,6f &RQVWUDLQW JXLGHG VHDUFK 6FKHGXOLQJ &DUQHJLH *URXS ,6,6f &RQVWUDLQW JXLGHG VHDUFK 6FKHGXOLQJ +LHUDUFKLFDO &DUQHJLH *URXS ,6,6f &RQVWUDLQW JXLGHG VHDUFK 6FKHGXOLQJ +LHUDUFKLFDO PXOWLSHUVSHFWLY H -DLQ DQG 2VWHUIHOG f (66f )UDPHV %DFNZDUG VLPXODWLRQ 6FKHGXOLQJ ([SHUW 6\VWHP HPEHGGHG LQ 6LPXODWLRQ

PAGE 69

7DEOH FRQWLQXHG $XWKRU 6\VWHPf .QRZOHGJH 5HSUHVHQWDWLRQ &RQWURO 6WUDWHJ\ $SSOLFDWLRQ 6WUXFWXUH /HDUQLQJ ([WHUQDO 0RGXOH .DN HW DO f )UDPHV 6HQVRU\ EDVHG 5RERWLF $VVHPEO\ .HUU DQG (EVDU\ f 5XOHV )RUZDUG FKDLQLQJ 6FKHGXOLQJ DVVHPEO\ QHWZRUN 6L[ VHW RI UXOHV (PEHGGHG LQ D UHODWLRQDO '%06 /DPDWVFK HW DO f 6&+('8/(f 5XOHV DOJRULWKPV 3UREOHP PDWFKLQJ DQG UHGXFWLRQ -REVKRS VFKHGXOLQJ $UF ZHLJKWV RI WKH UHGXFWLRQ GLJUDSK LV XSGDWHG GLVFXVVLRQf 25 6FKHGXOLQJ $OJRULWKPV /DZUHQFH DQG 0RUWRQ f 3$75,$5&+f +HXULVWLFV +HXULVWLF SULRULWL]DWLRQ +LHUDUFKLFDO DQG GLVWULEXWHG /HFRFT DQG *XLRW f &5236f 5XOHV HPEHGGHG LQ +31 3ODQ JHQHUDWLRQ 6FKHGXOLQJ LQ D )06 7KUHH OHYHO KLHUDUFK\ 6LPXODWLRQ IRU YDOLGDWLRQ /HH DQG 6XK f 3$06f 5XOHV IUDPHV DQG KHXULVWLFV )RUZDUG FKDLQLQJ 3DUDOOHO PDFKLQH VFKHGXOLQJ +LHUDUFKLFDO '%06 /HH f 3UHGLFDWHV 3URGXFWLRQ 6FKHGXOLQJ 0DUWLQH] HW DO f 3HWULQHW DQG FRQVWUDLQHG KHXULVWLF VHDUFK 5HDOWLPH VFKHGXOLQJ DQG FRRUGLQDWLRQ )RXU OHYHO RI KLHUDUFK\ 6LPXODWLRQ

PAGE 70

7DEOH FRQWLQXHG $XWKRU 6\VWHPf .QRZOHGJH 5HSUHVHQWDWLRQ &RQWURO 6WUDWHJ\ $SSOLFDWLRQ 6WUXFWXUH /HDUQLQJ ([WHUQDO 0RGXOH 0D\ HWDO f 08/7(;f %DFNZDUG DQG IRUZDUG FKDLQLQJ 0HGLDWRU 6FKHGXOLQJ 25 &RPSRQHQWV +HXULVWLF SULFLQJ VXEV\VWHP 0RKDQ &ODQF\ f 6,6f 5XOHV +HXULVWLFV 'LVSDWFKLQJ RQ WKH VKRS IORRU 5HDOWLPH RQOLQH GDWD EDVH &20(76 0XOOHU 6DPEODFN[ DQG 0DWWK\V f 5XOHV 6FKHGXOLQJ LQ HOHFWURSODWLQJ LQGXVWU\ ([WUDFWLQJ NQRZOHGJH E\ XVH RI VLPXODWLRQ 1HZPDQ DQG .HPSI f 5XOHV 5RERW 6FKHGXOLQJ 5XOH EDVH LV GLYLGHG LQWR VL[ OHYHOV 1LHZ /LP DQG +R f +HXULVWLF UXOHV DQG IUDPHV &RQVWUDLQW GULYHQ JRDO VDWLVIDFWLRQ 0DVWHU VFKHGXOLQJ IRU ,&fV 2JUDG\ DQG /HH f 3/$72=f 5XOHV IODYRXUV SURFHGXUHV DQG GLVSDWFKLQJ UXOHV 0XOWLEODFNERDUGDFWRU PRGHO 3URGXFWLRQ FHOO FRQWURO 'HFHQWUDOL]HG 2n.HHIH f 5XOHV %DFNZDUG FKDLQLQJ 6LPXODWLRQ &RQVWUXFWLRQ &DUQHJLH *URXS 23,6f 2SSRUWXQLVWLF FRQVWUDLQW JXLGHG VHDUFK 6FKHGXOLQJ +LHUDUFKLFDO EODFNERDUG DUFKLWHFWXUH

PAGE 71

7DEOH f§FRQWLQXHG $XWKRU 6\VWHPf .QRZOHGJH 5HSUHVHQWDWLRQ &RQWURO 6WUDWHJ\ $SSOLFDWLRQ 6WUXFWXUH /HDUQLQJ ([WHUQDO 0RGXOH &DUQHJLH *URXS 23,6f 2SSRUWXQLVWLF FRQVWUDLQW JXLGHG VHDUFK 5HDFWLYH VFKHGXOLQJ 2Z 6PLWK DQG 7KULH] f &RQVWUDLQW GLUHFWHG VHDUFK DQG FRQIOLFW DQDO\VLV 6FKHGXOLQJ 6LPXODWLRQ IRU SHUIRUPDQFH HYDOXDWLRQ 2Z 6PLWK DQG +RZLH f &66f 7ZR SDVV EHVW ILUVW VHDUFK ZLWK ELGGLQJ 6FKHGXOLQJ 'LVWULEXWHG FRRSHUDWLYH 3DUXQDN f &RQVWUDLQW GLUHFWHG VHDUFK 'LVWULEXWHG PDQXIDFWXULQJ V\VWHP 'LVWULEXWHG $, V\VWHP 3LUDPXWKX HW DO f 5XOHV 3DWWHUQ GLUHFWHG VHDUFK )06 DQG IORZ V\VWHP VFKHGXOLQJ ,QGXFWLYH E\ ,' 6LPXODWLRQ 3RZQHU DQG :DOEXUQ f 5XOHV DQG IUDPHV 6FKHGXOLQJ LQ D )06 $HURVSDFHf $XWRPDWHG NQRZOHGJH DFTXLVLWLRQ 6XJJHVWHGf )06 6LPXODWLRQ 5DJKDYDQ f 5XOHV UHSUHVHQWHG DV GHFLVLRQ WDEOHV 'XH GDWH VFKHGXOLQJ LQ D )06 'LVFRYHULQJ UXOHV E\ REVHUYDWLRQ QRW DXWRPDWLF 6LPXODWLRQ 5HDG\ 6LPPRQGV DQG 7DXQWRQ f 35263(;f 5XOHV -REVKRS VFKHGXOLQJ VXSSRUW WRRO 6LPXODWLRQ 21 3r

PAGE 72

7DEOH FRQWLQXHG $XWKRU 6\VWHPf .QRZOHGJH 5HSUHVHQWDWLRQ &RQWURO 6WUDWHJ\ $SSOLFDWLRQ 6WUXFWXUH /HDUQLQJ ([WHUQDO 0RGXOH 5HLQVFKPLGW 6ODWH DQG )LQQ f 5XOHV /3 DQG LQIHUHQFH HQJLQH 6FKHGXOLQJ )RXU VHWV RI UXOHV /3 6DULQ DQG 6DOJDPH f )UDPHV DQG UXOHV %ODFNERDUG PHWD OHYHO NQRZOHGJH 6FKHGXOLQJ ,QGHSHQGHQW NQRZOHGJH VRXUFHV 6DYHOL 3HUH] DQG .RK f 5XOHV 6FKHGXOLQJ LQ D VHPL FRQGXFWRU SODQW 'LVWULEXWHG NQRZOHGJH EDVH IRU HDFK FHOO 6KDZ f 3UHGLFDWHV %LGGLQJ DQG SODQQLQJ *HQHUDO MREVKRS VFKHGXOLQJ 'LVWULEXWHG DQG KLHUDUFKLFDO 6LPXODWLRQ 6KDZ Ef 3UHGLFDWHV %LGGLQJ DQG SODQQLQJ 6FKHGXOLQJ LQ &,0 HQYLURQPHQW 'LVWULEXWHG DQG KLHUDUFKLFDO 6LPXODWLRQ IRU SHUIRUPDQFH HYDOXDWLRQ 6KDZ DQG :KLQVWRQ f 3UHGLFDWHV IUDPHV DQG UXOHV +HXULVWLFV DQG UXOHV *HQHUDO MREVKRS VFKHGXOLQJ SUREOHP +LHUDUFKLFDO SUREOHP VROYLQJ 6KDZ Ff 7UDQVIRUPDWLRQ RSHUDWLRQV 3DWWHUQ 'LUHFWHG )06 6FKHGXOLQJ 6KHQ DQG &KDQJ f )UDPHV DQG UXOHV *HQHUDO MREVKRS VFKHGXOLQJ $OJRULWKPV IRU GHWDLO VFKHGXOLQJ 6KHQ DQG &KDQJ f )UDPHV DQG UXOHV )06 6FKHGXOLQJ 6FKHGXOLQJ $OJRULWKPV 6WHIIHQ DQG *UHHQH Df 3UHGLFDWHV &RQVWUDLQW GLUHFWHG VHDUFK ZLWK EDFNWUDFNLQJ 3DUDOOHO SURFHVVRUV LQ D )06 )LYH OHYHO KLHUDUFK\

PAGE 73

7DEOH f§FRQWLQXHG $XWKRU 6\VWHPf .QRZOHGJH 5HSUHVHQWDWLRQ &RQWURO 6WUDWHJ\ $SSOLFDWLRQ 6WUXFWXUH /HDUQLQJ ([WHUQDO 0RGXOH 6WHIIHQ DQG *UHHQH Ef 3UHGLFDWHV +LHUDUFKLFDO SODQQLQJ DQG FRQVWUDLQW GLUHFWHG VHDUFK 6FKHGXOLQJ +LHUDUFKLFDO 6WHIIHQ DQG *UHHQH f +HXULVWLFV DQG FRQVWUDLQW GLUHFWHG VHDUFK 3DUDOOHO PDFKLQH VFKHGXOLQJ +LHUDUFKLFDO *8(66O 6XEUDPDQ\DP DQG $VNLQ f 5XOHV 5HDOWLPH MRE VKRS VFKHGXOLQJ 7KUHH OHYHO KLHUDUFK\ 6XOOLYDQ DQG )RUG\FH f /06''0f )XQFWLRQREMHFW )25.f 6HPLFRQGXFWRU )DEULFDWLRQ 6FKHGXOLQJ 7KHVHQ DQG /HL f 5XOHV 0HWDUXOHV 5RERW VFKHGXOLQJ (OHFWURSODWLQJ /LQH ,QGXFWLYH E\ VLPXODWLRQ 6LPXODWLRQ IRU SHUIRUPDQFH HYDOXDWLRQ :DUZLFN DQG :DOWHUV f 02336f 5XOHV 0HWDUXOHV :RUN FHOO VFKHGXOLQJ +LHUDUFKLFDO NQRZOHGJH EDVH :RUUDOO DQG 0DF'RQDOG f 'LVSDWFKLQJ UXOHV 6FKHGXOLQJ :RRGKHDG 'RERO\L DQG 3HQQLQJWRQ f 5XOHV 6HPDQWLF 1HWV 5HODWLRQDO '%06 4XHU\ /DQJXDJH 3URFHVV 3ODQQLQJ
PAGE 74

7DEOH FRQWLQXHG $XWKRU 6\VWHPf .QRZOHGJH 5HSUHVHQWDWLRQ &RQWURO 6WUDWHJ\ $SSOLFDWLRQ 6WUXFWXUH /HDUQLQJ ([WHUQDO 0RGXOH
PAGE 75

&+$37(5 /($51,1* $Q 2YHUYLHZ RI 0DFKLQH /HDUQLQJ /HDUQLQJ LV D YHU\ EURDG WHUP WKDW GHQRWHV WKH ZD\ LQ ZKLFK SHRSOH LQFUHDVH WKHLU NQRZOHGJH DQG VNLOOV 0DFKLQH /HDUQLQJ 0/f FRQFHQWUDWHV RQ JHQHUDWLQJ V\VWHPV WKDW FDQ OHDUQ DQG WKXV DFTXLUH QHZ GHFODUDWLYH NQRZOHGJH LPSURYH WKHLU SHUIRUPDQFHV IRU SUREOHP VROYLQJ WKURXJK LQVWUXFWLRQ RU SUDFWLFH DQG RUJDQL]H DQG JHQHUDOL]H QHZ NQRZOHGJH &DUERQHOO 0LHKDOVNL DQG 0LWFKHOO f )RU H[DPSOH WKH NQRZOHGJH EDVH UHTXLUHG E\ DQ H[SHUW V\VWHP FDQ EH JHQHUDWHG E\ XVLQJ OHDUQLQJ DOJRULWKPV DQG WKHQ UHILQHG E\ WKH OHDUQLQJ VXEV\VWHP VR WKDW WKH H[SHUW V\VWHP SHUIRUPV EHWWHU WKDQ WKH QR OHDP FDVH 5HVHDUFK RQ 0/ GDWHV EDFN WR WKH HDUO\ fV &RKHQ DQG )HLJHQEDXP f 0RVW RI WKH LGHDV XVHG WRGD\ ZHUH LQLWLDWHG GXULQJ WKH HDUOLHU \HDUV RI 0/ UHVHDUFK )RU H[DPSOH DGDSWLYH V\VWHPV GHSHQGLQJ RQ UDQGRP PXWDWLRQ DQG VHOHFWLRQ ZHUH FUHDWHG KRSLQJ WKDW WKHVH SURFHVVHV ZRXOG UHVXOW LQ LQWHOOLJHQW V\VWHPV 9DULRXV DQDORJV RI QHXURQV ZHUH GHYHORSHG DQG WHVWHG 'XULQJ WKH PLG fV DQG HDUO\ fV LW EHFDPH DSSDUHQW WKDW OHDUQLQJ ZDV D KDUG WDVN DQG WKDW LW ZDV YLUWXDOO\ LPSRVVLEOH WR OHDUQ ZLWKRXW DQ\ SULRU NQRZOHGJH RI WKH GRPDLQ RU PHWD NQRZOHGJH DERXW WKH WDVN 7KLV OHG WR UHVHDUFK FRQFHQWUDWHG RQ V\VWHPV WKDW XWLOL]HV V\PEROLF FRQFHSWDFTXLVLWLRQ &DUERQHOO 0LHKDOVNL DQG 0LWFKHOO f

PAGE 76

)LQDOO\ ZLWKLQ WKH ODVW GHFDGH 0/ UHVHDUFK FHQWHUHG DURXQG WKH WKHRU\ RI OHDUQLQJ DV ZHOO DV LWV DSSOLFDWLRQV WR VSHFLILF GRPDLQV (YHQ WKRXJK WKH WKHRUHWLFDO DSSURDFKHV FRQVLGHU WKH PRVW JHQHUDO IRUP RI WKH OHDUQLQJ SUREOHP PRVW RI WKH DSSOLHG 0/ UHVHDUFK IRFXVHV RQ SUREOHPV VSHFLILF WR WKH GRPDLQ IRU ZKLFK LW LV EHLQJ GHYHORSHG &DUERQHOO 0LFKDOVNL DQG 0LWFKHOO GHVFULEH WKH WUHQG WKDW VWDUWHG PLG f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` +HUEHUW 6LPRQ LQ SUHVVf GHILQHV OHDUQLQJ DV DQ\ SURFHVV E\ ZKLFK D V\VWHP LPSURYHV LWV SHUIRUPDQFH ^` $ PRUH FRQVWUDLQHG YLHZ RI OHDUQLQJ DGRSWHG E\ PDQ\ SHRSOH ZKR ZRUN RQ H[SHUW V\VWHPV LV WKDW OHDUQLQJ LV DFTXLVLWLRQ RI H[SOLFLW NQRZOHGJH ^` $ WKLUG YLHZ LV WKDW OHDUQLQJ LV VNLOO DFTXLVLWLRQ f D IRUWK YLHZ RI OHDUQLQJ LV WKDW LW LV WKHRU\ IRUPDWLRQ K\SRWKHVLV IRUPDWLRQ DQG LQGXFWLYH LQIHUHQFH &RKHQ DQG )HLJHQEDXP SS f 0RVW $ DSSOLFDWLRQV UHJDUGOHVV RI ZKHWKHU WKH\ DUH OHDUQLQJ DSSOLFDWLRQV RU QRW LPSOLFLWO\ FRQVLGHU ^` 7KH GLVWLQFWLRQ DULVHV EDVHG RQ ZKHWKHU WKH V\VWHP GRHV LW LWVHOI RU LW LV KDUGFRGHG

PAGE 77

7KH DFTXLVLWLRQ RI H[SOLFLW NQRZOHGJH LV WKH PDLQ IRFXV RI (6 DSSOLFDWLRQV (YHQ WKRXJK (6V DUH QRW OHDUQLQJ V\VWHPV WKHPVHOYHV WKH SUREOHP RI NQRZOHGJH DFTXLVLWLRQ LQLWLDWHG D VXEVWDQWLDO DPRXQW RI UHVHDUFK RQ LVVXHV DERXW OHDUQLQJ ,W LV XVHIXO WR FRQVLGHU WKH HYROXWLRQ RI DSSURDFKHV WR NQRZOHGJH DFTXLVLWLRQ VLQFH ZH EHOLHYH LW GHPRQVWUDWHV LQ ZKLFK GLUHFWLRQ 0/ UHVHDUFK LV JRLQJ ,W LV QRW DQ H[DJJHUDWLRQ WR VD\ WKDW (6V HQMR\HG VXFFHVV LQ GRPDLQV ZKHUH H[SHUWLVH H[LVWHG DQG ZKHUH NQRZOHGJH GLG QRW EHFRPH REVROHWH LQ WLPH 7KLV LV H[DFWO\ RQH RI WKH UHDVRQV ZK\ (6V ZHUH QRW VXFFHVVIXO LQ WKH VFKHGXOLQJ GRPDLQ 7KH VFKHGXOLQJ GRPDLQ LV VR FRPSOH[ DQG G\QDPLF WKDW LW LV DOPRVW LPSRVVLEOH IRU KXPDQV WR XQGHUVWDQG WKH H[LVWLQJ FDXVDO UHODWLRQVKLSV +RZHYHU HOLFLWLQJ H[SHUW NQRZOHGJH LV WKH ERWWOHQHFN RI (6 GHYHORSPHQW &RKHQ DQG )HLJHQEDXP f LQGHHG LQ DQ\ NQRZOHGJH LQWHQVLYH V\VWHPV $IWHU UHDOL]LQJ WKLV WKH WUHQG LQ NQRZOHGJH DFTXLVLWLRQ VKLIWHG IURP FODVVLFDO WHFKQLTXHV OLNH SURWRFRO DQDO\VLV RU LQWHUYLHZV WR LQWHUDFWLYH WHFKQLTXHV ZKHUH WKH NQRZOHGJH DFTXLVLWLRQ WDVN ZDV JLYHQ WR WKH OHDUQLQJ V\VWHP 7KH OHDUQLQJ V\VWHP JXLGHG LWV VHDUFK IRU FRQFHSW IRUPDWLRQ E\ DVNLQJ TXHVWLRQV WR WKH H[SHUW DQG WKHQ UHILQLQJ LWV FXUUHQW K\SRWKHVLV EDVHG RQ WKH DQVZHU JLYHQ E\ WKH H[SHUW 2QH VXFK V\VWHP LV 7(,5(6,$6 E\ 'DYLV f ZKLFK LV XVHG IRU PHGLFDO GLDJQRVLV 'XULQJ WKH FRXUVH RI GHYHORSPHQW RI (6V UHVHDUFKHUV UHDOL]HG WR WKHLU GLVPD\ WKDW IRU VRPH GRPDLQV HYHQ LQWHUDFWLYH V\VWHPV SURYHG LQIHDVLEOH 7KHUH ZHUH QR H[SHUWV RU WKH H[SHUWV ZHUH QRW DEOH WR GHGLFDWH WLPH WR WKH NQRZOHGJH DFTXLVLWLRQ SURFHVV 7KLV OHG WR UHVHDUFK LQ OHDUQLQJ V\VWHPV ZKHUH WKH V\VWHP LWVHOI FDQ OHDUQ ZLWKRXW WKH H[SHUWfV

PAGE 78

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f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

PAGE 79

DVVXPLQJ WKDW LV WKH FDVHf DQG WULHV WR FDOFXODWH WKH SULFH LI SUHVHQWHG D \HOORZ FRORUHG FDU HYHQ LI LW KDV LQIRUPDWLRQ DERXW D UHG FRORUHG FDU RI WKH VDPH W\SH &RKHQ DQG )HLJHQEDXP H[SODLQ OHDUQLQJ E\ EHLQJ WROG RU DGYLFH WDNLQJ DV IROORZV /HDUQLQJ E\ EHLQJ WROG LQ ZKLFK WKH LQIRUPDWLRQ SURYLGHG E\ WKH HQYLURQPHQW LV WRR DEVWUDFW RU JHQHUDO DQG WKXV WKH OHDUQLQJ HOHPHQW PXVW K\SRWKHVL]H WKH PLVVLQJ GHWDLOV &RKHQ DQG )HLJHQEDXP f SS 7KH V\VWHP VKRXOG KDYH WKH NQRZOHGJH WR EH DEOH WR LQWHUSUHW KLJK OHYHO LQIRUPDWLRQ PDNH LW RSHUDWLRQDO IRU LWVHOI DQG WKHQ LQWHJUDWH LW WR WKH NQRZOHGJH EDVH &RKHQ DQG )HLJHQEDXP f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f GHVFULEH OHDUQLQJ E\ DQDORJ\ DV IROORZV /HDUQLQJ E\ DQDORJ\ LQ ZKLFK WKH LQIRUPDWLRQ SURYLGHG E\ WKH HQYLURQPHQW LV UHOHYDQW RQO\ WR DQ DQDORJRXV SHUIRUPDQFH WDVN DQG WKXV WKH OHDUQLQJ V\VWHP PXVW GLVFRYHU WKH DQDORJ\ DQG K\SRWKHVL]H DQDORJRXV UXOHV IRU LWV SUHVHQW SHUIRUPDQFH WDVN &RKHQ DQG )HLJHQEDXP S f $0 LV D OHDUQLQJ V\VWHP WKDW GLVFRYHUV FRQFHSWV LQ PDWKHPDWLF DQG VHW WKHRU\ 'XULQJ LWV VHDUFK $0 XVHV UHDVRQLQJ E\ YLHZV RU E\ DQDORJ\ ZKLFK LV RQH RI LWV WKLUW\ KHXULVWLF UXOHV &RKHQ DQG )HLJHQEDXP f 7KH $1$/2*< VORW RI WKH FRQFHSW IUDPH

PAGE 80

JLYHV YDJXH LQIRUPDWLRQ DERXW KRZ D SDUWLFXODU LQVWDQFH LV DQ LQVWDQFH RI DQRWKHU FRQFHSW $0 WULHV WR XWLOL]H WKLV LQIRUPDWLRQ WRJHWKHU ZLWK WKH LQIRUPDWLRQ VXSSOLHG LQ WKH 9,(:6 VORW WR PDS H[LVWLQJ H[DPSOHV LQWR H[DPSOHV RI WKH FRQFHSW XQGHU FRQVWUXFWLRQ &RKHQ DQG )HLJHQEDXP f 3HUKDSV WKH PRVW H[WHQVLYHO\ DQDO\]HG OHDUQLQJ VWUDWHJ\ LV OHDUQLQJ IURP H[DPSOHV 7KHUH DUH YHU\ GLIIHUHQW DSSURDFKHV WR OHDUQLQJ IURP H[DPSOHV VXFK DV OHDUQLQJ E\ LQGXFWLRQ H[SODQDWLRQ EDVHG JHQHUDOL]DWLRQ 1HXUDO 1HWZRUNV 11Vf DQG *HQHWLF $OJRULWKP *$f EDVHG OHDUQLQJ V\VWHPV :H ZLOO IRFXV RQ LQGXFWLRQ DQG OHDUQLQJ IURP H[DPSOHV LQ WKLV VHFWLRQ DQG RQO\ EULHIO\ PHQWLRQ QHXUDO QHWZRUNV 7KH *$ EDVHG V\VWHPV ZLOO EH FRYHUHG LQ &KDSWHU ,QGXFWLYH OHDUQLQJ LV D GDWD LQWHQVLYH DSSURDFK 4XLQODQ f ZKHUH WKH OHDUQLQJ WDVN LV WR JHQHUDWH D NQRZOHGJH EDVH DIWHU VHHLQJ D VHW RI H[DPSOHV $Q H[DPSOH LV DQ QDU\ WXSOH UHSUHVHQWLQJ Q DWWULEXWHV RI WKH REMHFW RI LQWHUHVW DQG LWV FODVV 7KH UHVXOWLQJ NQRZOHGJH EDVH VKRXOG FODVVLI\ DOO RI WKH WUDLQLQJ H[DPSOHV FRUUHFWO\ 0RVW RI WKH OHDUQLQJ V\VWHPV VXFK DV &/6 ,' $&/6 $66,67$17 XVH GHFLVLRQ WUHHV IRU NQRZOHGJH UHSUHVHQWDWLRQ DQG RWKHUV OLNH $45 &1 WU\ WR OHDUQ SURGXFWLRQ UXOHV &ODUN DQG 1LEOHWW f $ PRUH JHQHUDO NQRZOHGJH UHSUHVHQWDWLRQ LV GHFLVLRQ OLVWV 5LYHVW f 2PLWWLQJ WKH WHFKQLFDO GHWDLOV D GHFLVLRQ WUHH FRQVWUXFWLRQ DOJRULWKP FDQ EH VWDWHG DV IROORZV ,I DOO WKH LQVWDQFHV DUH IURP H[DFWO\ RQH FODVV WKHQ WKH FXUUHQW QRGH LV WKH DQVZHU QRGH FODVVLI\LQJ DOO WKH H[DPSOHV 2WKHUZLVH

PAGE 81

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

PAGE 82

6LQFH WKH PHWKRG LV GDWD GULYHQ WKH UHVXOWLQJ WUHH FDQ EH YHU\ GLIIHUHQW IRU GLIIHUHQW GDWD VHWV $OVR WKH WUHHV JHQHUDWHG ZLWK WKH VDPH H[DPSOH VHW PD\ GLIIHU GHSHQGLQJ RQ WKH PHWKRG XVHG WR FKRRVH DWWULEXWHV RQ ZKLFK WR VSOLW (YHQ WKRXJK WKH DFFXUDF\ RI WKH WUHH LV QRW VHQVLWLYH WR WKH VSOLW FULWHULD XVHG WKH GHSWK RI WKH WUHH LV YHU\ VHQVLWLYH WR WKLV PHDVXUH 0LQJHUV Df ,Q QRLV\ GRPDLQV ZKHUH WKHUH LV D ORW RI PHDVXUHPHQW HUURUV SUXQLQJ WKH GHFLVLRQ WUHH RIWHQ LPSURYHV WKH DFFXUDF\ RI WKH WUHH $JDLQ WKH VKDSH RI WKH WUHH DIWHU SUXQLQJ GHSHQGV RQ WKH SUXQLQJ PHWKRG DQG WKHUH LV QR NQRZQ RSWLPDO ZD\ RI SUXQLQJ 0LQJHUV Ef 'HFLVLRQ WUHHV KDYH EHHQ DSSOLHG WR GRPDLQV OLNH PHGLFLQH DJULFXOWXUH EDQNLQJ SURGXFWLRQ HWF 6SHFLILF DSSOLFDWLRQV FDQ EH IRXQG LQ 0HVVLHU DQG +DQVHQ f %UDXQ DQG &KDQGOHU f &DUWHU DQG &RWOHWW f DQG 3LUDPXWKX HW DO f ([SODQDWLRQ %DVHG /HDUQLQJ (%/fRU ([SODQDWLRQ %DVHG *HQHUDOL]DWLRQ (%*ff§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

PAGE 83

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

PAGE 84

/RJLF 7KHRULVW 2fURUNH f LV D V\VWHP WKDW XVHV (%/ PHWKRGV (%/ LV DOVR XVHG LQ QDWXUDO ODQJXDJH XQGHUVWDQGLQJ 'HMRQJ DQG 0RRQH\ f FRQFHSW GLVFRYHU\ DQG OHDUQLQJ VLPSOH WDVNV 0LWFKHOO .HOOHU DQG .HGDU&DEHOOL f 5HVHDUFK RQ (%/ IRFXVHV RQ DOWHUQDWH VWUDWHJLHV WR LPSURYH WKH HIILFLHQF\ RI OHDUQLQJ )ODQQ 'LHWWHULFK f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fV DQG ZDV ILUVW DQDO\]HG E\ :DUUHQ 0F&XOORFK DQG :DOWHU 3LWWV +HFKW1LHOVHQ f $IWHU DQ LQWHUUXSWLRQ IRU DERXW WHQ \HDUV UHVHDUFK LQ WKLV DUHD FRQFHQWUDWHG RQ QHWZRUN DUFKLWHFWXUHV DQG OHDUQLQJ DOJRULWKPV IRU 11V 7KH JHQHUDO PRGHO RI 11V KDV RI SURFHVVLQJ HOHPHQWV QRGHVf FRQQHFWLRQV DUFVf EHWZHHQ QRGHV DQG LQSXW DQG RXWSXW FRQQHFWLRQV (DFK QRGH KDV D WUDQVIHU IXQFWLRQ DQG D ORFDO PHPRU\ WKDW FRQVLVWV RI ZHLJKWV DQG QHFHVVDU\ YDULDEOHV 0RVW 11V KDYH DW OHDVW WKUHH OD\HUV DQ LQSXW OD\HU DQ RXWSXW OD\HU DQG D SURFHVVLQJ OD\HU 7KH QRGHV LQ WKH LQSXW DQG RXWSXW OD\HUV GR QRW SURFHVV WKH VLJQDOV 7KH\ VLPSO\ WUDQVPLW LW 7KH WUDQVIHU IXQFWLRQ FDQ JLYH RXWSXW WKDW FDQ HIIHFW ERWK WKH ORFDO PHPRU\ DQG WKH QRGHVf RXWSXW VLJQDO 2Q UHFHLYLQJ DQ LQSXW IURP DQ LQSXW FRQQHFWLRQ WKH WUDQVIHU IXQFWLRQ LV DFWLYDWHG

PAGE 85

ZKLFK WKHQ PD\ DFWLYDWH WKH QRGHV RXWSXW FRQQHFWLRQf§WKH QRGH ILUHV ,Q WKLV PDQQHU DQ LQSXW VLJQDO LV WUDQVIHUUHG WR WKH RXWSXW /HDUQLQJ LQ 11V LV DFFRPSOLVKHG E\ WUDLQLQJ 7UDLQLQJ FDQ EH LQ VXSHUYLVHG RU JUDGHG PRGH RU WKH QHWZRUN FDQ EH VHOI RUJDQL]LQJ +HFKW1LHOVHQ f :H ZLOO IRFXV RQ WKH ILUVW WZR PRGHV ,Q VXSHUYLVHG WUDLQLQJ D QHWZRUN LV JLYHQ D VHW RI H[DPSOHV FRQVLVWLQJ RI WKH SDLU [N\Nf ZKHUH \N LV WKH WUXH IXQFWLRQ YDOXH ,Q JUDGHG PRGH WKH QHWZRUN UHFHLYHV D JUDGH RI KRZ ZHOO LW KDV GRQH RQ HDFK H[DPSOH ,Q ERWK FDVHV HDFK QRGH LV H[SHFWHG WR XSGDWH LWV ORFDO PHPRU\ DQG WR DGMXVW LWV ZHLJKW YHFWRU ZLWK UHVSHFW WR WKH IHHGEDFN VR DV WR EH DEOH WR GLVFRYHU WKH WUXH IXQFWLRQ 11V KDYH VXFFHVVIXOO\ EHHQ DSSOLHG WR SDWWHUQ UHFRJQLWLRQ VXFK DV FKDUDFWHU UHFRJQLWLRQ DQG PDQ\ RWKHU GRPDLQV UDQJLQJ IRUP FUHGLW DSSURYDO WR LPDJH FRPSUHVVLRQ +HFKW1LHOVHQ f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

PAGE 86

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fV $0 DQG (85,6.2 V\VWHPV /HQDW f &DUERQHOO 0LFKDOVNL DQG 0LWFKHOO S f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

PAGE 87

WKHUH DUH GRPDLQV ZKHUH GHYHORSLQJ D OHDUQLQJ V\VWHP LV LPSRVVLEOH 'XULQJ WKH ODVW GHFDGH WKHUH KDV EHHQ DQ HQRUPRXV DPRXQW RI UHVHDUFK RQ WKH OHDUQDELOLW\ RI FHUWDLQ FRQFHSWV RQ WKH FRPSOH[LW\ RI OHDUQLQJ DQG RQ FKDUDFWHUL]LQJ WKH OHDUQLQJ WDVN HVSHFLDOO\ DIWHU WKH SLRQHHULQJ ZRUN RI 9DOLDQW f 5HVHDUFK KDV VKRZQ WKDW VRPH FRQFHSWV DUH OHDPDEOH E\ DW OHDVW RQH OHDUQLQJ DOJRULWKP DQG VRPH DUH QRW OHDUQDEOH LQ SRO\QRPLDO WLPH RU UHTXLUH DQ H[SRQHQWLDOO\ ODUJH VHW RI H[DPSOHV :H VWDUW RXU GLVFXVVLRQ RI WKHVH UHVXOWV ZLWK VRPH GHILQLWLRQV DQG QRWDWLRQ 9DOLDQW SURSRVHG WKH LGHD RI OHDUQLQJ D FRQFHSW ZLWK ORZ HUURU DQG GRLQJ WKLV ZLWK KLJK SUREDELOLW\ LQVWHDG RI OHDUQLQJ D FRQFHSW ZLWK FRPSOHWH DFFXUDF\ /DWHU WKLV ZDV UHIHUUHG WR DV 3UREDEO\ $SSUR[LPDWHO\ &RUUHFW 3$&fOHDUQLQJ +DXVVOHU f $ OHDUQLQJ DOJRULWKP FDOOV D URXWLQH QDPHG (;$03/(6 ZKLFK VHOHFWV H[DPSOHV ZLWK UHVSHFW WR D SUREDELOLW\ GLVWULEXWLRQ 3 DQG ODEHOV WKHP FRUUHFWO\ SRVVLEO\ E\ WKH KHOS RI DQ 25$&/( 7KH HUURU EHWZHHQ WKH K\SRWKHVL]HG FRQFHSW DQG D WDUJHW FRQFHSW LV GHILQHG DV WKH V\PPHWULF GLIIHUHQFH EHWZHHQ WZR FRQFHSWV $ OHDUQLQJ DOJRULWKP WULHV WR JHQHUDWH D FRQFHSW J VXFK WKDW WKH SUREDELOLW\ WKDW WKH HUURU EHWZHHQ J DQG WKH WDUJHW FRQFHSW I LV OHVV WKDQ H LH 3I$Jfe! ZKHUH $ LV WKH V\PPHWULF GLIIHUHQFH EHWZHHQ J DQG I $ 3$&OHDUQLQJ DOJRULWKP FDQ IRUPDOO\ EH GHILQHG DV IROORZV 1DWDUDMDQ f $Q DOJRULWKP $ LV D 3$& OHDUQLQJ DOJRULWKP IRU D FODVV RI FRQFHSWV ) LI D $ WDNHV LQSXWV H H @ f @ DQG Q H 1 ZKHUH H DQG DUH WKH HUURU DQG FRQILGHQFH SDUDPHWHUV UHVSHFWLYHO\ DQG Q LV WKH OHQJWK SDUDPHWHU E $ PD\ FDOO (;$03/( ZKLFK UHWXUQV H[DPSOHV IRU VRPH I H ) 7KH H[DPSOHV DUH FKRVHQ UDQGRPO\ DFFRUGLQJ WR 3

PAGE 88

;, F )RU DOO FRQFHSWV I H ) DQG DOO SUREDELOLW\ GLVWULEXWLRQV 3 $ RXWSXWV D FRQFHSW JH ) VXFK WKDW ZLWK SUREDELOLW\ DW OHDVW f 3I$Jf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f GLVFXVVHV WKH FODVVHV RI OHDUQDEOH FRQFHSWV +H VKRZV WKDW FHUWDLQ FODVVHV RI ERROHDQ FRQFHSWV OLNH N&1) FRQFHSWV PRQRWRQH '1) FRQFHSWV RU DUELWUDU\ FRQFHSWV ZLWK D YDULDEOH DSSHDULQJ RQO\ RQFH DUH OHDUQDEOH %XW KLV ILQGLQJV DUH QRW JHQHUDOL]DEOH WR OHVV UHVWULFWLYH DUELWUDU\ GRPDLQV +DXVVOHU ;;f ;f JLYHV ERXQGV RQ WKH VDPSOH FRPSOH[LW\ RI LQGXFWLYH OHDUQLQJ ZKLFK LV GHILQHG DV WKH QXPEHU RI H[DPSOHV QHFHVVDU\ WR 3$&OHDUQ D FRQFHSW

PAGE 89

+H DOVR JLYHV WKH QHFHVVDU\ FRQGLWLRQV IRU D FODVV RI FRQFHSWV WR EH OHDUQDEOH ZLWK SRO\QRPLDO VDPSOH FRPSOH[LW\ +H UHSRUWV WKDW DOO SXUH FRQMXQFWLYH GLVMXQFWLYH DQG LQWHUQDO GLVMXQFWLYH FRQFHSWV DUH 3$&OHDUQDEOH N&1) DQG N'1) FRQFHSWV DUH DOVR 3$&OHDUQDEOH ZLWK WKH H[FHSWLRQ WKDW ZKHQ N LV ODUJH FRPSXWDWLRQDO HIILFLHQF\ LV QRW JXDUDQWHHG $QJOXLQ DQG /LDUG f GHPRQVWUDWH WKH 3$&LGHQWLILDELOLW\ RI &1)NQf FRQFHSWV LQ QRLV\ GRPDLQV JLYHQ WKDW WKH QRLVH UDWH LV ERXQGHG DERYH E\ e ZKHUH 0 H &1)NQf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f VXJJHVW VXFK D VFHQDULR ZKHUH WKH V\VWHP WULHV WR OHDUQ PXOWLSOH FRQFHSWV LQGXFWLYHO\ ZKHQ WKHUH LV RQO\ SDUWLDO LQIRUPDWLRQ DERXW WKH ODEHOV RI WKH H[DPSOHV 7KH\ UHIHU WR WKLV DV VHPLVXSHUYLVHG OHDUQLQJ 7KH OHDUQLQJ HOHPHQW LV WUDLQHG ZLWK H[DPSOH SDLUV DQG WKH ODEHOLQJ WHOOV LI WKH\ EHORQJ WR WKH VDPH FODVV RU QRW 7KH DXWKRUV VKRZ WKDW PRVW FODVVHV WKDW DUH 3$&OHDPDEOH VXFK DV N&1) DQG N'1) DUH DOVR VHPLVXSHUYLVHG OHDUQDEOH

PAGE 90

0RVW RI WKH ZRUN GRQH LQ WKLV DUHD LV RI RQO\ WKHRUHWLFDO LQWHUHVW DQG PRVW RI WKH ERXQGV RQ VDPSOH FRPSOH[LW\ DUH ORRVH ERXQGV ZLWK OLWWOH SUDFWLFDO YDOXH ,Q SUDFWLFH PRVW RI WKH DOJRULWKPV GHYHORSHG IRU OHDUQDEOH FODVVHV SHUIRUP PXFK EHWWHU %XW VWLOO WKHUH DUH D IHZ RSHQ LVVXHV PRVW RI WKH DXWKRUV PHQWLRQ 9DOLDQW f +DXVVOHU f 0RVW RI WKH DOJRULWKPV DVVXPH WKDW WKHUH LV QHLWKHU FODVVLILFDWLRQ QRU PHDVXUHPHQW HUURUV RQ WKH H[DPSOHV 7KH FRQFHSWV ZKHUH 3$&OHDUQDELOLW\ LV SURYHQ DUH YHU\ UHVWULFWLYH GRPDLQV ,W LV DVVXPHG WKDW WKH DWWULEXWHV FRQVLGHUHG IRU GHVFULELQJ WKH GRPDLQ WKH LQGXFWLYH ELDV DUH HQRXJK IRU OHDUQLQJ 7KDW LV ZH DVVXPH WKHUH LV QR HUURU GXH WR RPLWWLQJ FHUWDLQ XVHIXO DWWULEXWHV ,W LV FOHDU WKDW PDQ\ GRPDLQV GR QRW KDYH WKHVH QLFH SURSHUWLHV ,Q WKH IROORZLQJ VHFWLRQ ZH ZLOO GLVFXVV WKH SURMHFWLRQ RI WKHVH LVVXHV GLVFXVVHG KHUH RQWR WKH VFKHGXOLQJ GRPDLQ 6FKHGXOLQJ DV D 0DFKLQH /HDUQLQJ 3UREOHP ,Q &KDSWHU ZH FKDUDFWHUL]HG WKH VFKHGXOLQJ SUREOHP DQG LWV GRPDLQ VWUXFWXUH )URP D 0/ SHUVSHFWLYH ZKDW FRQFHSWV QHHG WR EH OHDUQHG LQ WKLV GRPDLQ" +RZ FRXOG ZH FKDUDFWHUL]H WKH WDUJHW FRQFHSW" :KDW DUH WKH UHOHYDQW DWWULEXWHV RI WKH GRPDLQ DQG WKH FRQFHSW" /RRNLQJ DW WKH IRXU GLPHQVLRQV RI 0/ ZKLFK FKRLFHV DUH VXLWDEOH IRU OHDUQLQJ LQ WKH VFKHGXOLQJ GRPDLQ" %HIRUH ZH DQVZHU WKHVH TXHVWLRQV OHW XV EULHIO\ UHFDOO DVSHFWV RI WKH VFKHGXOLQJ GRPDLQ 7KH VKRS IORRU LV D KLJKO\ G\QDPLF HQWLW\ ZKHUH WKH FRQGLWLRQV DQG SHUIRUPDQFH FULWHULD FKDQJH IUHTXHQWO\ DQG WKHUH LV KLJK XQFHUWDLQW\ 7KH QXPEHU RI

PAGE 91

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f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

PAGE 92

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fV FRPSHWLWLYH PDQXIDFWXULQJ HQYLURQPHQW WKH PDQXIDFWXUHUV DUH DEOH WR FRPSHWH E\ LQWURGXFLQJ QHZ SURGXFWV 7KLV LQ UHWXUQ FKDQJHV WKHLU SURFHVVHV DQG VFKHGXOLQJ FKDUDFWHULVWLFV :H EHOLHYH WKDW D V\VWHP ZLOO QHHG D PHWKRG WKDW LV VXLWDEOH IRU ZRUNLQJ ZLWK LPSHUIHFW LQIRUPDWLRQ DQG WKDW FDQ FRQGXFW DQ HIILFLHQW VHDUFK

PAGE 93

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f 7KHVHQ DQG /HL f DQG
PAGE 94

$ VXUYH\ RI *$V DQG FODVVLILHU V\VWHPV ZLOO EH SUHVHQWHG LQ WKH QH[W FKDSWHU :H ZLOO DOVR GLVFXVV KRZ WKH\ FDQ EH XVHG DV OHDUQLQJ DOJRULWKPV IRU UXOH GLVFRYHU\ DQG UXOH UHILQHPHQW $OO RI WKH SDSHUV IRFXVLQJ RQ 0/ DSSOLFDWLRQV LQ VFKHGXOLQJ PDNH VLPSOLI\LQJ DVVXPSWLRQV ZKLFK OLPLWV WKHLU JHQHUDOL]DELOLW\ 1HYHUWKHOHVV WKHLU UHVXOWV KDYH EHHQ PRVW HQFRXUDJLQJ ,Q 7DEOH ZH VXPPDUL]H PDFKLQH OHDUQLQJ LQ VFKHGXOLQJ ZLWK UHVSHFW WR RXU IRXU GLPHQVLRQDO IUDPHZRUN

PAGE 95

7DEOH 6FKHGXOLQJ 5HVHDUFK IURP DQ 0/ 3HUVSHFWLYH $87+25 '(),1,7,21 0(7+2'2/2*< 1$785( 02'( %OHVVLQJ DQG :DWIRUG f 3HUIRUPDQFH ,PSURYHPHQW 5RWH /HDUQLQJ ,QFUHPHQWDO 6HPLVXSHUYLVHG &KU\VVRORXULV /HH DQG 'RPURHVH f /HDUQLQJ IURP ([DPSOHV ,QFUHPHQWDO +LOOLDUG DQG 5DQJDUDMDQ f ([SOLFLW .QRZOHGJH $FTXLVLWLRQ /HDUQLQJ IURP ([DPSOHV ,QFUHPHQWDO 6HPLVXSHUYLVHG ,, .RWRQ f 3HUIRUPDQFH ,PSURYHPHQW /HDUQLQJ IURP ([DPSOHV ,QFUHPHQWDO 6HPLVXSHUYLVHG /DPDWVFK HW DO f 3HUIRUPDQFH ,PSURYHPHQW /HDUQLQJ IURP ([DPSOHV $GDSWLYH 6XSHUYLVHG 1DNDVXND DQG
PAGE 96

&+$37(5 *(1(7,& $/*25,7+06 $1' &/$66,),(5 6<67(06 2YHUYLHZ RI *HQHWLF $OJRULWKPV *HQHWLF $OJRULWKPV *$Vf ILUVW VWXGLHG E\ +ROODQG DUH JHQHUDO SXUSRVH VHDUFK DOJRULWKPV EDVHG RQ DQ DQDORJ\ WR QDWXUDO VHOHFWLRQ RU VXUYLYDO RI WKH ILWWHVW *ROGEHUJ f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f &RPSDUHG WR RWKHU RSWLPL]DWLRQ WHFKQLTXHV *$V KDYH OHVV UHVWULFWLYH DVVXPSWLRQV 7KH EDVLF GLIIHUHQFHV FDQ EH VXPPDUL]HG DV IROORZV (*$V ZRUN ZLWK D FRGLQJ RI WKH SDUDPHWHU VHW QRW WKH SDUDPHWHUV WKHPVHOYHV *$V VHDUFK IURP D SRSXODWLRQ RI SRLQWV QRW D VLQJOH SRLQW *$V XVH SD\RII REMHFWLYH IXQFWLRQf LQIRUPDWLRQ QRW GHULYDWLYHV RU RWKHU DX[LOLDU\ NQRZOHGJH *$V XVH SUREDELOLVWLF WUDQVLWLRQ UXOHV QRW GHWHUPLQLVWLF UXOHV *ROGEHUJ D S f

PAGE 97

*$V DUH DOVR LQKHUHQWO\ SDUDOOHO DOJRULWKPV 8VXDOO\ WKH VWULQJV DUH GHILQHG RQ WKH ELQDU\ ^` DOSKDEHW )RU D SUREOHP WKDW XVHV VWULQJV RI OHQJWK \ IURP ELW WR ELW \f WKH SRVVLEOH QXPEHU RI VROXWLRQV WR FRQVLGHU LV \
PAGE 98

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f SRSXODWLRQ VL]H Qf FURVVRYHU SUREDELOLW\ [f PXWDWLRQ SUREDELOLW\ Sf D IXQFWLRQ If I[f IRU DOO [f WR EH RSWLPL]HG DQG D VWRSSLQJ FULWHULD 6HW W DQG JHQHUDWH DQ LQLWLDO SRSXODWLRQ 3 RI VL]H Q :KLOH WKH VWRSSLQJ FULWHULD LV QRW VDWLVILHG ^ )LQG WKH ILWQHVV ILf RI HDFK VWULQJ L LQ 3W /HW (IL! :KLOH DOO WKH HOHPHQWV RI QH[W JHQHUDWLRQ 3O, DUH QRW FUHDWHG ^ 6HOHFW SDUHQWV 6 DQG 6 EDVHG RQ Sf /HW 8 8f ZKHUH 8f LV D XQLIRUP SUREDELOLW\ GLVWULEXWLRQ ,I 8 [ FURVVRYHU 6 DQG 6 SXW WKH RIIVSULQJ 6? 6f LQ 3W

PAGE 99

HOVH FDUU\ 6 DQG 6 WR WKH QH[W JHQHUDWLRQ 6HOHFW WKH FKLOGUHQ 6f DQG 6f )RU L WR \f ^ LI 8 8f S IOLS WKH LK ELW ` ` 6HW W W ` 7KH UHVXOWLQJ SRSXODWLRQ LV WKH VROXWLRQ 'XH WR WKHLU VWRFKDVWLF QDWXUH *$V GR QRW JXDUDQWHH DQ RSWLPDO VROXWLRQ DW WKHLU WHUPLQDWLRQ +RZHYHU HPSLULFDO H[SHULHQFH KDV VKRZQ WKDW WKH\ FRQYHUJH WR JRRG TXDOLW\ QHDU RSWLPDO VROXWLRQV YHU\ TXLFNO\ ,Q WKH QH[W VHFWLRQ ZH ZLOO H[SODLQ WKLV EHKDYLRU RI *$V 7KH )XQGDPHQWDO 7KHRU\ RI *$V DQG ,PSOLFLW 3DUDOOHOLVP 6FKHPDWD WKHRU\ *ROGEHUJ f DQG LPSOLFLW SDUDOOHOLVP *ROGEHUJ f FRQFHSW DUH XVHIXO LQ H[SODLQLQJ ZK\ WKH *$V TXLFNO\ FRQYHUJH WR D KLJK ILWQHVV SRSXODWLRQ RI VWULQJV &RQVLGHU D VWULQJ RI OHQJWK \ GHILQHG RQ WKH DOSKDEHW ` DQG OHW 6 ^ `< 7KHQ D VFKHPD + GHILQHG RQ WKLV DOSKDEHW LV D VXEVHW RI 6 VXFK WKDW WKH VWULQJV LQ 6 KDYH WKH

PAGE 100

VDPH YDOXHV DW WKH VDPH ELW SRVLWLRQV IRU VRPH ELW SRVLWLRQV )RU H[DPSOH DVVXPH \ DQG DVVXPH ZH IL[ WKH YDOXHV DW WKH OVO DQG UG ELW SRVLWLRQ WKHQ + ^ ` + FDQ DOVR EH UHSUHVHQWHG DV D VWULQJ XVLQJ WKH DOSKDEHW ^r` ZKHUH r PHDQV HLWKHU D RU ,Q RXU H[DPSOH + LV rr 7KH OHQJWK RI D VFKHPD + +f LV WKH GLVWDQFH EHWZHHQ WKH ILUVW DQG WKH ODVW IL[HG SRVLWLRQV 7KH RUGHU RI D VFKHPD R+f LV WKH QXPEHU RI IL[HG SRVLWLRQV *ROGEHUJ f ,Q RXU H[DPSOH +f DQG R+f 7KH IXQGDPHQWDO WKHRUHP RI *$V VWDWHV WKDW VKRUW ORZ RUGHU DERYHDYHUDJH VFKHPDWD UHFHLYH H[SRQHQWLDOO\ LQFUHDVLQJ WULDOV LQ VXEVHTXHQW JHQHUDWLRQV *ROGEHUJ f SS 7KH H[SHFWHG QXPEHU RI PHPEHUV RI + LQ WKH QH[W JHQHUDWLRQ P+WOf LV ERXQGHG E\ P+WO f!P+Wf 7KH WHUP I+f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f [? \ + rr DQG + r + KDV EHWWHU

PAGE 101

FKDQFHV RI VXUYLYDO EHFDXVH I+f I+f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f VFKHPDWD ZLWKRXW DQ\ DGGLWLRQDO ERRNNHHSLQJ *ROGEHUJ Df 7KDW LV ZK\ WKH\ FDQ TXLFNO\ HOLPLQDWH D IDPLO\ RI VROXWLRQV WKDW DUH QRW SURPLVLQJ ZLWKRXW H[SOLFLWO\ FRQVLGHULQJ WKHP DQG WKXV FRQYHUJH WR D VROXWLRQ YHU\ UDSLGO\ $Q ([DFW 5HSUHVHQWDWLRQ RI D *$fV 6HDUFK %HKDYLRU 7KH VFKHPDWD WKHRUHP H[SODLQV ZK\ *$V DUH H[SHFWHG WR VWRFKDVWLFDOO\ FRQYHUJH WR D ILQDO SRSXODWLRQ ,W VLPSO\ VWDWHV WKDW DV WLPH SDVVHV VLPLODU VWULQJV WKDW DUH DERYH DYHUDJH ILWQHVV ZLOO LQFUHDVH LQ QXPEHU 7KH H[SUHVVLRQ IRU WKH QXPEHU RI VFKHPDWD LQ WKH QH[W JHQHUDWLRQ JLYHQ LQ f LV RQO\ DQ XSSHU ERXQG 0RUHRYHU LW GRHV QRW WHOO XV DQ\WKLQJ DERXW WKH LQGLYLGXDO VWULQJV LQ WKH QH[W JHQHUDWLRQ ,Q D VHULHV RI SDSHUV /LHSLQV 9RVH DQG 1L[ DWWDFN WKLV LVVXH DQG JLYH DQ H[DFW UHSUHVHQWDWLRQ RI WKH *$ EHKDYLRU

PAGE 102

/LHSLQV DQG 9RVH f VKRZ WKDW FURVVRYHU FDQ EH UHSUHVHQWHG E\ XVLQJ WKH ELWZLVH PXOWLSOLFDWLRQ p DQG H[FOXVLYH RU k RSHUDWRUV ZLWK D VWULQJ P UHIHUUHG WR DV D PDVN ZKRVH XVH ZLOO EH FOHDU VRRQ 7KURXJKRXW WKLV FKDSWHU DQG FKDSWHU ZH ZLOO XVH WKH QRWDWLRQ LQWURGXFHG EHORZ :H ZLOO UHIHU WR ELQDU\ VWULQJV E\ WKH LQWHJHUV WKH\ UHSUHVHQW )UHTXHQWO\ LQGH[HV ZLOO PHDQ SRSXODWLRQ PHPEHUV /HW \ EH WKH VWULQJ OHQJWK 1 EH WKH WRWDO QXPEHU RI VWULQJV WKDW ZH FDQ JHQHUDWH ZLWK \ ELWV LH 1 < 7 EH D ELQDU\ VWULQJ RI OHQJWK \ ZLWK DOO LWV ELWV HTXDO WR  EH WKH VHW RI DOO ELQDU\ VWULQJV RI OHQJWK \ UHSUHVHQWLQJ LQWHJHUV IURP 1O Uc MNf EH WKH SUREDELOLW\ RI REWDLQLQJ N DV DQ RIIVSULQJ ZKHQ FRPELQLQJ SDUHQWV LMHL7 Q EH WKH SRSXODWLRQ VL]H W EH WKH LWHUDWLRQ RU SRSXODWLRQ LQGH[ Sn EH D YHFWRU RI VL]H 1 ZKHUH S FRUUHVSRQGV WR WKH SURSRUWLRQ RI VWULQJ L LQ SRSXODWLRQ W V EH D YHFWRU RI VL]H 1 ZKHUH VnLV WKH SUREDELOLW\ RI VHOHFWLQJ L IRU UHFRPELQDWLRQ LQ SRSXODWLRQ W ) EH DQ 1[1 GLDJRQDO PDWUL[ ZKHUH )X ILf ILf IRU L 1 DQG I LV WKH IXQFWLRQ RI WR EH PD[LPL]HG

PAGE 103

0 EH DQ 1[1 PDWUL[ ZKHUH WUA ‘ ULMf 0} EH DQ 1[1 PDWUL[ ZKHUH P$c P (>[@ EH WKH H[SHFWHG YDOXH RI D UDQGRP YDULDEOH [ 1O EH D QRUP RQ ;H51 GHILQHG DV A [ L 'HILQLWLRQ /LHSLQV DQG 9RVH f )RU DQ\ P 4 P Pk7 'HILQLWLRQ /LHSLQV DQG 9RVH f ; LV D FURVVRYHU RSHUDWRU LI WKHUH H[LVWV DQ PHIL VXFK WKDW ;[\f Pp[fIILPp[f 7KHRUHP /LHSLQV DQG 9RVH f/HW ; EH D FURVVRYHU ^RSHUDWRU` DV GHILQHG DERYH 7KHQ ; FRPPXWHV ZLWK DGGLWLRQ DQG SURMHFWLRQ DQG SUHVHUYHV VFKHPDWD &RQYHUVHO\ OHW ; EH D ELQDU\ UHFRPELQDWLRQ RSHUDWRU WKDW SUHVHUYHV VFKHPDWD DQG FRPPXWHV ZLWK DGGLWLRQ DQG SURMHFWLRQ 7KHQ ; LV D FURVVRYHU RSHUDWRU 7KHRUHP /LHSLQV DQG 9RVH f /HW ; EH DQ\ DUELWUDU\ IL[HG FURVVRYHU RSHUDWRU DQG [\He /HW ;[\f XYf 7KHQ ;XYf [\f 0RUHRYHU LI ;P DQG ; DUH FURVVRYHU P RSHUDWRUV ZLWK PDVNV P DQG P UHVSHFWLYHO\ WKHQ IRU DQ\ [ \H4 ; [\f [B\[f f fn P 9RVH DQG /LHSLQV Df IXUWKHU FKDUDFWHUL]H WKH *$ EHKDYLRU E\ GHULYLQJ H[DFW SUREDELOLWLHV IRU WKH H[LVWHQFH RI DQ LQGLYLGXDO LQ WKH QH[W JHQHUDWLRQ JLYHQ WZR VWULQJV [ DQG \ DUH VHOHFWHG IRU UHFRPELQDWLRQ 7KH\ DOVR VKRZ WKDW WKH LWHUDWHV RI D *$ ZLWK LQILQLWH SRSXODWLRQ VL]H FDQ EH PRGHOHG DV WKH LWHUDWHV RI D QRQOLQHDU RSHUDWRU

PAGE 104

%HORZ /HPPD FKDUDFWHUL]HV WKH H[SHFWHG SURSRUWLRQV RI HDFK VWULQJ N LQ WKH QH[W SRSXODWLRQ /HPPD 9RVH DQG /LHSLQV Df 1O 1O @ ( ( VLWVc 9Nf L L /HPPD 9RVH DQG /LHSLQV Df ,I UHFRPELQDWLRQ LV D FRPELQDWLRQ RI PXWDWLRQ DQG FURVVRYHU WKHQ ULMNpOf ULkNMkN /HPPD VWDWHV WKDW SUREDELOLW\ RI SURGXFLQJ D FKLOG T WKDW FDQ EH UHSUHVHQWHG E\ NkO LV HTXDO WR SURGXFLQJ RQH RI WKH RSHUDQGV ZKHQ WKH SDUHQWV DUH VKLIWHG G\DGLFO\ E\ WKH RWKHU FKLOG ,Q RWKHU ZRUGV WKH SUREDELOLW\ RI SURGXFLQJ D FKLOG LV LQYDULDQW XQGHU D G\DGLF WUDQVODWLRQ /HPPD GRHV QRW VD\ WKDW ERWK VLGHV RI WKH HTXDOLW\ ZLOO UHVXOW LQ WKH VDPH RIIVSULQJ EXW VLPSO\ VWDWHV WKDW WKH SUREDELOLWLHV DUH WKH VDPH )RU 6U? OHW V7 GHQRWH WKH WUDQVSRVH RI V /HW Rc LV D SHUPXWDWLRQ GHILQHG RQ 51 2M M f 'HILQH P DV 0Vf DVf70DVfD1BVf70D1 'HILQLWLRQ )RU DOO [ \ H 51 f [ \ LI DQG RQO\ LI IRU VRPH "L! [ ;\

PAGE 105

7KHRUHP 9RVH DQG /LHSLQV Df (>V@a)0V nff :H ZLOO JLYH DQ REYLRXV H[WHQVLRQ RI 7KHRUHP LQ /HPPD /HPPD 7KH H[SHFWHG SUREDELOLWLHV LQ WKH QH[W JHQHUDWLRQ DUH JLYHQ E\ (>VO BAOO _)0V rf 9RVH DQG /LHSLQV Df IXUWKHU FKDUDFWHUL]H WKH EHKDYLRU WKH ) DQG 0 PDWULFHV 7KH\ VKRZ WKDW WKH EDVLQ RI DWWUDFWLRQ RI D IL[HG SRLQW RI ) LV WKH LQWHUVHFWLRQ RI WKH XQLW VSKHUH 6 DQG WKH HOOLSVRLG JLYHQ E\ 1O Y L ILf !c IMf 7KH\ IXUWKHU GLVFXVV WKH IL[HG SRLQWV RI RSHUDWRU @\M DQG VWDWH WKH IROORZLQJ WKHRUHP 7KHRUHP 9RVH DQG /LHSLQV Df /HW [c LYL ZKHUH 0 LV WKH VHW RI IL[HG IL[HG IL[HG SRLQWV RI RSHUDWRU ` ,I WKH PDWUL[ 0 LV SRVLWLYH WKHQ [ LV DV\PSWRWLFDOO\ VWDEOH ZKHQHYHU WKH VHFRQG ODUJHVW HLJHQYDOXH RI 0 OHVV WKDQ 7KH\ IXUWKHU FRQMHFWXUH WKDW WKH VHFRQG ODUJHVW YDOXH RI 0 LV X DQG WKH WKLUG f ODUJHVW HLJHQYDOXH RI 0 LV /DWHU LW ZDV VKRZQ E\ .RHKOHU f WKDW WKH IXOO VSHFWUXP RI 0 FDQ EH FDOFXODWHG E\

PAGE 106

\ \ L Sf_c_ L [ZLGLf L < \ ZKHUH ZLGLf LV WKH QXPEHU RI ELWV VWULFWO\ EHWZHHQ WKH KLJKHVW DQG WKH ORZHVW QRQ]HUR ELWV RI L 7KLV UHVXOW VKRZV WKDW WKH RSHUDWRU P KDV D VWDEOH IL[HG SRLQW )LQDOO\ WKH DXWKRUV H[SODLQ WKH H[SHFWHG EHKDYLRU RI *$V 7KH SRSXODWLRQ SURSRUWLRQV PRYH WR D IL[HG SRLQW RI 0 XQGHU WKH LQIOXHQFH RI ) LQ FRQWUDVW WR D JHQHWLF GULIW DQG ZLOO MXPS RXW RI WKDW SRLQWfV EDVLQ RI DWWUDFWLRQ LI WKDW SRLQW LV QRW PD[LPDOO\ ILW WR EH WUDSSHG LQ WKH EDVLQ RI DWWUDFWLRQ RI DQRWKHU IL[HG SRLQW 7KLV FOHDUO\ H[SODLQV ZK\ *$V ILUVW VORZ GRZQ LQ LPSURYLQJ WKH VROXWLRQ DQG WKHQ VXGGHQO\ MXPS WR DQRWKHU VROXWLRQ 3DUDOOHO WR WKLV UHVHDUFK 'DYLV \\ f DQDO\]HG WKH EHKDYLRU RI *$V IURP DQRWKHU SRLQW RI YLHZ +H PRGHOOHG HDFK SRSXODWLRQ DV D VWDWH RI D 0DUNRY &KDLQ 0&f DQG KH DOVR JDYH H[SUHVVLRQV IRU H[DFW WUDQVLWLRQ SUREDELOLWLHV IRU UHSURGXFWLRQ RQO\ IRU UHSURGXFWLRQ DQG FURVVRYHU DQG ILQDOO\ IRU UHSURGXFWLRQ FURVVRYHU DQG PXWDWLRQ +H DVVXPHG WKH PXWDWLRQ UDWH WR EH YDU\LQJ DQG GHULYHG HUJRGLFLW\ ERXQGV RQ WKH PXWDWLRQ UDWH *ROGEHUJ DQG 6HJUHVW \f DOVR GLVFXVV *$ EHKDYLRU E\ PRGHOLQJ LW DV 0& 7KHLU PRGHO LV IDU IURP UHSUHVHQWLQJ WKH UHDO EHKDYLRU RI *$V VLQFH WKH\ FRQVLGHU D SRSXODWLRQ FRPSRVHG RI RQH ELW VWULQJV 7KH\ DQDO\]H JHQHWLF GULIW DQG FRQYHUJHQFH XQGHU UHSURGXFWLRQ 7KH\ XVH WKH ILUVW SDVVDJH WLPHV WR DQDO\]H WKH H[SHFWHG WLPH WR GLIIHUHQW OHYHOV RI FRQYHUJHQFH

PAGE 107

9RVH DQG /LHSLQV Df GHULYH DQ H[DFW SUREDELOLW\ H[SUHVVLRQ IRU WKH SUREDELOLW\ RI JHQHUDWLQJ E\ UHFRPELQDWLRQ RQ L DQG M 7KH\ VKRZ WKDW ZKHUH $ N f6!L N f6f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f ZH ZLOO VKRZ KRZ WKH H[DFW WUDQVLWLRQ SUREDELOLWLHV DUH FDOFXODWHG

PAGE 108

)RU H[DPSOH OHW \ DQG Q 7KHQ e ^ff ` DQG 3 ^ ` ^` ` ` ^` ` ` ` ` ` ` 7KHQ WKH LQFLGHQFH PDWUL[ = LV = 1L[ DQG 9RVH f VKRZHG WKDW WKH WUDQVLWLRQ SUREDELOLWLHV IURP VWDWH RU SRSXODWLRQ L WR M DUH PXOWLQRPLDOO\ GLVWULEXWHG DQG DUH JLYHQ E\ W 1L RfU Q )! \M / \ ] \M 7KH DXWKRUV IXUWKHU VKRZHG WKDW DV WKH SRSXODWLRQ VL]H LQFUHDVHV WKH LWHUDWHV RI WKH 0& FRQYHUJH WR WKH LWHUDWHV RI WKH RSHUDWRU L *Vf 0 ? ? \ 7KH\ DOVR VKRZHG WKDW VLQFH WKH PXWDWLRQ UDWH LV QRQ]HUR 4 LV HUJRGLF DQG D OLPLWLQJ VWHDG\ VWDWH GLVWULEXWLRQ W H[LVWV 7KH\ DOVR SURYHG WKDW DV Q WHQGV WR LQILQLW\ WKH OLPLWLQJ GLVWULEXWLRQ Q FRQYHUJHV WR Wr ZKHUH

PAGE 109

Wr OLPW f§.R 0RUHRYHU MWr ZLOO KDYH SRVLWLYH YDOXHV IRU HOHPHQWV WKDW FRUUHVSRQG WR WKH IL[HG SRLQWV RI 7KDW LV IRU ODUJH SRSXODWLRQ VL]HV WKH LWHUDWHV RI 0& FRQYHUJH WR WKH LWHUDWHV RI RSHUDWRU &XUUHQW 5HVHDUFK 2Q *$V *$ 5HVHDUFK FDQ EH VXPPDUL]HG LQWR WZR FDWHJRULHV UHVHDUFK XVLQJ *$V DV VHDUFK DOJRULWKPV LQ DQ DSSOLFDWLRQ GRPDLQ DQG UHVHDUFK RQ LVVXHV DERXW *$V VXFK DV GHFHSWLYHQHVV ORQJ WHUP EHKDYLRU VKRUW WHUP EHKDYLRU FRQYHUJHQFH FRGLQJ HWF ,Q WKLV VHFWLRQ ZH ZLOO GLVFXVV ERWK ZLWK WKH HPSKDVLV RQ VFKHGXOLQJ DSSOLFDWLRQV DQG WKH VHDUFK EHKDYLRU RI *$V $V H[SODLQHG HDUOLHU GHFHSWLYHQHVV LV D FUXFLDO LVVXH LQ *$ RSWLPL]DWLRQ 5HVHDUFKHUV KDYH VKRZQ ZD\V RI FKDUDFWHUL]LQJ GHFHSWLYH IXQFWLRQV DQG IDLOXUH PRGHV /LHSLQV DQG 9RVH f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f

PAGE 110

6DPSOLQJ HUURU RFFXUV ZKHQ WKH *$ FDQ QRW HVWLPDWH WKH XWLOLW\ WKH DYHUDJH ILWQHVV RI WKH VFKHPD DQG IRFXVHV RQ RWKHU LQIHULRU VFKHPDWD ,QFUHDVLQJ VDPSOLQJ VL]H UDQGRPL]LQJ WKH LQLWLDO SRSXODWLRQ DQG NHHSLQJ RQO\ RQH FRS\ RI HDFK LQGLYLGXDO VXJJHVWHG VROXWLRQV /LHSHQV DQG 9RVH f &URVVRYHU GLVUXSWLRQ LV D WKUHDW WR WKH *$ ZKHQ WKH FXUUHQW SRSXODWLRQ KDV ORQJ GHILQLQJ OHQJWK VFKHPDWD 6XFK VFKHPDWD DUH PRUH VXVFHSWLEOH WR H[WLQFWLRQ GXH WR FURVVRYHU $VVXPH WKH RSWLPDO VROXWLRQ IRU D ELW SUREOHP LV DQG DVVXPH WKDW WKH FXUUHQW SRSXODWLRQ FRQWDLQV VFKHPDWD VXFK DV rrr DQG rrr (YHQ WKRXJK WKH ILUVW VFKHPD FRQWDLQV WKH RSWLPDO VROXWLRQ LW LV YHU\ XQOLNHO\ WR VXUYLYH EHFDXVH RI FURVVRYHU 2QH UHPHG\ IRU WKLV FDVH LV XVLQJ DQ LQYHUVLRQ RSHUDWRU /LHSHQV DQG 9RVH f 6RPH IXQFWLRQV DUH NQRZQ WR EH GHFHSWLYH IRU *$V )XQFWLRQV ZKHUH ORZ RUGHU VFKHPDWD OHDG WR VXERSWLPDO VROXWLRQV DUH GHFHSWLYH IXQFWLRQV DQG *$V KDYH GLIILFXOW\ ZLWK ILQGLQJ WKH RSWLPXP RI VXFK IXQFWLRQV ,W LV DQDORJRXV WR WKH VLWXDWLRQ ZKHUH WKH HVWLPDWH RI WKH JUDGLHQW RI WKH IXQFWLRQ OHDGV WKH VHDUFK WR D VXERSWLPDO SRLQW /LHSHQV DQG 9RVH Ef VKRZ WKDW LW LV SRVVLEOH WR LPSOHPHQW GHFHSWLYH IXQFWLRQV DV D FRPELQDWLRQ RI DQ HDV\ IXQFWLRQ DQG D VSLNH IXQFWLRQ 7KH\ DOVR VKRZ WKDW LW LV DOVR SRVVLEOH WR FRQYHUW GHFHSWLYH IXQFWLRQV WR HDV\ IXQFWLRQV E\ DIILQH WUDQVIRUPDWLRQV +RZHYHU XQGHU WKH QHZ PDSSLQJ WKHUH PD\ EH DQRWKHU IXQFWLRQ WKDW LV GHFHSWLYH *ROGEHUJ Ef Ff H[SODLQV KRZ WR DQDO\]H GHFHSWLYHQHVV E\ XVLQJ :DOVK WUDQVIRUPV :DOVK WUDQVIRUPV ILUVW VXJJHVWHG E\ %HWKNH *ROGEHUJ Df DUH XVHIXO SDUWLFXODUO\ LQ FDOFXODWLQJ DYHUDJH VFKHPDWD ILWQHVVHV *ROGEHUJ DOVR JLYHV DQ DOJRULWKP $12'( WR DQDO\]H GHFHSWLYHQHVV 2QH GUDZEDFN RI WKH DOJRULWKP LV WKDW LW UHTXLUHV WKH

PAGE 111

RSWLPDO YDOXH RI WKH IXQFWLRQ ,Q D UHDOOLIH RSWLPL]DWLRQ SUREOHP WKH RSWLPDO YDOXH LV DOPRVW QHYHU DYDLODEOH *ROGEHUJ .RUE DQG 'HE f f DQDO\]H D QHZ FODVV RI *$V FDOOHG PHVV\ *$V P*$Vf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f EHFDXVH RI LWV KLJK FRXSOLQJ ZLWK WKH MREVKRS SUREOHP 763 LV D ZHOO VWXGLHG 13 FRPSOHWH SUREOHP *DU\ DQG -RKQVRQ f 7KH SUREOHP FDQ EH VWDWHG DV IROORZV *LYHQ D JUDSK *9(f DQG UHODWHG DUF FRVWV ILQG D PLQLPXP FRVW VLPSOH WRXU VXFK WKDW HDFK QRGH LV YLVLWHG RQO\ RQFH $OO *$ DSSURDFKHV WR 763 IRFXV RQ FRGLQJ WKH SUREOHP VXFK WKDW D SDUWLFXODU VWULQJ UHSUHVHQWV D IHDVLEOH WRXU LH WKH ELWV RI WKH VWULQJ DUH RUGHUHG 7KHUH DUH QXPHURXV RSHUDWRUV GHYHORSHG DQG WHVWHG WKDW JXDUDQWHH IHDVLEOH WRXUV LQ WKH QH[W

PAGE 112

JHQHUDWLRQ 2QH VXFK RSHUDWRU LV GHVFULEHG LQ :KLWOH\ 6WDUNZHDWKHU DQG )XTXD\ f 7KH HGJH UHFRPELQDWLRQ RSHUDWRU LV GHVLJQHG WR SUHVHUYH WKH FRPPRQ HGJHV DSSHDULQJ LQ ERWK SDUHQWV 7KH HGJH UHFRPELQDWLRQ RSHUDWRU GRHV QRW QHHG DQ\ ORFDO LQIRUPDWLRQ VXFK DV WKH FRVW RI WKH HGJHV EXW UDWKHU ZRUNV ZLWK JOREDO LQIRUPDWLRQ 7KH RSHUDWRU KDV EHHQ VXFFHVVIXOO\ DSSOLHG WR WKH 763 SUREOHP DV ZHOO DV WR WKH MREVKRS SUREOHP &OHYHODQG DQG 6PLWK f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f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

PAGE 113

VWDJH 7KH VWUHQJWK RI DUELWUDWRUV DUH XSGDWHG WKURXJKRXW WKH VLPXODWLRQ $V D UHVXOW WKH V\VWHP GLVFRYHUHG QRW RQO\ JRRG SODQQLQJVFKHGXOLQJ VWUDWHJLHV EXW DOVR OHDUQHG HIIHFWLYH FRQIOLFW UHVROXWLRQ SODQV 7KH V\VWHP LV UHSRUWHG WR UHGXFH ERWK PDFKLQLQJ FRVWV DQG WRWDO HODSVHG WLPH *$ %DVHG /HDUQLQJ 6\VWHPV DQG &ODVVLILHU 6\VWHPV *$ %DVHG /HDUQLQJ 6\VWHPV *$%/6Vf DUH XVXDOO\ K\EULG V\VWHPV WKDW XVH *$V IRU GLVFRYHULQJ XVHIXO UXOHV IRU WKH GRPDLQ RI LQWHUHVW 2QH IDPLO\ RI *$ OHDUQLQJ V\VWHPV DUH &ODVVLILHU 6\VWHPV &6Vf &6V DUH GLVWLQJXLVKHG E\ WKH ZD\ WKH\ XVH WKH UXOHV DQG E\ WKHLU FRQIOLFW UHVROXWLRQ DQG UHZDUG PHFKDQLVPV &ODVVLILHU 6\VWHPV &6Vf ILUVW SURSRVHG E\ +ROODQG *ROGEHUJ Df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` ZKHUH PHDQV GR QRW FDUH RU PDWFK HYHU\WKLQJ ,I WKH SUHPLVH RI WKH UXOH PDWFKHV RQH RI WKH PHVVDJHV LQ WKH PHVVDJH OLVW LW ILUHV DQG WKXV SRVWV LWV RZQ PHVVDJH WR WKH PHVVDJH OLVW RU WR WKH H[WHUQDO HQYLURQPHQW 0HVVDJHV DUH XVXDOO\ GHILQHG RQ WKH DOSKDEHW ^`

PAGE 114

(DFK FODVVLILHU LV DVVLJQHG DQ LQLWLDO VWUHQJWK %DVHG RQ LWV PHVVDJH WKH V\VWHP UHFHLYHV D UHZDUG IURP WKH H[WHUQDO ZRUOG $ FUHGLW DVVLJQPHQW DOJRULWKP LV XVHG WR GHWHUPLQH KRZ WR GLVWULEXWH WKLV UHZDUG EDFN WR WKH UXOHV WKDW WRRN SDUW LQ SRVWLQJ WKH RXWSXW PHVVDJH 2QH VXFK DOJRULWKP LV WKH %XFNHW %ULJDGH %%f DOJRULWKP SURSRVHG E\ +ROODQG *ROGEHUJ Df %% VLPXODWHV D PDUNHW HFRQRP\ ZKHUH HDFK UXOH WKDW PDWFKHV WKH FXUUHQW PHVVDJH PDNHV D ELG EDVHG RQ WKHLU ILWQHVV YDOXHV 7KRVH ZKR ELG WKHQ SRVW WKHLU PHVVDJH RQ WKH PHVVDJH OLVW DQG SD\ WKH ELG DPRXQW WR WKH RZQHU RI WKH PHVVDJH WKH\ KDG PDWFKHG 7KLV LV FDUULHG RXW XQWLO RQH FODVVLILHU SRVWV DQ RXWSXW PHVVDJH DQG UHFHLYHV D UHZDUG ,Q WKLV DOJRULWKP WKH H[WHUQDO UHZDUG LV JLYHQ RQO\ WR WKH RZQHU RI WKH RXWSXW PHVVDJH 7KH VWUHQJWK RI FODVVLILHU L DW WLPH W LV JLYHQ DV 6MWf 6LWf 3MWf 7Wf 5cWf 7KH WHUP 3cWf LV WKH ELG DPRXQW 7cWf LV WKH WD[ DPRXQW DQG 5cWf LV WKH UHZDUG FODVVLILHU L UHFHLYHVf§UHZDUG PD\ EH ]HUR 7KLV LV QRW WKH RQO\ ZD\ RI GLVWULEXWLQJ WKH UHZDUG EDFN :H ZLOO GLVFXVV RWKHU PHWKRGV ODWHU LQ WKLV VHFWLRQ 'XH WR WKH LQFUHDVH LQ WKH FRPSXWDWLRQDO FRPSOH[LW\ ZKHQ PXOWLSOH UXOHV DUH ILUHG DOO NQRZOHGJH EDVHG V\VWHPV QHHG D PHFKDQLVP WR EUHDN WLHV DQG VHOHFW D UXOH WR DSSO\ DPRQJ WKRVH FRPSHWLQJ 0RVW &6V XVH D FRPSHWLWLRQ EDVHG FRQIOLFW UHVROXWLRQ 2QH FRQIOLFW UHVROXWLRQ PHFKDQLVP LV FDOOHG QRLV\ ELGGLQJ ZKHUH WKH ELG PDGH E\ WKH FODVVLILHU LV &EMG6 H ZKHUH Ha1RKM_f 2QO\ D VXEVHW RI WKH PDWFKLQJ FODVVLILHUV DUH VHOHFWHG WR EH ILUHG EDVHG RQ WKHLU ELG YDOXHV *ROGEHUJ Df 2QH RWKHU VFKHPH XVHV

PAGE 115

WKH &EL6L YDOXHV WR FRQVWUXFW D SUREDELOLW\ GLVWULEXWLRQ D URXOHWWH ZKHHOf ZKLFK LV XVHG WR VHOHFW RQO\ D VXEVHW RI WKH FODVVLILHUV ,I D &6 KDG RQO\ WKH FODVVLILHUV DQG WKH FUHGLW DVVLJQPHQW DOJRULWKP LW ZRXOG EH DEOH WR GLVFRYHU UXOHV WKDW XVHIXO RQO\ DPRQJ WKRVH WKDW LQLWLDOO\ DUH JLYHQ WR WKH V\VWHP :KDW LI WKHUH DUH RWKHU XVHIXO UXOHV WKDW ZRXOG UHVXOW LQ LPSURYHG SHUIRUPDQFHnn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f *UHIHQVWHWWH f GHVFULEH D V\VWHP 6$08(/ WKDW XWLOL]HV *$V IRU UXOH GLVFRYHU\ &RQIOLFW UHVROXWLRQ LV EDVHG RQ D XWLOLW\ PHDVXUHf§QRW GHVFULEHG LQ WKH SDSHU DVVRFLDWHG ZLWK WKH DFWLYH UXOHV $OO DFWLYH UXOHV KDYH WKHLU VWUHQJWKV DGMXVWHG LQFUHPHQWDOO\ DW WKH HQG RI HDFK HSLVRGH 7KH DXWKRU XWLOL]HV ERWK WKH PHDQ VWUHQJWK DQG WKH YDULDQFH WR UHSUHVHQW WKH FXUUHQW VWUHQJWK RI WKH UXOH $IWHU D IHZ HSLVRGHV WKH UXOHV

PAGE 116

DUH XSGDWHG E\ XVLQJ JHQHWLF RSHUDWRUV 7KH DXWKRU UHSRUWV IDVW FRQYHUJHQFH WR XVHIXO UXOHV *$ XVH LV ZLGH VSUHDG *UHHQH DQG 6PLWK f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f 6RPH UHVHDUFK FRQFHQWUDWHV RQ FRPSDULQJ WKH SHUIRUPDQFHV RI FUHGLW DVVLJQPHQW DQG FRQIOLFW UHVROXWLRQ DOJRULWKPV *UHIHQVWHWWH f FRPSDUH %% DQG WKH 3URILW 6KDULQJ 3ODQ 363f DOJRULWKPV 363 GLVWULEXWHV WKH H[WHUQDO UHZDUG WR DOO WKH UXOHV WKDW KHOSHG WR JHW WKLV UHZDUG ZKHUHDV LQ %% RQO\ WKH ODVW UXOH LQ WKH FKDLQ JHWV WKH H[WHUQDO UHZDUG 7KH VWUHQJWK XSGDWH LQ 363 LV H[SODLQHG E\ 6LWOf 6LWfE6MWfESWf 7KH DXWKRU VKRZV WKDW 363 LV EHWWHU LQ SUHGLFWLQJ WKH H[WHUQDO UHZDUGV WKDW LV WKH VWHDG\ VWDWH VWUHQJWK RI UXOHV FRPSDUHG WR %% 7KH DXWKRU IXUWKHU VXJJHVWV WKDW %% LV D VXEJRDO UHZDUG VFKHPH WKDW WHQGV WR HYHQ RXW WKH VWUHQJWKV RI WKH UXOHV LQ D JLYHQ FKDLQ )XUWKHUPRUH %% LV PRUH VXLWDEOH IRU SDUDOOHO UXOH ILULQJV WKDQ 363 /LHSLQV HW DO f FRPSDUHV WKH VWHDG\ VWDWH EHKDYLRU RI %DFNZDUGV $YHUDJLQJ %$f %% DQG 363 %$ DQG

PAGE 117

363 XVH WKH VDPH FUHGLW DVVLJQPHQW VFKHPH 7KH RQO\ GLIIHUHQFH LV %$ UHGXFHV WKH UHZDUG E\ D FRQVWDQW IDFWRU EXW 363 GRHV QRW ,Q %$ DVVXPLQJ WKHUH LV D FKDLQ RI Q FODVVLILHUV WKH VWUHQJWK LV XSGDWHG E\ 6MWOf 6LWf E6MWf E$QanS IRU ; 7KH\ VKRZ WKDW %% DQG %$ KDYH WKH VDPH VWHDG\ VWDWH VWUHQJWKV IRU D OLQHDU FKDLQ ZKHQ %% XVHV IL[HG SHUFHQWDJH WD[ VFKHPH 7KH\ DOVR UHSRUW WKDW %$ GRHV QRW HQIRUFH WKH GHYHORSPHQW RI VKRUW FKDLQ RI UXOHV =KRX f GLVFXVVHV DQG GHPRQVWUDWHV WKH XVHIXOQHVV RI D ORQJ WHUP PHPRU\ IRU D FODVVLILHU V\VWHP *ROGEHUJ f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f 7KH DXWKRU VKRZV WKDW URXOHWWH ZKHHO ELGGLQJ LV HTXLYDOHQW WR 30 DQG QRLV\ ELGGLQJ FDQ EH PRGLILHG WR PLPLF ERWK 30 DQG WKH RSWLPDO GHFLVLRQV +H DOVR SURSRVHV ELGGLQJ VFKHPH YDULDQFHVHQVLWLYH ELGGLQJ ZKHUH %M (>%M@ D%Mf )LQDOO\ WKH DXWKRU VKRZV WKDW YDULDQFHVHQVLWLYH ELGGLQJ LV PRUH IOH[LEOH LQ KDQGOLQJ FKDQJHV LQ WKH LQIRUPDWLRQ )RU H[DPSOH WKLV KDQGOHV WKH FDVH ZKHUH WKH SUREDELOLW\ RI HDFK RXWFRPH LV UHYHUVHG

PAGE 118

,OO &6V KDYH EHHQ DSSOLHG LQ DOPRVW HYHU\ GRPDLQ EXW /LHSLQV DQG :DQJ f VKRZ WKDW WKHUH DUH GRPDLQV ZKHUH WKH\ DUH QRW VXLWDEOH 7KH\ JLYH D VNHWFK RI WKHLU LGHDV DV WR ZK\ *$V DUH QRW VXLWDEOH IRU VWDWLRQDU\ FRQFHSWV 7KH\ DOVR VWDWH WKDW D &6 LV XQLTXHO\ ZHOO VXLWHG IRU QRQVWDWLF GRPDLQV 7KHLU UHVXOWV DUH LQ DJUHHPHQW ZLWK *ROGEHUJfV f *ROGEHUJ FRQFOXGHV WKDW &6V KDYH DQ LQKHUHQW PHFKDQLVP WR KDQGOH FKDQJLQJ LQIRUPDWLRQ SDWWHUQV VLQFH WKH\ XWLOL]H SUREDELOLW\ PDWFKLQJ EXW PD\ EH VXERSWLPDO IRU VWDWLF HQYLURQPHQWV 7KH ILQGLQJV E\ *ROGEHUJ DQG /LHSLQV DQG :DQJ f VXJJHVW WKDW WKH &6V DUH VXLWDEOH IRU GRPDLQV ZKHUH WKHUH LV D ORW RI XQFHUWDLQW\ DQG SRVVLEOH QRLVH LQ WKH LQFRPLQJ GDWD 7KH &6V DUH UREXVW HQRXJK WR KDQGOH VXFK FDVHV :LOVRQ f GHVFULEHV WKH DQLPDW SUREOHP $FFRUGLQJ WR KLV GHVFULSWLRQ DQ DQLPDO LV ERUQ ZLWK VRPH DVVRFLDWLRQV EXW WKH UHVW RI WKH NQRZOHGJH QHFHVVDU\ PXVW EH OHDUQHG WKURXJK H[SHULHQFH KDV WR OHDP LQFUHPHQWDOO\ GRHV QRW KDYH WKH OX[XU\ RI D WHDFKHUOLNH HQYLURQPHQW WR WHOO LW ZKLFK DFWLRQ LV ULJKW LQ HDFK VLWXDWLRQ RU HYHQ WR SURYLGH DQ HUURU VLJQDO ,QVWHDG RQ WKRVH UHODWLYHO\ UDUH RFFDVLRQV ZKHQ DFWLRQ EULQJV LPPHGLDWH VDWLVIDFWLRQ ^SD\RII` RI D FXUUHQW QHHG WKH EHVW WKH DQLPDO FDQ GR LV UDWH WKH DFWLRQ DQG WKH UHVSRQVLEOH UXOHf DFFRUGLQJ WR WKH GHJUHH RI VDWLVIDFWLRQ :LOVRQ S f KDV WR OHDUQ XQGHU SD\RII WKDW PD\ QRW EH DYDLODEOH ULJKW DIWHU DFWLRQ VKRXOG KDYH WKH FDSDELOLW\ WR GLVUHJDUG WKH LUUHOHYDQW DWWULEXWHV RI WKH HQYLURQPHQW DQG JHQHUDOL]H LWV ILQGLQJV DV PXFK DV SRVVLEOH

PAGE 119

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f DQG LW FDQ EH FRQWLQXRXVO\ FKDQJLQJ LQ WLPH 7KH V\VWHP KDV WR XQGHUVWDQG WKH UHODWLYH PHULW RI HDFK UXOH UXOH XVHIXOQHVV GLVFRYHU\f )LQDOO\ WKH V\VWHP KDV WR XVH LWV SDVW NQRZOHGJH WR GLUHFW LWV VHDUFK IRU QHZ NQRZOHGJH (YHQ WKRXJK ZH GR QRW KDYH D MXVWLILFDWLRQ \HW EDVHG RQ WKH UHVXOWV RI *ROGEHUJ f :LOVRQ f DQG /LHSLQV DQG :DQJ f ZH EHOLHYH WKDW D *$ EDVHG OHDUQLQJ DSSURDFK LV PRVW VXLWDEOH IRU WKH VFKHGXOLQJ GRPDLQ ,Q WKH QH[W FKDSWHU ZH ZLOO GLVFXVV VRPH WHFKQLFDO LVVXHV RI *$V DQG LQ &KDSWHU ZH ZLOO VKRZ KRZ D *$ EDVHG OHDUQLQJ V\VWHP FDQ EH XVHG IRU SHUIRUPDQFH LPSURYHPHQW DV ZHOO GLVFRYHULQJ XVHIXO GLVSDWFKLQJ UXOHV LQ VFKHGXOLQJ

PAGE 120

&+$37(5 ,668(6 21 ),1,7( *$V $Q ,VVXH RQ 6WRSSLQJ &ULWHULD 7R GDWH DOO FRQYHUJHQFH SURSHUWLHV RI *$V KDYH EHHQ HPSLULFDOO\ VWXGLHG ZLWK WKH JHQHUDO FRQVHQVXV WKDW WKH\ FRQYHUJH +RZHYHU *$V DUH VWRFKDVWLF DOJRULWKPV ZKLFK XVH SUREDELOLVWLF SLYRWLQJ UXOHV LQ FRQWUDVW WR GHWHUPLQLVWLF SLYRWLQJ UXOHV RI VD\ WKH VLPSOH[ PHWKRG +HQFH LW LV QRW SRVVLEOH WR WDON DERXW FRQYHUJHQFH WR D SRLQW 1RQHWKHOHVV ZH FDQ WDON DERXW D VWHDG\ VWDWH EHKDYLRU RI D *$ 1L[ DQG 9RVH f VKRZHG WKDW D VWHDG\ VWDWH EHKDYLRU H[LVWV DQG WKDW LW LV QRW SRVVLEOH IRU D *$ WR EH WUDSSHG DW D SDUWLFXODU LQIHULRU VROXWLRQ LQGHILQLWHO\ 7KH SUREDELOLW\ RI YLVLWLQJ D JRRG VROXWLRQ LQFOXGLQJ WKH RSWLPDOf LV FRQVLGHUDEO\ KLJKHU WKDQ RWKHU VROXWLRQV 7KLV SRLQW ZDV ILUVW GLVFXVVHG E\ 9RVH DQG /LHSLQV Df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

PAGE 121

WKH VHDUFK VSDFH LV FRPSRVHG RI LQWHJHU SRLQWVf 2XU PRGHO LV EDVHG RQ ZRUN E\ 1L[ DQG 9RVH f 'DYLV f 9RVH DQG /LHSLQV Df DQG WKH FRQFHSW RI ILUVW SDVVDJH WLPH GLVWULEXWLRQV RI 0DUNRY &KDLQV ,Q 6HFWLRQ ZH GLVFXVV VRPH SUHOLPLQDULHV GHYHORS RXU PRGHO DQG GHULYH RXU H[DFW ERXQG :H DOVR SUHVHQW D ERXQG VXIILFLHQW WR JXDUDQWHH D GHVLUHG FRQILGHQFH OHYHO DQG LV HDV\ WR FRPSXWH ,Q 6HFWLRQ ZH GLVFXVV VRPH SURSHUWLHV RI WKH ERXQG 6WRSSLQJ &ULWHULD IRU *$V ,Q WKLV VHFWLRQ ZH ZLOO XVH WKH PRGHO GHYHORSHG E\ 1L[ DQG 9RVH f DQG 'DYLV f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c GHQRWH WKH VWDWH WKH 0& LV LQ DW WLPH L 3 EH WKH VHW RI DOO VWDWHV RI WKH 0&

PAGE 122

4 EH WKH 0DUNRY VWDWH WUDQVLWLRQ PDWUL[ IRU RXU *$ :H DVVXPH WKDW WKH PXWDWLRQ UDWH LV SRVLWLYH VR WKDW 4 LV HUJRGLF :H DOVR DVVXPH WKDW WKH PXWDWLRQ UDWH LV OHVV WKDQ 4c^;W M`EH WKH SUREDELOLW\ WKDW WKH 0& LV DW VWDWH M DW WLPH W VWDUWLQJ IURP VWDWH L 7 EH WKH LWK WLPH WKH 0& KDV YLVLWHG VWDWH M 7 LV WKH WLPH RI WKH ILUVW YLVLW WR VWDWH M 2NLMf EH WKH SUREDELOLW\ WKDW LW WDNHV WKH 0& N WUDQVLWLRQV WR YLVLW VWDWH M VWDUWLQJ DW VWDWH -fNLf EH HTXDO WR G?LMf IRU DOO L H ( DQG IRU VRPH IL[HG M f! EH D 3 [ YHFWRU ZKHUH ffNLf LV WKH SUREDELOLW\ WKDW LW WDNHV WKH 0& N WUDQVLWLRQV WR ILUVW HQWHU VWDWH M VWDUWLQJ DW VWDWH L IRU VRPH IL[HG M HM EH D 1[O XQLW YHFWRU ZLWK ]HURV HYHU\ZKHUH H[FHSW IRU WKH M SRVLWLRQ EH WKH 3 3 LGHQWLW\ PDWUL[ H EH D YHFWRU RI RQHV S$f EH WKH VSHFWUDO UDGLXV RI PDWUL[ $ :H FDQ GHULYH 2NLMf IRU WZR FDVHV )RU N 2NLMf 3URE-7 ` 3URE-; M` 4LMf f DQG IRU N rNLMf 3URILO; E` 3UREK^;rM ;NBrM;NB M` EH(MO f &RPELQLQJ f DQG f ZH KDYH

PAGE 123

4LMf N O 4LEf2N EMf N! EH ( ^M` )LQDOO\ (TXDWLRQ f FDQ EH VWDWHG LQ PDWUL[ IRUP IRU IL[HG M E\ O!N 44HMH7f_!NB IRU N! RU HTXLYDOHQWO\ _!N 44H H 7fNn4H IRU N!O $Q 8SSHU %RXQG RQ WKH 1XPEHU RI ,WHUDWLRQV 2XU SUREOHP FDQ EH GHILQHG DV IROORZV *LYHQ D GHVLUHG FRQILGHQFH OHYHO WKH SRSXODWLRQ VL]H DQG WKH VWULQJ OHQJWK KRZ PDQ\ LWHUDWLRQV GRHV D *$ UHTXLUH EHIRUH ZH FDQ VWRS VR WKDW ZH ZLOO KDYH VHHQ DQ RSWLPDO VROXWLRQ ZLWK DW OHDVW SUREDELOLW\ 7KDW LV ILQG WKH OHDVW W VXFK WKDW 3URE ^ $Q RSWLPDO VROXWLRQ KDV EHHQ IRXQG 7KH *$ KDG DW OHDVW W LWHUDWLRQV` 2XU SUREOHP FDQ EH HTXLYDOHQWO\ IRUPXODWHG DV 3UREOHP f PD[^PLQW` VXEMHFW WR ;f 44HMH7fLB4HM H f L %HIRUH ZH SURFHHG WR VROYH 3UREOHP LW LV QRWHZRUWK\ WR JLYH VRPH EDVLF UHVXOWV RQ WKH VXP RI WKH SRZHU RI PDWULFHV DQG WKH VSHFWUDO SURSHUWLHV RI QRQQHJDWLYH PDWULFHV

PAGE 124

7KH IROORZLQJ WULYLDO HTXDOLW\ KROGV IRU DQ\ PDWUL[ $ ZKHQ ,$f H[LVWV W ,$n+,$fn f L O 7KHRUHP 6HQHWD f 7KH 6XELQYDULDQFH 7KHRUHPf /HW 7 EH D QRQQHJDWLYH LUUHGXFLEOH PDWUL[ V D SRVLWLYH QXPEHU DQG \! \rIf D YHFWRU VDWLVI\LQJ 7\V\ 7KHQ Df \ DQG Ef V!U! ZKHUH U S7f LV WKH 3HUURQ)UREHQLXV HLJHQYDOXH RI 7 0RUHRYHU V U LI DQG RQO\ LI 7\ U\ 2XU ILUVW UHVXOW LV JLYHQ EHORZ 7KHRUHP 7KH PLQLPDO QXPEHU RI LWHUDWLRQV UHTXLUHG WR JXDUDQWHH WKDW ZH KDYH VHHQ WKH RSWLPDO VROXWLRQ ZLWK SUREDELOLW\ DW OHDVW LV 3URRI &RQVLGHU PD[ OQ f ,Q S 4 4HAHf W 4 f4HMHMfLa4HM L %\ XVLQJ f ZH FDQ ZULWH f DV >,44HMHM7fW@,44HMH7U4H 7R XVH f ZH QHHG WR VKRZ WKDW ,44HMHf LV QRQVLQJXODU 7R VHH WKLV FRQVLGHU WKH FKDUDFWHULVWLF HTXDWLRQ RI 44HAHMf ZKLFK LV HTXDO WR GHW $,44HMHM7f

PAGE 125

:H NQRZ WKDW WKH VROXWLRQ VHW RI WKLV FKDUDFWHULVWLF HTXDWLRQ GRHV QRW LQFOXGH ; EHFDXVH WKH URZ VXPV RI 4 4HcHM7f DUH VWULFWO\ OHVV WKDQ DQG WKXV WKH PD[LPDO HLJHQYDOXH FDQ QRW EH VHH 7KHRUHP EHORZf +HQFH 4 4HMHMnf FDQ QRW EH VLQJXODU DQG WKXV LWV LQYHUVH H[LVWV &ODLP 44HMHM7fn4HM H f 3URRI RI &ODLP $VVXPH WKH FODLP LV QRW FRUUHFW 0XOWLSO\ ERWK VLGHV RI f E\ 4 4HMHM7f 7KH ULJKW VLGH JLYHV H H 4HVLQFH 4H H +HQFH ZH VHH WKDW WKH DVVXPSWLRQ LPSOLHV 4HA4A D FRQWUDGLFWLRQ 7KXV WKH FODLP LV WUXH +HQFH f FDQ EH UHZULWWHQ DV O&44HA7fr H H ;f :H QRZ VKRZ XVLQJ 7KHRUHP WKDW VDWLVI\LQJ f LV HTXLYDOHQW WR VDWLVI\LQJ 3 7?W 4HMH nf f f :H FDQ QRW GLUHFWO\ DSSO\ 7KHRUHP WR 4 4HMHM f VLQFH LW LV QRW LUUHGXFLEOH +RZHYHU 4 f KDV WKH VDPH HLJHQYDOXHV DV WKH PDWUL[ T ZKHUH 4 LV WKH 3 [ 3 PDWUL[ REWDLQHG E\ GHOHWLQJ WKH MK FROXPQ DQG URZ RI PDWUL[ 4 7R VHH WKLV FRQVLGHU WKH FKDUDFWHULVWLF HTXDWLRQ RI 4 2HAH f GHW 4 4HAM f 1RWLFH

PAGE 126

WKDW WKH PDWUL[ 4 4A f KDV DOO ]HURV LQ LWV MnK FROXPQ 7KHQ WKH FKDUDFWHULVWLF HTXDWLRQ ZLOO EH RI WKH IRUP $ %XW Q KDV WKH VDPH HOHPHQWV RI 4 4HcH_U f H[FHSW IRU WKH MWK FROXPQ DQG WKH MWK URZ HOHPHQWV WKXV WKH RQO\ GLIIHUHQFH EHWZHHQ WKH FKDUDFWHULVWLF HTXDWLRQV RI WKH WZR LV WKH ILUVW WHUP $ ZKLFK PXVW EH HTXDO WR ]HUR VLQFH WKH FKDUDFWHULVWLF HTXDWLRQ LV RI WKH IRUP $ )LQDOO\ ZH NQRZ WKDW VLQFH WKH PXWDWLRQ UDWH LV QRQ ]HUR DOO VWDWHV RI 4 FRPPXQLFDWH ZLWK HDFK RWKHU +HQFH LW LV LUUHGXFLEOH DQG ZH FDQ VDIHO\ XVH 7KHRUHP RQ 4 DQG WKXV REWDLQ UHVXOWV IRU 4 2HAn f +HQFH E\ 7KHRUHP ZH FDQ UHZULWH f DV S844HMHfn@ f %XW S$nf Sf$f 7KXV ZH FDQ ZULWH %\ WDNLQJ WKH ORJDULWKPV RI ERWK VLGHV ZH JHW ,Q f ,QS&44HMH7f 5HDUUDQJLQJ WHUPV JLYHV

PAGE 127

1RZ ZH FDQ UHVWDWH 3UREOHP DV PD[ ^ PLQ W` M VXEMHFW WR ,Q f ,QSL44HHAf 3UREOHP KDV D VROXWLRQ Wr JLYHQ E\ PD[ M ,Q f ,QS&44HMH ZKLFK SURYHV WKH WKHRUHP 4(' 'HWHUPLQLQJ WKH VSHFWUDO UDGLXV IRU HDFK 4 4Af LV QRW HDV\ +RZHYHU ZH FDQ ILQG DQ XSSHU ERXQG IRU HDFK VSHFWUDO UDGLXV DQG FKRRVH WKH PD[LPXP WR SURYLGH DQ XSSHU ERXQG RQ W /HW D EH DQ\ QXPEHU VXFK WKDW SO44HHMf D DQG OHW OQOf ,Q D M 7KHQ IRU W PD[ W M M

PAGE 128

ZH ZLOO KDYH W Wr 7KH QH[W UHVXOW JLYHV XV RQH ZD\ WR FKRRVH RWM YDOXHV 7KHRUHP 0LQH ;f ,I $ LV D QRQQHJDWLYH PDWUL[ ZLWK VSHFWUDO UDGLXV U DQG URZ VXPV U UQ WKHQ PLQU U PD[U f f +HQFH XVLQJ 7KHRUHP RQH FKRLFH IRU W LV WR XVH D PD[4 4HH fH ‘ Z A M M nL O ZKLFK \LHOGV a ,Q f OQO PLQ4f f D O +HQFH LI ZH FDQ ILQG WKH PLQLPXP HOHPHQW RI WKH VWDWH WUDQVLWLRQ PDWUL[ 4 ZH ZLOO EH DEOH WR ILQG DQ XSSHU ERXQG RQ WKH QXPEHU RI LWHUDWLRQV UHTXLUHG IRU WKH ILUVW SDVVDJH WLPH SUREDELOLWLHV :H ZLOO VKRZ WKDW D XQLTXH PLQLPXP H[LVWV IRU PDWUL[ 4 E\ SURYLQJ WZR OHPPDV /HPPD 7KH PLQLPXP HOHPHQW RI PDWUL[ 4 LV ERXQGHG EHORZ E\ SQ\ 3URRI :H ZLOO SURYH /HPPD E\ SURYLQJ WZR FODLPV &ODLP 7KH PLQLPXP HOHPHQW RI D PXOWLQRPLDO GLVWULEXWLRQ ZKHUH WKH PLQLPXP LV EHLQJ WDNHQ RYHU DOO SRVVLEOH FRPELQDWLRQV RI Qc YDOXHV DQG ZKHUH WKH PXOWLQRPLDO

PAGE 129

GLVWULEXWLRQ LV JLYHQ E\ PLQ ^ Sc` fQ 3URRI RI &ODLP 6XSSRVH WKH Sc YDOXHV DUH UDQNHG LQ DVFHQGLQJ RUGHU LH S LV PLQLPXPf 7KHQ &ODLP FDQ EH ZULWWHQ DV PLQ3^Q,YQN` 3^Q` :H ZLOO SURYH WKLV E\ LQGXFWLRQ RQ Q IRU D JLYHQ N YDOXH %DVH &DVH )RU Q O (TXDWLRQ f FDQ EH ZULWWHQ DV N PLQ3^ QUQN` PLQMMSQL L n n )LQDOO\ E\ RXU DVVXPSWLRQ LW IROORZV WKDW PLQ3^ QQN` L 3^` S ,QGXFWLYH +\SRWKHVLV $VVXPH WKH FODLP LV WUXH IRU VRPH DUELWUDU\ Q

PAGE 130

1RZ ZH QHHG WR VKRZ WKDW LW KROGV IRU Q 7KDW LV PLQ3^ ` 3^Q ` SfQO %\ WKH LQGXFWLRQ K\SRWKHVLV ZH NQRZ WKDW PLQ3^ QQQN` Q 3LQ3r3N Q 7KHQ S PLQ 3^ Q,QMQN` Q L Q Q f 33Q3 3Nr Qf Q Q f f Q Q 2 UQUU3O 1RZ FRQVLGHU WKH 4cM H[SUHVVLRQ GHILQHG HDUOLHU ([SDQGLQJ WKH DERYH HTXDWLRQ JLYHV

PAGE 131

&RQVLGHU 7KHQ 1O 1O L f M 1O 1O 1O 1O PLQU \f A LrM %\ XVLQJ /HPPD ZH JHW 1O 1O 1O 1O f DQG ILQDOO\ ((I]LKIM]MKUL\ff L M ((I]LKIM]MKPLQULH\Mk\ L M OM eeI L f M ] I] LK MK Uc\f I ] I] L LK M MK 1O 1O PLQILMrf ( ( ILk\=Lk\KIMk\=-k\ f L M 1O 1O L M 6LQFH WKH GRXEOH VXP RQ WKH OHIW LV FRQVWDQW WKLV PRWLYDWHV WKH QHHG WR GHWHUPLQH WKH PLQLPDO HOHPHQW RI 0 ZKLFK FRQVLVWV RI WKH Uc cf YDOXHV &ODLP 7KH PLQLPXP HOHPHQW RI 0DWUL[ 0 LV ERXQGHG EHORZ E\ S7 IRU IM 3URRI RI &ODLP &RQVLGHU WKH H[SUHVVLRQ IRU UcMf UHSUHVHQWLQJ WKH SUREDELOLW\ RI SURGXFLQJ IURP SDUHQWV L DQG M 7KLV LV JLYHQ E\ 5HZULWLQJ WKH DERYH H[SUHVVLRQ ZH JHW

PAGE 132

&RQVLGHU WKH IROORZLQJ LQHTXDOLWLHV IRU U? ULOcO a[f A 7I2 [f VLQFH _L_\ f Uf8, L Af Uf< a[f VLQFH M
PAGE 133

:H ZLOO QRZ SURYH WKDW WKH ERXQG LV DFKLHYDEOH WKDW LV WKH PLQLPXP RI 4 LV DFWXDOO\ S< /HPPD 7KH PLQLPXP HOHPHQW RI 4 LV SQ< IRU S 3URRI &RQVLGHU WKH SUREDELOLW\ RI SURGXFLQJ WKH VWULQJ IURP SDUHQWV 1O DQG 1O %\ DSSO\LQJ FURVVRYHU WKH RQO\ SRVVLEOH FKLOG ZH FDQ JHW LV DJDLQ 1O +HQFH WKH RQO\ ZD\ ZH FDQ JHW D LV WR PXWDWH DOO WKH ELWV 7KHQ WKH SUREDELOLW\ RI JHWWLQJ D IURP WKHVH WZR SDUHQWV LV S< 7KXV U1BAf S< 6R WKH PLQLPXP RI 0 LV DFWXDOO\ S< +HQFH E\ XVLQJ &ODLP WKH ORZHU ERXQG JLYHQ LQ /HPPD LV WLJKW 4(' )LQDOO\ ZH FDQ GHULYH DQ XSSHU ERXQG RQ WKH PLQLPXP QXPEHU RI LWHUDWLRQV UHTXLUHG IRU D GHVLUHG OHYHO RI FRQILGHQFH &RUROODU\ 7KH VXIILFLHQW QXPEHU RI LWHUDWLRQV UHTXLUHG WR ILQG DQ RSWLPDO VROXWLRQ ZLWK D GHVLUHG OHYHO RI FRQILGHQFH LV ERXQGHG DERYH E\ ,Q f ,Q S
PAGE 134

/HPPD 7KH PLQLPXP HOHPHQW RI PDWUL[ 4 LV ERXQGHG EHORZ E\ SfQ\ IRU IM 3URRI :H ZLOO ILUVW SURYH D FODLP &ODLP DQG WKHQ FRPELQH LW ZLWK &ODLP WR DFKLHYH WKH GHVLUHG UHVXOW &ODLP 7KH PLQLPXP HOHPHQW RI PDWUL[ 0 LV ERXQGHG EHORZ E\ OSf< IRU S 3URRI RI &ODLP &RQVLGHU WKH H[SUHVVLRQ IRU UcMf UHSUHVHQWLQJ WKH SUREDELOLW\ RI SURGXFLQJ IURP SDUHQWV L DQG M 7KLV LV JLYHQ E\ 77n2 a; \a L < R $fMNf QOMOL [ N O 5HZULWLQJ WKH DERYH H[SUHVVLRQ ZH JHW &RQVLGHU WKH IROORZLQJ LQHTXDOLWLHV IRU U? ; ; 0 [f A + a;f 6LQFH L f 8O &f U_r bf VLQFH M f \a L < Q SL B$LMN N ;7_ VLQFH $r A r f
PAGE 135

WZR UHSUHVHQW WKH FKLOGUHQ &RPELQLQJ f f f DQG f ZH JHW U f LMY n 0BA> L BAfUMr ‘ A f§Rf§R ;f7f ;7 ;7 f )LQDOO\ VLPSOLI\LQJ f ZH JHW Uf /AWL +HQFH VLQFH 7fr Uf OSf< 7KLV SURYHV &ODLP %\ FRPELQLQJ &ODLP DQG &ODLP ZH JHW 4/M OSfQ< ZKHUH Q LV DV GHILQHG LQ &ODLP DQG WKLV SURYHV /HPPD 4(' :H ZLOO QRZ SURYH WKDW WKH ERXQG LV DFKLHYDEOH WKDW LV WKH PLQLPXP RI 4 LV DFWXDOO\ OSf< IRU S /HPPD 7KH PLQLPXP HOHPHQW RI 4 LV OSfQ< IRU S 3URRI &RQVLGHU WKH SUREDELOLW\ RI SURGXFLQJ WKH VWULQJ IURP SDUHQWV DQG %\ DSSO\LQJ FURVVRYHU WKH RQO\ SRVVLEOH FKLOG ZH FDQ JHW LV DJDLQ +HQFH WKH RQO\ ZD\ ZH FDQ JHW D LV QRW WR PXWDWH DQ\ RI WKH ELWV 7KHQ WKH SUREDELOLW\ RI JHWWLQJ D IURP WKHVH WZR SDUHQWV LV OSf< 7KXV Uf OSf< 6R WKH PLQLPXP RI 0 LV DFWXDOO\ OSf< +HQFH E\ XVLQJ &ODLP WKH ORZHU ERXQG JLYHQ LQ /HPPD LV WLJKW 4(' )LQDOO\ ZH FDQ GHULYH DQ XSSHU ERXQG RQ WKH PLQLPXP QXPEHU RI LWHUDWLRQV UHTXLUHG IRU D GHVLUHG OHYHO RI FRQILGHQFH

PAGE 136

&RUROODU\ 7KH VXIILFLHQW QXPEHU RI LWHUDWLRQV UHTXLUHG WR ILQG DQ RSWLPDO VROXWLRQ ZLWK D GHVLUHG OHYHO RI FRQILGHQFH LV ERXQGHG DERYH E\ ,Q f ,Q PLQO Sf
PAGE 137

%HIRUH ZH ILQG WKH RSWLPDO VROXWLRQ WR 3UREOHP ZH ZLOO VWDWH WKUHH WKHRUHPV WKDW ZH ZLOO XVH WR ILQG WKH RSWLPDO 7KHRUHP =DQJZLOO f $ GLIIHUHQWLDEOH IXQFWLRQ K ( f§! ( LV SVHXGRFRQFDYH LI 9K[ff\[f LPSOLHV K\f K[f $ IXQFWLRQ K LV WHUPHG SVHXGRFRQYH[ LI K LV SVHXGRFRQFDYH 'HILQLWLRQ $ IXQFWLRQ K ( f§! ( LV FDOOHG TXDVLFRQFDYH LI JLYHQ [? [ H (Q IRU DQ\ K[ f[f PLQ>K[nf K[f@ $ IXQFWLRQ K LV TXDVLFRQYH[ LI K LV TXDVLFRQFDYH $Q\ SVHXGRFRQFDYH IXQFWLRQ LV TXDVLFRQFDYH 7KHRUHP %D]DUDD DQG 6KHWW\ f /HW 6 EH D QRQHPSW\ SRO\KHGUDO VHW LQ ( DQG OHW I ( f§! ( EH TXDVLFRQYH[ DQG FRQWLQXRXV RQ 6 &RQVLGHU WKH SUREOHP WR PD[LPL]H I[f VXEMHFW WR [ H 6 7KHQ WKHUH H[LVWV DQ RSWLPDO VROXWLRQ [r WR WKH SUREOHP ZKHUH [f LV DQ H[WUHPH SRLQW RI 6 7KHRUHP 7KH RSWLPDO VROXWLRQ RI 3UREOHP LV [f SfQrf f 3URRI :H ZLOO ILUVW VKRZ WKDW W LV SVHXGRFRQFDYH IRU IL[HG Q 7KH SDUWLDO GHULYDWLYH RI W ZLWK UHVSHFW WR S LV JLYHQ EHORZ GWSQf B OQ GMQ\Sn GS SfOQ SQ
PAGE 138

,W LV FOHDU WKDW IRU IHDVLEOH YDOXHV RI S DQG IRU IL[HG Q f LV DOZD\V QHJDWLYH 6HOHFW WZR IHDVLEOH SRLQWV [\ H 0 VXFK WKDW \ [ Df ZKHUH D LV SRVLWLYH &OHDUO\ [ DQG \ ZLOO VDWLVI\ 9K[ff\[f ,W ZLOO VXIILFH WR VKRZ WKDW K[f K\f KROGV :H KDYH WR VKRZ WKDW OQO f OQO6f OQO SQ7f f OQ>O S DfQ\@ f f LV HTXLYDOHQW WR SQ\ S DfQ7 $VVXPH f LV QRW FRUUHFW 7KHQ OQSDf OQSf ZKLFK LV D FRQWUDGLFWLRQ +HQFH WKH FODLP LV WUXH 6R W LV SVHXGRFRQFDYH IRU IL[HG Q %\ GHILQLWLRQ W LV TXDVLFRQFDYH DQG W LV TXDVLFRQYH[ IRU IL[HG Q ,QVWHDG RI VROYLQJ 3UREOHP ZH ZLOO VROYH 3UREOHP ZKLFK LV GHILQHG EHORZ )L[ Q VXFK WKDW Q Q WKHQ 3UREOHP f PD[ WSQff VXEMHFW WR S Q Qf Qf Q LQWHJHU

PAGE 139

6LQFH WSQf LV TXDVLFRQFDYH WSQff LV TXDVLFRQYH[ 7KH FRQVWUDLQW VHW LV D QRQn HPSW\ FRPSDFW SRO\KHGUDO VHW 7KHQ E\ 7KHRUHP WKH VROXWLRQ WR WKLV SUREOHP ZLOO RFFXUV DW WKH H[WUHPH SRLQWV 7KH VHW KDV WZR H[WUHPH SRLQWV QRf DQG Qf &OHDUO\ WKH PLQLPXP RFFXUV DW Qff 1RZ ZH KDYH WR VKRZ WKDW WSfQf WS?QOf ,W ZLOO VXIILFH WR VKRZ WKDW Srf< SrfQ !< f $VVXPH f LV QRW FRUUHFW 7KHQ Q\ Q Of\ ZKLFK LV D FRQWUDGLFWLRQ 7KHQ WSrQf WS?QOf 7KLV SURYHV WKDW WKH PLQLPXP ZLOO RFFXU DW Q +HQFH WKH VROXWLRQ WR 3UREOHP LV WSrQrf f 4('

PAGE 140

&+$37(5 /($51,1* ',63$7&+,1* 58/(6 )25 6&+('8/,1* 86,1* 6,08/$7,21 2YHUYLHZ ,Q SUHYLRXV FKDSWHUV ZH WULHG WR PRWLYDWH WKH QHHG IRU DQ LQWHOOLJHQW 'HFLVLRQ 6XSSRUW 6\VWHP '66f WKDW LV DEOH WR OHDUQ DGDSWLYHO\ ,Q WKLV FKDSWHU ZH VKRZ KRZ PDFKLQH OHDUQLQJ PHWKRGV FDQ EH LQWHJUDWHG ZLWKLQ D VLPXODWLRQ HQYLURQPHQW WR VFKHGXOH 7KH KRSH LV WKDW WKLV DSSURDFK ZLOO UHOLHYH WKH FRPSOH[ VHDUFK QHHGHG ZLWK D SXUH VLPXODWLRQ PRGHO DQG HQDEOH RQH WR DYRLG WKH QHHG WR DFTXLUH QHZ NQRZOHGJH XVLQJ WLPH FRQVXPLQJ $, NQRZOHGJHDFTXLVLWLRQ DSSURDFKHV 7KH V\VWHP ZLOO WHDFK LWVHOI KRZ WR UXQ WKH HQYLURQPHQW 1RWH WKDW WKLV DSSURDFK EHDUV VRPH VLPLODULW\ WR SHUWXUEDWLRQ DQDO\VLV LQ WKDW FKDQJHV DUH PDGH DV WKH VLPXODWLRQ SURJUHVVHV +RZHYHU QR REMHFWLYH IXQFWLRQ LV QHHGHG DQG QR JUDGLHQWV DUH HVWLPDWHG )XUWKHUPRUH ZH SHUPLW D PRUH IOH[LEOH VLPXODWLRQ HQYLURQPHQW ZKHUH LQIHUHQFH GULYHV GHFLVLRQV QRW ULJLG UXOHV VXFK DV TXHXLQJ GLVFLSOLQHVf 7KH PDLQ SDUDGLJP VKLIW RIIHUHG LQ RXU VWXG\ LV WKH H[SOLFLW LQFRUSRUDWLRQ RI LQWHOOLJHQW REMHFWV LQ WKH VLPXODWLRQ HQYLURQPHQW 7KHVH REMHFWV FDQ GUDZ ERWK GHGXFWLYH DQG LQGXFWLYH LQIHUHQFHV WR LPSURYH WKH SURFHVV DV WKH VLPXODWLRQ SURJUHVVHV ,Q DGGLWLRQ WKHVH REMHFWV FDQ DOWHU WKH YHU\ QDWXUH RI WKH HQYLURQPHQW )RU H[DPSOH ZH SHUPLW WKH GLVSDWFKHU WR G\QDPLFDOO\ FKDQJH WKH TXHXH GLVFLSOLQH

PAGE 141

7R LOOXVWUDWH WKLV DGDSWLYH OHDUQLQJ SURFHVV D VLPSOH VLPXODWLRQ HQYLURQPHQW LV FRQVLGHUHG 6WDQGDUG GLVSDWFKLQJ UXOHV DUH VHOHFWHG XVLQJ D NQRZOHGJHEDVH %DVHG XSRQ D SHUIRUPDQFH PHDVXUH VXSSOLHG E\ D XVHU D OHDUQLQJ GHYLFH IRUPV D QHZ NQRZOHGJHn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fV SHUIRUPDQFH 2WKHU REMHFWV OLNH TXHXHV MREV VHUYHUV HWFf UHDFW DV WKH\ DUH GHVLJQHG DQG DV FKDQFH GLFWDWHV )LJXUH VKRZV DQ H[DPSOH WKDW LOOXVWUDWHV WKLV DSSURDFK ,W LV D VLPSOH VHWWLQJ FRQVLVWLQJ RI SDUDOOHO PDFKLQHV ZLWK GLIIHUHQW UDWHV -REV MRE REMHFWVf HQWHU D TXHXH 48(8( D TXHXH REMHFWf (DFK MRE LV VWDPSHG ZLWK LWV HQWU\ WLPH DQG GXH GDWH 'XH GDWHV DUH JHQHUDWHG UDQGRPO\ XVLQJ D XQLIRUP GLVWULEXWLRQ

PAGE 142

)LJXUH *$ %DVHG /HDUQLQJ 6\VWHP 3HUIRUPDQFH )HHGEDFN -RE RXW LQ D 6LPXODWLRQ (QYLURQPHQW

PAGE 143

:KHQHYHU D VHUYHU REMHFW VHUYHUV DUH PDUNHG 6, 6 6 6 6f LV IUHH D GLVSDWFKHU REMHFW 'Of GHFLGHV ZKLFK MRE LQ WKH TXHXH ZLOO EH UHOHDVHG IRU VHUYLFH 7KH GLVSDWFKHU LV DQ H[DPSOH RI DQ LQWHOOLJHQW REMHFW ,QWHOOLJHQFH LV H[KLELWHG E\ GHFLVLRQ PDNLQJ 'HFLVLRQ PDNLQJ PD\ EH WKH UHVXOW RI DOJRULWKPLF SURFHVVHV WDEOH ORRNXSV LQIHUHQFH RU RWKHU SURFHVVHV VXFK DV IOLSSLQJ D FRLQf :KHQ D V\VWHP LV EHLQJ VWXGLHG E\ VLPXODWLRQ PHWKRGV WKH GHFLVLRQPDNLQJ REMHFWV DUH WKH IRFXV RI WKH UHVHDUFKHUfV DWWHQWLRQ 7KH UHVHDUFKHU PXVW GHFLGH KRZ GHFLVLRQV DUH WR EH PDGH WR RSWLPL]H WKH V\VWHPfV SHUIRUPDQFH ,Q WKH DEVHQFH RI WKHRUHWLFDO JXLGDQFH RU FRPSXWLQJ WLPH OLPLWDWLRQV IRU 13 KDUG SUREOHPVf GHFLGLQJ KRZ GHFLVLRQV DUH WR EH PDGH WR RSWLPL]H D V\VWHPfV SHUIRUPDQFH LV D WLPHFRQVXPLQJ WDVN RIWHQ LQYROYLQJ ODUJH QXPEHUV RI FDUHIXOO\ GHVLJQHG H[SHULPHQWV +HUH LV SUHVHQWHG D PDFKLQH OHDUQLQJ DSSURDFK WKDW ZLOO HQDEOH WKH LQWHOOLJHQW REMHFWV WR OHDUQ KRZ WR PDNH EHWWHU GHFLVLRQV ,QWHOOLJHQW REMHFWV ZLOO EH HQGRZHG ZLWK D NQRZOHGJHEDVH DQG OHDUQLQJ FRPSRQHQW ,Q )LJXUH WKH GLVSDWFKHU REMHFW RZQV D NQRZOHGJH EDVH .EDVH f DQG D OHDUQLQJ HOHPHQW FDOOHG *$f :KHQ D VHUYHU EHFRPHV LGOH DQG WKH LQSXW TXHXH LV QRW HPSW\ WKH GLVSDWFKHU XVHV DQ LQIHUHQFH SURFHVV ZLWK KLV NQRZOHGJH EDVH WR GHFLGH ZKLFK MRE WR URXWH WR WKH LGOH VHUYHU 6HUYHUV RI WKH VDPH YDULHW\ DUH DVVXPHG WR EH DEOH WR SHUIRUP WKH VDPH DFWLYLWLHV EXW PD\ GR VR ZLWK GLIIHUHQW UDWHV $OVR WKHLU EUHDNGRZQ DQG UHSDLU UDWHV PD\ EH

PAGE 144

GLIIHUHQW ,Q JHQHUDO VHUYHUV FDQ EH HQGRZHG ZLWK D KRVW RI GLIIHUHQW DWWULEXWHV 7KH VHUYHUV LQ )LJXUH DUH DVVXPHG WR EH RI WKH VDPH YDULHW\ EXW KDYH GLIIHUHQW VHUYLFH UHSDLU DQG EUHDNGRZQ UDWHV :KHQ D VHUYHU FRPSOHWHV D MRE WKH MRE PRYHV WR DQ HYDOXDWLRQ HOHPHQW (9$/f 7KH HYDOXDWLRQ FRPSRQHQW FDQ EH D VLPSOH FRVW PRGHO D PRGHO PHDVXULQJ WKH V\VWHPV SHUIRUPDQFH EDVHG RQ YDULRXV SHUIRUPDQFH HOHPHQWV RU DQ LQIHUHQFH DJDLQVW D NQRZOHGJH EDVH WKDW FDSWXUHV PDQDJHPHQWfV FRPSOH[ ZD\ RI WUDGLQJ RII PXOWLSOH DQG VRPHWLPHV FRQIOLFWLQJ REMHFWLYHV 7KH HYDOXDWLRQ FRPSRQHQW SURYLGHV D IHHGEDFN PHFKDQLVP WR WKH OHDUQLQJ FRPSRQHQW 3HULRGLFDOO\ WKH OHDUQLQJ FRPSRQHQW XSGDWHV WKH NQRZOHGJH EDVH WR UHIOHFW WKH UHVXOWV RI SDVW GHFLVLRQV DQG WKHLU LPSDFW RQ WKH V\VWHPfV SHUIRUPDQFH *HQHWLF /HDUQLQJ DQG ,QIHUHQFH 7KH OHDUQLQJ FRPSRQHQW LV D FODVVLILHU V\VWHP EDVHG RQ D *HQHWLF $OJRULWKP *$f ,Q SDUWLFXODU LW HPSOR\V WKH 0LFKLJDQ DSSURDFK +ROODQG f %HORZ DUH GHVFULEHG WKH VSHFLILFV RI WKH UXOH VWUXFWXUH LQIHUHQFH SURFHVV DQG OHDUQLQJ PHWKRG $Q LQLWLDO NQRZOHGJH EDVH LV HLWKHU UDQGRPO\ JHQHUDWHG RU SURYLGHG E\ WKH XVXDO NQRZOHGJHDFTXLVLWLRQ PHWKRGV $V GHFLVLRQV DUH PDGH WKH MREV DUH WDJJHG E\ WKH NQRZOHGJH XVHG LQ WKHLU VHOHFWLRQ $IWHU WKH MREV DUH SURFHVVHG DQG WKH V\VWHPfV SHUIRUPDQFH HYDOXDWHG IRU WKLV MRE WKH UHVSRQVLEOH NQRZOHGJH LV FUHGLWHG ZLWK SHUIRUPDQFH ZKLFK PD\ EH JRRG RU SRRUf 3HULRGLFDOO\ WKH FXPXODWLYH SHUIRUPDQFH RI HDFK SLHFH RI NQRZOHGJH LV XVHG WR IRUP D QHZ NQRZOHGJH EDVH XVLQJ UHSURGXFWLRQ FURVVRYHU DQG PXWDWLRQ RSHUDWRUV E\ WKH

PAGE 145

*$ 7KURXJK WKLV VXUYLYDORIWKHILWWHVW DSSURDFK ZH VKRZ WKDW WKH VXFFHVVLYH JHQHUDWLRQV RI NQRZOHGJH WHQG WR LPSURYH WKHLU SHUIRUPDQFH $ UXOH LV GHILQHG XVLQJ FRQMXQFWLRQV RI 1'79 WUXWK YDOXHV +HUH 1'79 VWDQGV IRU WKH QXPEHU RI GLVSDWFKLQJ UXOH WUXWK YDOXHV GHVFULEHG EHORZf 7KH ILUVW WUXWK YDOXH LV RI WKH IRUP 6HUYHUB,' L f ZKLFK HYDOXDWHV WR 758( RU )$/6( +HUH PHDQV HTXDO WR (DFK UXOH LV DVVRFLDWHG ZLWK D SDUWLFXODU VHUYHU 7KH UHPDLQLQJ 1'79 WUXWK YDOXHV KDYH WKH IROORZLQJ VWUXFWXUH -2% GBUXOHf RU r f ZKHUH GBUXOHf LV D VWDQGDUG KHXULVWLF GLVSDWFKLQJ UXOH ,W FDQ EH WKRXJKW RI DV D IXQFWLRQ WKDW UHWXUQV D MRE LG WKDW VDWLVILHV LWV UHTXLUHPHQWV :KHQ PXOWLSOH MREV VDWLVI\ WKH FULWHULRQ WLHV DUH EURNHQ E\ D )LUVW&RPH )LUVW6HUYHG GHFLVLRQ ,I QR MRE VDWLVILHV WKH FULWHULRQ D 18// YDOXH LV UHWXUQHG 7KH DUJXPHQWV IRU WKH IXQFWLRQ DUH VXSSUHVVHG EXW PD\ LQFOXGH REMHFWV IURP WKH HQYLURQPHQW 7KXV LI D VSHFLILHG -2% LV LGHQWLFDO WR WKH MRE VHOHFWHG E\ WKH GLVSDWFK UXOH WKH H[SUHVVLRQ HYDOXDWHV WR 758( r f LV 758( IRU DQ\ -2% 7KHUH DUH PDQ\ KHXULVWLF GLVSDWFKLQJ UXOHV %ODFNVWRQH 3KLOOLSV DQG +RJJ f 7KH GLVSDWFKLQJ UXOHV LQFOXGHG LQ WKLV VWXG\ DUH )&)6 )LUVW&RPH )LUVW6HUYHG 6, 6KRUWHVW ,PPLQHQW RSHUDWLRQ /, /RQJHVW ,PPLQHQW RSHUDWLRQ

PAGE 146

)52 )HZHVW 5HPDLQLQJ 2SHUDWLRQV 052 0RVW 5HPDLQLQJ 2SHUDWLRQV 65 6KRUWHVW 5HPDLQLQJ SURFHVVLQJ WLPH /5 /RQJHVW 5HPDLQLQJ SURFHVVLQJ WLPH 72, PLQLPXP 7RWDO 2SHUDWLRQV GLYLGHG E\ ,PPLQHQW GXUDWLRQ 537, PLQLPXP 5HPDLQLQJ 3URFHVVLQJ 7LPH GLYLGHG E\ ,PPLQHQW WLPH *7: *UHDWHVW 7RWDO :RUN ('' (DUOLHVW 'XH 'DWH 067 0LQLPXP 6ODFN 7LPH 6/$&.231 /HDVW 6/$&. SHU 23HUDWLR1 -65 -RE 6ODFN 5DWLR 6LQFH WKHUH ZDV RQO\ RQH RSHUDWLRQ LQ WKH VLPSOH PRGHO )LJXUH f WKH IROORZLQJ DUH HTXLYDOHQW WR )&)6 LQ RXU HQYLURQPHQW 6, /, )52 052 65 /5 537, DQG *7: )RU 1'79 VHW WR D IHZ H[DPSOHV RI UXOHV DUH 6HUYHU-' 6f$rf$ -2% (''f f 7KLV UXOH HYDOXDWHV WR 758( LI VHUYHU 6 LV ,'/( DQG -2% LV WKH MRE ZLWK WKH HDUOLHVW GXH GDWH 6HUYHUB,' 6 f$rf$rf 7KLV UXOH HYDOXDWHV WR 758( IRU DQ\ -2% LI WKH LGOH VHUYHU LV 6, 6HUYHU-' 6 f $ -2% 067ff $ -2% (''ff 7KLV UXOH HYDOXDWHV WR 758( LI VHUYHU 6 LV ,'/( DQG -2% LV WKH MRE ZLWK WKH HDUOLHVW GXH GDWH $1' WKH PLQLPXP VODFN WLPH

PAGE 147

$ VHUYHU LV UDQGRPO\ SLFNHG IURP WKH OLVW RI LGOH VHUYHUV ,I D UXOH HYDOXDWHV WR 758( IRU WKLV LW PD\ YRWH IRU WKH MRE LW VHOHFWHG 7KLV LQIHUHQFH SURFHVV UHOLHV RQ ELGGLQJ $OO UXOHV FRRSHUDWH RQ WKH VHOHFWLRQ RI HDFK MRE 2WKHU H[DPSOHV RI ELGGLQJ V\VWHPV FDQ EH IRXQG LQ 6KDZ f 6KDZ f $IWHU DOO WKH YRWHV DUH WDOOLHG D MRE LV SLFNHG UDQGRPO\ DFFRUGLQJ WR WKH YRWLQJ IUHTXHQFLHV 7KLV LQIHUHQFH SURFHVV DOORZV IRU FDVHV ZKHUH DQ RSWLPDO VWUDWHJ\ PD\ EH D PL[HG VWUDWHJ\f ,I QR MRE UHFHLYHV D YRWH D -2% LV VHOHFWHG UDQGRPO\ 7KH VHOHFWHG MRE LV WKHQ WDJJHG ZLWK DOO UXOHV WKDW YRWHG IRU LW 7KHVH UXOHV ZLOO UHFHLYH IHHGEDFN DV WKH MRE H[LWV WKH V\VWHP 7KH IHHGEDFN LV UHIOHFWHG LQ WKH UXOHfV SHUIRUPDQFH IURP ZKLFK ILWQHVV PHDVXUHV DUH FRPSXWHG ,GHDOO\ WKH SHUIRUPDQFH PHDVXUH ZLOO UHIOHFW PDQDJHPHQWfV HYDOXDWLRQ RI DQG WUDGHRIIV EHWZHHQ D QXPEHU RI FULWHULD ,Q WKLV VWXG\ QR PDQDJHPHQW H[LVWV WR VXSSO\ HYDOXDWLRQ FULWHULD ,Q WKH DEVHQFH RI VXFK FULWHULD WKH V\VWHPfV SHUIRUPDQFH RQ HDFK MRE LV PHDVXUHG E\ D VHUYLFH TXDOLW\ FULWHULD %HIRUH ZH GHVFULEH WKH SHUIRUPDQFH IXQFWLRQ ZH ZLOO LQWURGXFH VRPH QRWDWLRQ /HW 3 nfEH WKH SHUIRUPDQFH RI UXOH L RQ MRE M 3L EH WKH DWWDLQHG SHUIRUPDQFH RQ MRE M 3L EH WKH DYHUDJH ILWQHVV RI UXOH L 7KDW LV Sc 3Xf ZKHUH LV WKH VHW RI MREV IRU ZKLFK UXOH L YRWHG LQ EHWZHHQ WR OHDUQLQJ HSLVRGHV IM EH WKH ILWQHVV RI UXOH L Uc EH WKH WLPH UHOHDVH WLPH RI MRE M W6 EH WKH WLPH WKH VHUYLFH VWDUWV RQ MRE M

PAGE 148

WHM EH WKH WLPH ZKHQ VHUYLFH HQGV RQ MRE M DQG LW OHDYHV WKH V\VWHP DQG W EH WKH FXUUHQW WLPH 7KH SHUIRUPDQFH RI WKH NQRZOHGJH EDVH RQ DQ\ MRE LV JLYHQ E\ WH WV 3M f§ WHU M M $ UXOHfV WRWDO SHUIRUPDQFH LV DQ DYHUDJH RYHU WKH SHUIRUPDQFH IRU HDFK MRE WDJJHG E\ WKH UXOH ,WV ILWQHVV LV FRPSXWHG E\ I S a 7KLV PHDVXUH RI ILWQHVV VHYHUHO\ SHQDOL]HV SRRU SHUIRUPDQFH 7KH H[SRQHQW LV FDOOHG WKH HPSKDVLV FRHIILFLHQW 7KH ILWQHVV PHDVXUH LV XVHG E\ *$ WR UDQGRPO\ VHOHFW UXOHV IURP WKH FXUUHQW NQRZOHGJH EDVH 7KH KLJKHU D UXOHfV ILWQHVV WKH PRUH OLNHO\ LW ZLOO EH FKRVHQ IRU PDWLQJ RU VXUYLYDO 'XULQJ NQRZOHGJH EDVH XSGDWLQJ D UXOH LV VHOHFWHG UDQGRPO\ EDVHG RQ WKH ILWQHVV PHDVXUHV $ VHFRQG UXOH LV WKHQ VHOHFWHG UDQGRPO\ DJDLQ EDVHG RQ ILWQHVV EXW ZLWK WKH UHVWULFWLRQ WKDW LW KDV WKH VDPH 6HUYHU ,' 2QFH VHOHFWHG WKH WZR UXOHV HLWKHU PDWH ZLWK WKH FURVVRYHU SUREDELOLW\f RU VXUYLYH 0DWLQJ LQYROYHV UDQGRPO\ SLFNLQJ D FURVVRYHU SRLQW LH UDQGRPO\ SLFNLQJ D WUXWK YDOXH WHUP DW FRQMXQFWLRQ SRVLWLRQ 1'79f DQG VZDSSLQJ WKH WUXWK YDOXH WHUPV RI WKH WZR UXOHV VWDUWLQJ DW WKLV SRLQW )RU H[DPSOH WKH WZR PDWLQJ SDUHQWV 6HUYHUB,' 6 f $ -2% 0674f $ -2% (''ff 6HUYHUB,' 6 f $ -2% )&)64f $ -2% 6,4f

PAGE 149

PLJKW FURVVRYHU DW WKH VHFRQG WUXWK YDOXH WHUP DIWHU WKH 6HUYHUB,' WHUPf \LHOGLQJ WKH FKLOGUHQ 6HUYHU-' 6 f $ -2% 0674f $ -2% 6,ff 6HUYHU-' 6 f $ -2% )&)6f! $ -2% (''ff 6XUYLYLQJ SDUHQWV RU QHZO\ FUHDWHG FKLOGUHQ UXOHV DUH WKHQ VXEMHFW WR PXWDWLRQ ZLWK D PXWDWLRQ SUREDELOLW\f ,I VHOHFWHG IRU PXWDWLRQ D UDQGRPO\ SLFNHG WUXWK YDOXH WHUP DW SRVLWLRQ 1'79 LV UDQGRPO\ DOWHUHG WR DQRWKHU WHUP )RU H[DPSOH LI WKH UXOH 6HUYHU-' 6 f $ -2% 067ff $ -2% 6,ff ZHUH VHOHFWHG IRU PXWDWLRQ DQG PXWDWLRQ ZHUH WR RFFXU DW WKH ILUVW WUXWK YDOXH WHUP DIWHU WKH 6HUYHU-' WHUPf WKH IROORZLQJ PLJKW UHVXOW 6HUYHU-' 6 f $ -2% (''ff $ -2% 6,ff 7KLV SURFHVV FRQWLQXHV XQWLO D QHZ NQRZOHGJH EDVH RI WKH VDPH VL]H LV FUHDWHG 5HVWULFWLRQV ZHUH DGGHG VR WKDW WKHUH ZDV DQ HTXDO QXPEHU RI UXOHV LQ WKH NQRZOHGJH EDVH IRU HDFK 6HUYHU-' 7KLV GLG QRW LPSDFW WKH VROXWLRQ 7KH FURVVRYHU DQG PXWDWLRQ RSHUDWRUV DUH VLPLODU LQ LGHD WR WKH LQWHJHU DSSURDFK RI )UH\ DQG 6ODWH f %RWK RSHUDWRUV DUH UHVWULFWHG WR WKH GLVSDWFK UXOH IUDJPHQWV 7KDW LV RQO\ UXOHV ZLWK WKH VDPH VHUYHU PD\ PDWH +RZHYHU DQ HQFRGLQJ VFKHPH RQ WKH DOSKDEHW ^` FRXOG KDYH EHHQ HPSOR\HG DV IROORZV $VVXPH WKHUH DUH P VHUYHUV G GLVSDWFKLQJ UXOH DQG WKH QXPEHU RI FRQMXQFWV LV 1'79 7KHQ WRWDO QXPEHU RI SRVVLEOH FRPELQDWLRQV RI UXOHV LV JLYHQ E\ 1'79 ff 1'79G DQG JLYHQ WKDW ZH GLVWLQJXLVK EHWZHHQ VHUYHUV WRWDO QXPEHU RI UXOHV ZH QHHG WR VHDUFK LV

PAGE 150

1'79 P H L [ )LQDOO\ E\ XVLQJ D VWULQJ RI OHQJWK ORJ ? 1'79 P n nG 9 ( L n \ ZH FDQ UHSUHVHQW DOO SRVVLEOH VWUDWHJLHV )RU LPSOHPHQWDWLRQDO FRQYHQLHQFH ZH HPSOR\HG WKH LQWHJHU FRGLQJ ,I D UXOH LV WR EH PXWDWHG D WUXWK YDOXH FRPSRQHQW LV UDQGRPO\ FKRVHQ DQG WKHQ UHSODFHG ZLWK D UDQGRPO\ FKRVHQ GLIIHUHQWf GLVSDWFK UXOH ZKLFK PD\ EH WKH ZLOGFDUG rf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f XVLQJ &7 7KH IROORZLQJ REMHFWV ZHUH GHILQHG &/$66 'HVFULSWLRQ 1RGH /LVW 1RGH REMHFWV DUH XVHG WR OLQN RWKHU REMHFWV $ OLVW LV D VWULQJ RI OLQNHG REMHFWV

PAGE 151

4XHXH $ TXHXH REMHFW LV D OLVW IROORZLQJ VRPH RUGHULQJ ILUVW LQ ILUVW RXW ),)2 ODVW LQ ODVW RXW /,)2 RU 6257(' RQ DQ DWWULEXWHf WKDW PD\ EH DWWDFKHG WR VHUYHUV RWKHU TXHXHV DQG D GLVSDWFKHU 6HUYHU $ VHUYHU REMHFW RSHUDWHV RQ MREV 5XOH $ UXOH REMHFW HQFRGHV D UXOH LQ WKH NQRZOHGJH EDVH ODQJXDJH .EDVH $ NEDVH REMHFW LV D FROOHFWLRQ RI UXOHV 'LVSDWFKHU $ GLVSDWFKHU REMHFW GHFLGHV ZKLFK MRE ZLOO EH VHOHFWHG DQG SURFHVVHG E\ DQ LGOH VHUYHU (YHQW $Q HYHQW REMHFW LV SODFHG RQ WKH IXWXUH HYHQW OLVW IHOf DQG LQGLFDWHV ZKDW LV WR EH GRQH DQG ZKHQ -RE $ MRE REMHFW PRYHV WKURXJK WKH VLPXODWLRQ HQYLURQPHQW )LJXUH VKRZV WKH UHODWLRQVKLSV DPRQJ WKH YDULRXV FODVVHV RI REMHFWV ,Q &rr D )5,(1' REMHFW KDV DFFHVV WR DQRWKHU REMHFWfV SULYDWH PHWKRGV DQG GDWD ILHOGVf 7KH VLPXODWLRQ HQYLURQPHQW LV VWUXFWXUHG DV IROORZV )LUVW DOO VHUYHU REMHFWV TXHXHV GLVSDWFKHUV DQG WKH IXWXUH HYHQWV OLVW IHOf DUH GHFODUHG 1H[W WKH IHO LV LQLWLDOL]HG ZLWK WKH ILUVW MRE DUULYDO WKH ILUVW EUHDNGRZQ IRU HDFK VHUYHU WKH VLPXODWLRQ WHUPLQDWLRQ DQG WKH WLPH RI WKH ILUVW XSGDWH RI WKH NQRZOHGJH EDVH

PAGE 152

)LJXUH &ODVV +LHUDUFK\

PAGE 153

)LQDOO\ WKH WRSRORJ\ RI WKH VLPXODWLRQ HQYLURQPHQW LV GHILQHG 7KH IROORZLQJ DFWLYLWLHV DUH SHUIRUPHG LQ D VLPSOH HYHQWRULHQWHG ORRS DV WKH VLPXODWLRQ H[HFXWHV (9(17 $55,9$/ 6(783B67$57 6(783B(1' 6(59(5B67$57 6(59(5B(1' 'HVFULSWLRQ $ QHZ MRE LV FUHDWHG DQG D QH[W DUULYDO JHQHUDWHG -REV DUH FUHDWHG ZLWK YDULRXV DWWULEXWHV SULRULW\ GXH GDWH HWFf ,I WKHUH LV DQ ,'/( VHUYHU WKHQ WKH GLVSDWFKHU LV DVNHG WR VHOHFW D TXHXH PHPEHU 7KLV PHPEHU LV UHPRYHG OLQNHG WR WKH VHUYHU DQG D 6(783B(1' LV VFKHGXOHG LI QR VHUYHU EUHDNGRZQ ZLOO RFFXU GXULQJ VHWXS 5HOHYDQW VWDWLVWLFV DUH XSGDWHG DQG D 6(59(5B67$57 HYHQW LV VFKHGXOHG $ 6(59(5-(1' HYHQW LV VFKHGXOHG LI QR EUHDNGRZQ ZLOO RFFXU GXULQJ VHUYLFH 6WDWLVWLFV DUH XSGDWHG 5HOHYDQW VWDWLVWLFV DUH XSGDWHG 7KH MRE LV WUDQVIHUUHG IURP WKH LQVHUYLFH EXIIHU WR WKH VHUYHG MREV EXIIHU ,I WKH SUHFHGLQJ TXHXH VWLOO KDV PHPEHUV D 6(783B67$57 LV VFKHGXOHG $Q $55,9$/ WR WKH QH[W TXHXH LV VFKHGXOHG LI RQH H[LVWV 2WKHUZLVH D /($9( HYHQW LV VFKHGXOHG

PAGE 154

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

PAGE 155

6HUYHUB,' 6, f $ r f $ r f 6HUYHUB,' 6, f $ -2% f§ )&)6f f $ r f 6HUYHU-' 6, f $ -2% f§ (''f f $ r f 6HUYHUB,' 6, f $ -2% f§ 6,f f $ r f 6HUYHUB,' 6, f $ r f $ -2% )&)6f f 6HUYHUB,' 6, f $ r f $ -2% (''f f 6HUYHUB,' 6, f $ r f $ -2% 6,f f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

PAGE 156

([SHULPHQW DQG 5HVXOWV 7R LOOXVWUDWH WKH LGHD SUHVHQWHG KHUH )LJXUH ZDV GHFODUHG DQG WKUHH VLPXODWLRQV ZHUH UXQ IRU WLPH XQLWV HDFK 5XQQLQJ WKH V\VWHP ORQJHU SURGXFHG QR GLVFHUQLEOH FKDQJH LQ SHUIRUPDQFH 7KH WKUHH UXQV LQFOXGH D *$ OHDUQLQJ UXQ SOXV WZR EDVHOLQH UXQV )&)6 GLVSDWFKLQJ DQG ('' GLVSDWFKLQJ RQO\f $ QHZ NQRZOHGJH EDVH ZDV JHQHUDWHG HYHU\ WLPH XQLWV ,Q WLPH XQLWV DQ DSSUHFLDEOH QXPEHU RI MREV ZHUH GLVSDWFKHG DQG VHUYLFHG UHVXOWLQJ LQ UHDVRQDEOH HVWLPDWHV RI WKH YDOXH RI LQGLYLGXDO UXOHV7KH VLPXODWLRQ VWDUWHG DW WLPH ]HUR 7KHUH ZDV QR LQLWLDO ZDUPLQJXS SHULRG 7KH VSHFLILF VFHQDULR LPSOHPHQWHG LQ )LJXUH LV GHVFULEHG DV IROORZV 7KH GLVSDWFKHU NQRZV DQ H[LVWLQJ MREfV DUULYDO WLPH DQG GXH GDWH WKH OLVW RI LGOH VHUYHUV DQG WKH H[SHFWHG VHUYLFH WLPH RI HDFK VHUYHU 'LIIHUHQW VHUYHUV PD\ KDYH GLIIHUHQW VSHHGV EXW WKH H[SHFWHG VHUYLFH WLPH IRU HDFK MRE LV WKH VDPH IRU D JLYHQ VHUYHU ZKLFK DFFRXQWV IRU WKH HTXLYDOHQFH EHWZHHQ /, DQG 6, DQG EHWZHHQ /5 DQG 65 GLVSDWFKLQJ UXOHVf 1HLWKHU IXWXUH DUULYDO WLPHV RU DFWXDO VHUYLFH WLPHV DUH NQRZQ E\ WKH GLVSDWFKHU %RWK DUULYDO DQG VHUYLFH SURFHVVHV DUH LQGHSHQGHQW 3RLVVRQ $OO DUULYDOV EUHDNGRZQV UHSDLUV DQG VHUYLFH WLPHV DUH H[SRQHQWLDO UDQGRP YDULDEOHV 6HUYHU YDOXHV DUH 6HUYHU 6(59,&( 077) 0775 6, 6 6 6 6

PAGE 157

DQG WKH DUULYDO UDWH ZDV SHU WLPH XQLW 1'79 ZDV VHW WR LQ WKLV FDVH EXW LV QRW OLPLWHG WR WZR LQ JHQHUDO ,Q )LJXUH WKH SRSXODWLRQfV DYHUDJH SHUIRUPDQFH
PAGE 158

7R DQVZHU WKLV TXHVWLRQ WKH DUULYDO UDWH ZDV LQFUHDVHG WR MREV SHU WLPH XQLW 7KLV UHVXOWHG LQ D )&)6 SHUIRUPDQFH RI DERXW b GRZQ IURP b $V FDQ EH VHHQ LQ )LJXUH WKH V\VWHP SHUIRUPHG EHVW ZLWK OHDUQLQJ ('' VWLOO GRPLQDWHG )&)6 :KLOH WKHVH GRPLQDWLRQV DUH FOHDU WKH V\VWHP VHHPV PXFK PRUH VHQVLWLYH WR UDUH HYHQWV OLNH PDFKLQH EUHDNGRZQV ZKLFK FDXVHG WKH VKDUS GRZQZDUG VSLNHV $OVR DW VHYHUDO SRLQWV RWKHU WKDQ WKH LQLWLDO IHZ SHULRGVf ('' KDG D EHWWHU SHUIRUPDQFH WKDQ GLG WKH V\VWHP XVLQJ OHDUQLQJ 7KH ILQDO NQRZOHGJH EDVH FRQWDLQHG VRPHWLPHV PXOWLSOH FRSLHV RIf WKH IROORZLQJ UXOHV 6HUYHU ,' 6,f $ -2% )&)62f $ -2% -652f 6HUYHUB,' 6f $ -2% )&)62f $ -2% 6/$&.231f 6HUYHUB,' 6f $ -2% )&)62f $ -2% 72,ff 6HUYHU-' ,, &' e R &2 LL )&)62f $ -2% 067ff 6HUYHUBO' 6f $ -2% )&)62f $ -2% -652f 6HUYHU ,' ,, 44 R FG ,, -65ff $ -2% 0672f 6HUYHU ,' 6f $ -2% )&)62f $ -2% (''2f 'LVFXVVLRQ RI 5HVXOWV )LJXUH VKRZV WKDW WKH NQRZOHGJH EDVH HYROYHG WR JLYH DQ DYHUDJH SHUIRUPDQFH WKDW GRPLQDWHG WKH WZR EDVHOLQH UXQV XVLQJ WKH )&)6 DQG ('' UXOHV UHVSHFWLYHO\ /HDUQLQJ SURGXFHG GLVSDWFKLQJ WKDW DFKLHYHG DQ b SHUIRUPDQFH DSSUR[LPDWHO\f ('' OHG WR b SHUIRUPDQFH DSSUR[LPDWHO\f ZKLOH )&)6 KDG D b SHUIRUPDQFH DSSUR[LPDWHO\f

PAGE 159

:LWK D PRUH FRQJHVWHG HQYLURQPHQW )LJXUH VKRZV WKDW WKH NQRZOHGJH EDVH HYROYHG WR JLYH DQ DYHUDJH SHUIRUPDQFH WKDW VWLOO GRPLQDWHG WKH WZR EDVHOLQH UXQV XVLQJ WKH )&)6 DQG ('' UXOHV UHVSHFWLYHO\ /HDUQLQJ SURGXFHG GLVSDWFKLQJ WKDW DFKLHYHG D b SHUIRUPDQFH DSSUR[LPDWHO\f ('' OHG WR b SHUIRUPDQFH DSSUR[LPDWHO\f ZKLOH )&)6 KDG D b SHUIRUPDQFH DSSUR[LPDWHO\f 7KH UHVXOWLQJ NQRZOHGJH EDVH LV UDWKHU LQWHUHVWLQJ $OPRVW HYHU\ UXOH KDV $ )&)6 FRQMXQFW DQG D GXH GDWH UHODWHG PHDVXUH ,W LV NQRZQ WKDW )&)6 LV D JRRG KHXULVWLF WR PLQLPL]H WKH YDULDQFH RI WKH DYHUDJH ZDLWLQJ WLPH DQG LQ WKLV VWXG\ EHFDXVH RI WKH ZD\ GXH GDWHV ZHUH DVVLJQHG GXH GDWH UHODWHG UXOHV KDG DQ LQKHUHQW VXSHULRULW\ RYHU )&)6 :H DUH XQDEOH WR SURYH LW DQDO\WLFDOO\ EXW WKH OHDUQLQJ HOHPHQW VHHPV WR KDYH GLVFRYHUHG WKHVH FKDUDFWHULVWLFV DQG XVH GXH GDWH UHODWHG KHXULVWLFV IRU PHDQ SHUIRUPDQFH DQG )&)6 IRU UHGXFLQJ YDULDELOLW\ 5HIHU WR RXU FODLP DERYH DERXW ('' SHUIRUPLQJ EHWWHU WKDQ )&)6 2QH TXHVWLRQ WKDW DULVHV LV 6LQFH WKH SHUIRUPDQFH PHDVXUH LV QRW D IXQFWLRQ RI GXH GDWH ZK\ GRHV ('' RXWSHUIRUP )&)6" 7KH DQVZHU OLHV LQ WKH FKRLFH RI SHUIRUPDQFH PHDVXUH 5HFDOO WKDW WH WV 3M f§ WH U M M ,Q WKLV PRGHO D JLYHQ VHUYHU ZLOO SURFHVV DQ\ MRE SUHVHQWHG WR LW DW D JLYHQ WLPH ZLWK WKH VDPH VHUYLFH WLPH UHJDUGOHVV RI ZKDW GLVSDWFKLQJ UXOH LV XVHG 2I FRXUVH WKH VHUYLFH WLPH LWVHOI LV D UDQGRP YDULDEOHf 6R DW D JLYHQ GLVSDWFK GHFLVLRQ WVVM WKH WRWDO WLPH VSHQW LQ VHUYLFH E\ MRE M ZLOO EH WKH VDPH IRU DQ\ VHOHFWHG MRE

PAGE 160

1RZ ZH FDQ UHZULWH WRWDO WLPH VSHQW LQ V\VWHP DV WKH VXP RI WLPH VSHQW LQ TXHXH W6M UMI DQG WVVM +HQFH WKH SHUIRUPDQFH PHDVXUH IRU MRE M VHOHFWHG E\ WKH GLVSDWFKHU ZLOO EH WV U WVV M M M )&)6 ZLOO DOZD\V VHOHFW WKH MRE VXEVFULSWHG E\ IFIVf ZLWK WKH ORZHVW Uc YDOXH ('' PD\ VHOHFW WKLV MRE EXW PD\ VHOHFW DQRWKHU ZLWK DQ HDUOLHU GXH GDWH ZLWK D ODWHU DUULYDO WLPHf 6XEVFULSW WKLV MRE XVLQJ HGG 7KHQ ,Q WKLV HQYLURQPHQW DQG %XW WKHQ WAIFIV EH LV A W66IFIF WV/O8> UH-G WVVHGf 7KH GHQRPLQDWRU RI SHUIRUPDQFH XQGHU )&)6 GLVSDWFKLQJ ZLOO EH JUHDWHU WKDQ RU HTXDO WR WKH GHQRPLQDWRU RI SHUIRUPDQFH XQGHU ('' 7KXV DQG (''fV SHUIRUPDQFH ZLOO EH EHWWHU WKDQ WKH SHUIRUPDQFH RI )&)6

PAGE 161

)LJXUH KDV VHYHUDO SRLQWV RI LQWHUHVW ZRUWK GLVFXVVLQJ )LUVW ZKLOH V\VWHP SHUIRUPDQFH GHFUHDVHV ZLWK FRQJHVWLRQ WKH UHVXOWV XQGHU OHDUQLQJ VHHP WR GHFUHDVH DW D VORZHU UDWH DQG KHQFH LPSURYH UHODWLYH WR )&)6 DQG ('' $ VHFRQG SRLQW RI LQWHUHVW LV WKDW WKH V\VWHP ZDV YHU\ VHQVLWLYH WR UDUH HYHQWV OLNH PDFKLQH EUHDNGRZQV 7KLV LV WUXH IRU HDFK W\SH RI FRQWURO ZKHWKHU IRU )&)6 ('' RU OHDUQLQJ $Q REYLRXV LQVLJKW LV WR LQFOXGH IDFWRUV LQWR WKH UXOH VWUXFWXUH WKDW FRXOG DQWLFLSDWH WKHVH W\SHV RI RFFXUUHQFHV )RU H[DPSOH D WUXWK YDOXH RI WKH IRUP WLPHBVLQFHBODVWBEUHDNGRZQ  ;;; f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

PAGE 162

HQDEOHG XV WR VWXG\ TXHVWLRQ f DQG WR UHPRYH SRVVLEOH REIXVFDWLRQ GXH WR PDMRU GLIIHUHQFHV LQ WKH VHUYHUV $W WKH VWDUW RI D VLPXODWLRQ UXQ DQ H[SHFWHG VHUYLFH UDWH ZDV VHW E\ GUDZLQJ D XQLIRUP UDQGRP QXPEHU IURP > @ 7KH DFWXDO VHUYLFH WLPHV ZHUH H[SRQHQWLDO ZLWK WKLV YDOXH 7KH VHFRQG FKDQJH ZDV WR LQFUHDVH WKH IDLOXUH UDWH ZKLFK KHOSHG LQ VWXG\LQJ 4XHVWLRQ f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fW LGHQWLI\ VLJQLILFDQW IHDWXUHV 7KLV OHG WR DVNLQJ ZKHWKHU D SXUHO\ UDQGRP SROLF\ ZRXOG SHUIRUP DV ZHOO DV *$ OHDUQLQJ ,Q WKH VHFRQG UXQ WKH *$ OHDUQLQJ PHWKRG ZDV FRPSDUHG WR WKH GLVSDWFKLQJ UXOH 6,52 6HUYLFH ,Q 5DQGRP 2UGHU 7KH UHVXOWV DUH VKRZQ LQ )LJXUH *$ OHDUQLQJ SHUIRUPV DW DERXW WKH b OHYHO ZKHUH 6,52 RQO\ SHUIRUPV DW WKH b OHYHO

PAGE 163

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r r FRVLQH r 7LPH f f ZKHUH 5$7( LV WKH YDOXH XVHG HDUOLHU *$ OHDUQLQJ VWLOO GRPLQDWHV 7KH IRXU UXQV JLYH 5XQ 3HUIRUPDQFH *$ /HDUQLQJ b )&)6 b ('' b 6,52 b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

PAGE 164

OHDUQLQJ RUGHU YHUVXV WKH RUGHU UHTXLUHG XQGHU WKH 6, UXOH ZKLFK LV NQRZQ WR PLQLPL]H IORZ WLPH LQ WKLV FDVHf 1RWH WKDW WKLV LV D SHUIRUPDQFH PHDVXUH GLIIHUHQW IURP WKDW XVHG LQ WKH UHVW RI WKLV SDSHU ,Q D VHULHV RI UXQV WKH QXPEHU RI MREV UDQJLQJ IURP WR f UHOHDVHG DQG WKH QXPEHU RI OHDUQLQJ F\FOHV UDQJLQJ IURP WR f ZDV YDULHG $OO JDYH VLPLODU UHVXOWV )LJXUH VKRZV WKH UHVXOWV RI D W\SLFDO UXQ +HUH ZH VKRZ MREV EHLQJ UHOHDVHG LQ HDFK RI OHDUQLQJ F\FOHV WKH ILUVW RI D F\FOH UXQf 1RWLFH WKDW WKH *$ OHDUQLQJ TXLFNO\ FRQYHUJHV WR WKH RSWLPDO SROLF\ )LJXUH VKRZV WKH VDPH HQYLURQPHQW UXQ ZLWK *$ OHDUQLQJ YHUVXV )&)6 ('' DQG 6,52 EDVHOLQHV *$ OHDUQLQJ RXWSHUIRUPHG HDFK

PAGE 165

XRLMVV6XFT MR SRMMJ S\ DDQ6LJ DD iXLXQH DJ DPLL FR FR FR FR &2 LPL+LLLLWWPPLWQWPLLPLQLQL++LL ZZ PQWWLQWQLQQPL ]R + ‘ 0 G &' 2 R &' 6G'G 38% 44+ 6$ 6XLXLHDT MR DQXQXXRMMRJ e DDQ£LJ DDD 6-2G fff999n999999 6XPV DJ DLPL FR FR LLLLLL+LL++WP++LL+LQLPQQ+++LQLPLLLL+LLLPL+8LLLLQL ‘]R +f A 0 &' R i R '

PAGE 166

,W U f f 7 U P f f f R Lr } ff9 f P Y\ fDrf !r ; $UIn i ,IU IYO UR 1 2Y@ 82 UR 9@ XR RR 2ZO UR XR UZM U 7LPH )LJXUH 5HYLVHG 6\VWHP 5HVXOWVf§2ULJLQDO 6HWWLQJ

PAGE 167

6XPDV >QXL6XRf§V>W"$8M\ XRVVLRM VQRXD6RLXRTXR1 [ LQ6LM r1/ FR FR FR FR /2 BQ m/2 FR FR FR FR FR FR FR HQ FR &M2 FR FR FR FR m/2 &2 FR fO 8 ,+ 8 + + + + W M 4 /r } } ;; .Z Y ; ," i! : t0 f f f f f f ‘ r f f } m r} Y[ D ;f6 Yrr f6 SY rYY MQY r\ (V} IUR IUn2 2 i 2 &' 6XPDV >HXL6XTf§XRSDDSV XLRSXH\ VD 6XLXMUHDT  DLQ6LM 2+ ,6 6XLXUHHA RRRRRFA???[RFFFF????YF! DPLL FR FAR FR FR FR FR FR &A2&A2&A2&2&2&2&2&A/&2&2&2 R UR ‘‘W" 0 G &' R % i R &'

PAGE 168

&2 /2 FYL &' f &' 2 /2 f f M:0&AZ f ::: f f :$9$:AAA:$9 9AY\ 9999n 999999 YYYY ‘ \ ? L L  9  V W A A A W A 0 0 0 W , W I0f§I+ +W+ +0 +.+ + ,, , O8+O &2 /2 &2 &2 /2 Wf§ &2/2A&2Wf§ &2/2 &?-2-2-2r-&?-&2&2&2&2&2 &2 /2 /2 /HDUQLQJ (SLVRGHV /HDUQLQJ 637 )LJXUH /HDUQLQJ YV 637 5XOHf§37RWDO )ORZ 7LPH )LJXUH /HDUQLQJ YV )&)6 ('' 6,5237RWDO )ORZ 7LPH

PAGE 169

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f LQYHQWRU\ (DFK TXHXH LV FRQWUROOHG E\ D GLVSDWFKHU ZKR SRVVHVVHV VRPH NQRZOHGJH RI WKH HQYLURQPHQW -REV DUH GLVSDWFKHG DFFRUGLQJ WR WKH GLVSDWFKHUfV NQRZOHGJH DW WKH WLPH RI GLVSDWFK $IWHU D MRE LV FRPSOHWHG LW LV HYDOXDWHG ZLWK UHVSHFW WR WKH SHUIRUPDQFH PHDVXUH VSHFLILHG DQG WKLV LQIRUPDWLRQ LV VHQW EDFN WR WKH GLVSDWFKHU WR XVH IRU XSGDWLQJ LWV NQRZOHGJH EDVH )LJXUH VXPPDUL]HV WKLV LGHD

PAGE 170

)ORZVKRS )LJXUH $ )ORZVKRS ZLWK ,QWHOOLJHQW 'LVSDWFKHUV 21 X!

PAGE 171

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f DQG IRU D UHDO YDOXHG DWWULEXWH OLNH 3URFHVVLQJ7LPH DQ DWRP PD\ VSHFLI\ 3URFHVVLQJ7LPH f 6XFK DWRPV DUH UHIHUUHG WR DV 6LPSOH $WRPV &RPSRXQG DWRPV DUH FRPSULVHG RI GLVMXQFWLRQ RI 6LPSOH $WRPV RI WKH VDPH DWWULEXWH )RU H[DPSOH 3URFHVVLQJ7LPH Y 3URFHVVLQJ7LPH f LV D &RPSRXQG $WRP ZKHUH Y LV WKH ORJLFDORU RSHUDWRU &HUWDLQ DWWULEXWHV PD\ EH MREUHODWHG LQ WKH VHQVH WKDW WKH\ PD\ HYDOXDWH WR GLIIHUHQW YDOXHV IRU GLIIHUHQW MREV LQ WKH TXHXHV 7KH HYDOXDWLRQ RI DQ DWRP RI VXFK DQ DWWULEXWH GHILQHV D VXEVHW RI MREV ZKRVH UHODWHG DWWULEXWH YDOXHV DUH LQ WKH FXUUHQW YDOXH VHW RI WKH DWRP $WRPV WKDW DUH QRW MREUHODWHG VHOHFW WKH FXUUHQW VHW RI WKH MREV DV WKH

PAGE 172

VXEVHW 7KH\ GR QRW GLVWLQJXLVK DPRQJ MREV UDWKHU WKH\ ORRN DW ZKHWKHU FHUWDLQ HQYLURQPHQW SDUDPHWHUV DUH VDWLVILHG RU QRW $ 3UHGLFDWH LV D IXQFWLRQ WKDW VHOHFWV D VXEVHW RI WKH FXUUHQW MREV ZLWK UHVSHFW WR LWV VHOHFWLRQ FULWHULD 6WDQGDUG GLVSDWFKLQJ UXOHV OLNH 637 ('' HWF DUH PRGHOOHG DV SUHGLFDWHV 7KRXJK VLPSOH GLVSDWFKLQJ UXOHV GR QRW VHOHFW PRUH WKDQ RQH MRE H[FHSW IRU WLHVf 3UHGLFDWHV UHWDLQ WKH IOH[LELOLW\ IRU UHSUHVHQWLQJ RWKHU PRUH FRPSOH[ DOJRULWKPV IRU GLVSDWFKLQJ 7UDGLWLRQDO 3URGXFWLRQ 5XOHV RU ,)7+(1 UXOHV FDOOHG &$BUXOHV LQ RXU WHUPLQRORJ\f DUH XVHG WR PRGHO YDULRXV NQRZQ VFKHGXOLQJ KHXULVWLFV 7KHVH PD\ EH VWUDWHJLHV WKDW KXPDQ H[SHUWV KDYH IRXQG XVHIXO RU KHXULVWLFV SXEOLVKHG LQ OLWHUDWXUH NQRZQ WR ZRUN ILQH IRU VRPH HQYLURQPHQWV $OO FRQMXQFWV UHWXUQ D WUXWK YDOXH ZKLFK PD\ WDNH YDOXHV IURP WKH VHW ^7UXH )DOVH 8QNQRZQ` $Q DWRP HYDOXDWHV WR 7UXH LI WKH FXUUHQW V\VWHP DWWULEXWH YDOXH LV LQ WKH YDOXH VHW RI WKH $WRP 3UHGLFDWHV DOZD\V UHWXUQ WUXH VLQFH WKH\ FDQ DOZD\V VHOHFW D MRE JLYHQ WKDW WKH TXHXH LV QRW HPSW\ $ &$BUXOH HYDOXDWHV WR 7UXH LI LWV FRQGLWLRQ SDUW HYDOXDWHV WR 7UXH %1) )RUP RI WKH 5XOH /DQJXDJH > @ DQ\ SDUDPHWHU OLVWHG LQ WKH VTXDUH EUDFNHWV LV RSWLRQDO ^ ` DQ\ SDUDPHWHU OLVWHG LQ WKH EUDFHV KDV WR EH VSHFLILHG WUXWK YDOXH RQH RI WUXH IDOVH XQNQRZQ

PAGE 173

UXOH $1' FRQMXQFWf FRQMXQFW DWRP SUHGLFDWH FDMUXOH DWRP VLPSOHBDWRP FRPSRXQGBDWRP FRPSRXQG DWRP 25VLPSOHBDWRPcf VLPSOHBDWRP YDOXH OLQHDUBDWWULEXWH YDOXHf QRPLQDOBDWWULEXWH YDOXHf SUHGLFDWH I;!< ZKHUH
PAGE 174

ORJLFDOBH[SUHVVLRQ DWRP >ORJLFDOBXQDU\BRSU@DWRP > ^ORJLFDOBELQDU\BRSU` ORJLFDOBH[SUHVVLRQ@ ORJLFDOBRSU ORJLFDOBXQDU\ RSU RQH RI 127f ORJLFDOBELQDU\BRSU RQH RI t$1'f 25f YDOXH QXPEHU V\PERO DWWULEXWH OLQHDUBDWWULEXWH QRPLQDOBDWWULEXWH IXQFWLRQBRIDWWULEXWHf IXQFWLRQBRIDWWULEXWHf I'f§}; ZKHUH LV WKH GRPDLQ RI WKH DWWULEXWH DQG ; LV VRPH QRPLQDO RU FRQWLQXRXV YDOXHG VHW 5XOH /HYHO 5HFRPELQDWLRQ 2SHUDWRUV )RXU RSHUDWRUV DUH GHILQHG IRU JHQHWLF UHFRPELQDWLRQ FURVVRYHU ;f PXWDWLRQ Sf JHQHUDOL]DWLRQ *f DQG VSHFLDOL]DWLRQ 6f &URVVRYHU DQG PXWDWLRQ DUH UXOH OHYHO RSHUDWRUV

PAGE 175

LH WKH\ RSHUDWH RQ HQWLUH UXOHV *HQHUDOL]DWLRQ DQG VSHFLDOL]DWLRQ DUH GHILQHG WR RSHUDWH RQ FHUWDLQ FRQMXQFWV ZLWKLQ UXOHV $ FRQMXQFW OHYHO PXWDWLRQ RSHUDWRU LV DOVR GHILQHG $OO WKHVH RSHUDWRUV ZLWK WKH H[FHSWLRQ RI PXWDWLRQ DUH EDVHG RQ WKH ILWQHVVYDOXHV RI WKH FRQMXQFWV LQ WKH UXOHV FRQVLGHUHG IRU UHFRPELQDWLRQ &URVVRYHU 7KLV LV DQ DGDSWDWLRQ RI WKH XQLIRUP FURVVRYHU RSHUDWRU XVHG ZLWK ELQDU\ FRGHG *$V *LYHQ WZR SDUHQWV GLIIHUHQW &RQMXQFWV DUH SUREDELOLVWLFDOO\ VHOHFWHG IRU FURVVRYHU EDVHG RQ WKHLU ILWQHVV YDOXHV ZLWK KLJKHU ILWQHVV &RQMXQFWV KDYLQJ JUHDWHU SUREDELOLW\ RI SDUWLFLSDWLQJ LQ WKH FURVVRYHU )RU HDFK 5XOH WKH QXPEHU RI VHOHFWLRQV LV DSSUR[LPDWHO\ KDOI WKH QXPEHU FRQMXQFWV LQ WKH UXOH HDFK VHOHFWLRQ LV PDGH SUREDELOLVWLFDOO\ EDVHG RQ WKH FRQMXQFW ILWQHVV YDOXHV DQG WKXV WKH VDPH FRQMXQFW PD\ EH VHOHFWHG PRUH WKDQ RQFHf &RQVLGHU WKH SDUHQWV 5 Ff $ & $ &MM $ &L &, DQG &L FKRVHQ IRU &URVVRYHUf 5 Ff $ &$ Ff $ &M &M DQG &M FKRVHQ IRU &URVVRYHUf &KLOGUHQ PD\ EH IRUPHG LQ WZR ZD\V +HUH &KLOGc LV REWDLQHG IURP 5XOHc DIWHU UHSODFLQJ WKH VHOHFWHG FRQMXQFWV ZLWK WKRVH IURP WKH RWKHU SDUHQW &KLOGM LV VLPLODUO\ REWDLQHG

PAGE 176

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` EH WKH VHW RI YDOXHV WKDW LW FDQ WDNH /HW D EH DQ DWRP GHILQHG RQ WKDW DWWULEXWH /HW $ ^ D DN ` $ F 9 EH WKH FXUUHQW ELQGLQJ RI WKH DWRP D /HW ,9, Q DQG ,$, N /HW 8ONf N H 1 EH D GLVFUHWH XQLIRUP GLVWULEXWLRQ WKDW UHWXUQV LQWHJHUV EHWZHHQ DQG N /HW 8DEf DE f 0 EH D FRQWLQXRXV XQLIRUP GLVWULEXWLRQ WKDW UHWXUQV UHDO QXPEHUV EHWZHHQ D DQG E

PAGE 177

,I WKH DWWULEXWH LV QRPLQDO LW ZLOO EH DVVXPHG WKDW Y LV D VHW RI QRPLQDO YDOXHG HOHPHQWV DQG VR LV D ,I WKH DWWULEXWH LV FRQWLQXRXV WKHQ LW ZLOO EH DVVXPHG WKDW Yc >YLRYLZKHUH 9_fYL f 5 DQG VR LV Dc 0XWDWLRQ 0XWDWLRQ LV RQH RI WKH UDQGRP RSHUDWRUV WKDW LV XVHG WR MXPS VWDUW WKH FXUUHQW SRSXODWLRQ +HUH LQ WKLV FRQWH[W PXWDWLRQ RSHUDWRU UDQGRPO\ VHOHFWV DQ HOHPHQW LQ WKH FXUUHQW ELQGLQJ DQG DOWHUV LW DFFRUGLQJ WR WKH W\SH RI WKH HOHPHQW 0RUH IRUPDOO\ LW LV GHILQHG DV IROORZV /HW L 8ONf NH1 /HW DcH$ WKHQ SDf $^Dc`X^9M` ZKHUH M 8OQf DQG YH9n M ([DPSOH /HW TXHXHBOHQJWK EH DQ DWWULEXWH /HW 9 ^ >@ ` /HW TXHXHBOHQJWKBT EH DQ DWRP GHILQHG RQ TXHXHBOHQJWK /HW $ ^ >@ >@ ` ,I ZH FRQVLGHU WKLV DV SDUW RI D SURGXFWLRQ UXOH WKHQ LW UHDGV DV LI TXHXHBOHQJWKBTO 9 TXHXHBOHQJWKBTO f 0XWDWLRQ RSHUDWRU STXHXHBOHQJWKBTOf ZLOO SLFN RQH RI WKH HOHPHQWV LQ $ DQG DOWHU LW UDQGRPO\ E\ FKHFNLQJ WKH GRPDLQ $VVXPH >@ LV SLFNHG WR EH FKDQJHG DQG DVVXPH QHZ ORZHU DQG XSSHU ERXQGV DUH DQG 7KHQ WKH UHVXOWLQJ VHW $ LV ^ >@ ` 8 ^ >@ ` ZKLFK HTXDOV ^ >@ ` ([DPSOH /HW VHUYHUBUDWH EH DQ DWWULEXWH /HW \ ^ ` /HW VHUYHUBUDWHBV EH QRPLQDO DWRP GHILQHG RQ VHUYHUBUDWH /HW D ^ ` $JDLQ DV D SURGXFWLRQ UXOH WKLV UHDGV DV LI VHUYHU UDWH V 9 VHUYHU UDWH VL

PAGE 178

7KHQ SVHUYHUBUDWHBVOf ZLOO SLFN RQH RI WKH HOHPHQWV LQ $ DQG DOWHU LW DFFRUGLQJ WR WKH XQLIRUP GLVWULEXWLRQ GHILQHG RQ WKH GRPDLQ $VVXPH LV VHOHFWHG WR EH FKDQJHG DQG DVVXPH LV VHOHFWHG IURP WKH GRPDLQ 7KHQ VHW $ ^`X^` ^` *HQHUDOL]DWLRQ *HQHUDOL]DWLRQ LV SHUIRUPHG ZKHQ WKH VWUHQJWK RI WKH DWRP LV OHVV WKHQ D VSHFLILHG WKUHVKROG 1RWH WKDW D ORZ VWUHQJWK FDQ RFFXU LI WKH DWRP LV WRR VSHFLILF WR PDWFK DQ\ VWDWH VHHQ VR IDU $ JHQHUDOL]DWLRQ ZLOO UHOD[ WKH WHPSRUDO FRQVWUDLQW LPSRVHG RQ WKH DWRP /HW D EH FRQWLQXRXV WKHQ *Df $ ^D` Y ZKHUH Yn fD DQG YnF9/HW D EH ? n O f O f L L f§ QRPLQDO WKHQ *Df $ ^Y` ZKHUH Yc $ ([DPSOH &RQVLGHU WKH VDPH DWWULEXWH RI ([DPSOH RI PXWDWLRQ WKHQ *TXHXHBOHQJWKBTOf ZLOO SLFN RQH RI WKH HOHPHQWV DQG PDNH LWV XSSHU DQG ORZHU ERXQG VWULFWO\ ORRVHU 7KH UHVW LV H[DFWO\ WKH VDPH DV WKH PXWDWLRQ HOHPHQW ,Q WKH QRPLQDO FDVH D QHZ HOHPHQW IURP WKH GRPDLQ ZLOO EH DGGHG WR WKH VHW $ 6SHFLDOL]DWLRQ &RQWUDU\ WR WKH VLWXDWLRQ PHQWLRQHG DERYH VRPHWLPHV WKH VWUHQJWK RI DQ DWRP PD\ EH WRR KLJK ZKLFK LV SRVVLEOH ZKHQ WKH FRQVWUDLQWV RQ WKH DWRP DUH WRR ORRVH LH LW LV WRR JHQHUDO 7KLV VLWXDWLRQ ZLOO OHDG WR RYHU JHQHUDOL]DWLRQ ZKLFK ZLOO RQ WKH ORQJ UXQ GHWHULRUDWH WKH DYHUDJH V\VWHP SHUIRUPDQFH LH LW ZLOO SURGXFH EDG UXOHV WKDW ILUH DOO WKH WLPH 7R DYRLG WKLV VLWXDWLRQ WKH VSHFLDOL]DWLRQ RSHUDWRU LV XVHG LI WKH VWUHQJWK LV KLJKHU WKDQ D WKUHVKROG /HW Y EH FRQWLQXRXV WKHQ *Df $^D ` ?n ZKHUH YnFD f /HW Y EH QRPLQDO ? Ln L f L L WKHQ *Df $^DL` ZKHUH DA$

PAGE 179

([DPSOH &RQVLGHU WKH DWWULEXWH PHQWLRQHG LQ H[DPSOH RI PXWDWLRQ WKHQ 6VHUYHUBUDWHBVOf ZLOO WDNH RXW RQH RI WKH HOHPHQWV LQ VHW $ ,Q WKH FRQWLQXRXV FDVH DQ HOHPHQW ZLOO EH SLFNHG UDQGRPO\ DQG WKH XSSHU DQG ORZHU ERXQGV ZLOO EH PDGH VWULFWO\ WLJKWHU ,QIHUHQFH 6WUDWHJLHV &RQVLGHU D UXOH 5M DV 5M &M $1' &M $1' $1' &QM (DFK &\ KHUH LV FDOOHG D FRQMXQFWf ,Q RUGHU WR IRUPDOL]H WKH LQIHUHQFH VWUDWHJ\ ZH GHILQH WKH IROORZLQJ 'HILQLWLRQ 5XOH 5M LV DFWLYH LI DOO &cM HYDOXDWH WR 7UXH LH LI HYDOXDWH&cMf 758( IRU DOO L O WR Q 'HILQLWLRQ 5XOH 5 LV FRQVLVWHQW LI LW LV DFWLYH DQG WKHUH LV DW OHDVW RQH FRPPRQ MRE YRWHG IRU E\ DOO WKH FRQMXQFWV FRQVWLWXWLQJ 5M LH LI HYDOXDWH&cMf 758( IRU DOO L O WR Q DQG $1' 9\f 18// ZKHUH 9\ VXEVHW RI MREV YRWHG IRU E\ FRQMXQFW 4 DQG 18// LV WKH QXOO VHW 'HILQLWLRQ $ UXOH JLYHV DFWXDO YRWHV LI LW LV FRQVLVWHQW $OO MREV YRWHG IRU E\ WKLV UXOH UHFHLYH DFWXDO YRWHV 'HILQLWLRQ $ FRQMXQFW DOZD\V JLYHV YLUWXDO YRWHV LI LW HYDOXDWHV WR WUXH 1RWH WKDW HYHQ WKRXJK 5XOH 5M PD\ QRW EH DFWLYH DQ\ &RQMXQFW &cM FDQ JLYH YLUWXDO YRWHV WR MREV DV ORQJ DV HYDOXDWHAf 758( 7KH HYDOXDWLRQ RI D UXOH SURFHHGV DV IROORZV )LUVW WKH DWRPV LQ WKH UXOH DUH HYDOXDWHG DQG LQWHUVHFWLRQ RI WKHLU YRWHV LV IRXQG ,I WKDW LV QXOO WKDQ WKH UXOH LV QRW

PAGE 180

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f SURFHHGV WKURXJK WKH HYDOXDWLRQ RI DOO WKH UXOHV LQ WKH NQRZOHGJH EDVH RI WKH FRQFHUQHG GLVSDWFKHU ,Q HYDOXDWLQJ D UXOH DOO WKH FRQMXQFWV LQ WKH UXOH DUH HYDOXDWHG ,I D FRQMXQFW HYDOXDWHV WR 758( LW \LHOGV D VHW RI MREV ZLWK YLUWXDO YRWHV $ UXOH LI IRXQG FRQVLVWHQW DIWHU HYDOXDWLRQ DOVR \LHOGV D VHW RI MREV ZLWK DFWXDO YRWHV 7KH FXPXODWLYH YRWH GLVWULEXWLRQ RI WKH MREV WR EH GLVSDWFKHG LV JHQHUDWHG DW WKDW SDUWLFXODU GHFLVLRQ SRLQW E\ XVLQJ DFWXDO YRWHV LI WKHUH H[LVWV DQ\ ,I WKHUH DUH QR FRQVLVWHQW UXOHV LH QR DFWXDO YRWHV WKH DIRUHPHQWLRQHG GLVWULEXWLRQ LV JHQHUDWHG E\ XVLQJ YLUWXDO YRWHV ,I WKHUH DUH QR YLUWXDO YRWHV WKHQ D GLVFUHWH XQLIRUP GLVWULEXWLRQ LV XVHG DV WKH YRWH GLVWULEXWLRQ $IWHU WKH FXPXODWLYH YRWH GLVWULEXWLRQ LV JHQHUDWHG D MRE LV VHOHFWHG UDQGRPO\ E\ XVLQJ WKDW GLVWULEXWLRQ %DVLFDOO\ WKH PRUH YRWHV D MRE JHWV WKH PRUH DUH WKH RGGV WKDW LW LV JRLQJ WR EH VHOHFWHG IRU SURFHVVLQJ

PAGE 181

&UHGLW $VVLJQPHQW /HW )&cMf EH WKH ILWQHVV RI WKH LnK &RQMXQFW 4M LQ 5XWHM :H GHILQH 2YHUDOO 5XOH )LWQHVV )5cf DV )5cf >e )&SZ@Z O Zf) f ZKHUH Z FRPHV IURP D ZHLJKW IXQFWLRQ FXUUHQWO\ DOO HTXDOf Z LV WKH LPSRUWDQFH JLYHQ WR WKH DYHUDJH FRQMXQFW ILWQHVVHV DQG ) LV WKH DYHUDJH VWUHQJWK DFTXLUHG E\ WKH UXOH WKURXJK LVVXLQJ DFWXDO YRWHV 3DUWLDO &UHGLW IRU &RQMXQFWV 6LQFH FRQMXQFWV PD\ JLYH 9LUWXDO 9RWHV HYHQ ZKHQ WKH DVVRFLDWHG UXOH LV QRW DFWLYH SDUWLDO FUHGLW LV DVVLJQHG WR LQGLYLGXDO FRQMXQFWV +HUH VLQFH WKH UXOH LV QRW DFWLYH WKH UXOH ILWQHVV )5Mf VKRXOG QRW LQFUHDVH SURSRUWLRQDWHO\ ZLWK WKH LQFUHDVH LQ DQ\ )&cMf 7KH IROORZLQJ FRPSHQVDWLRQ VFKHPH LV SURSRVHG $)L&MMf IYLUWXDO YRWHVf IRU VRPH IXQFWLRQ I ZKLFK PD\ EH GHILQHG DV RI YLUWXDO YRWHV DVVLJQHG E\ & WR WKH VHOFWHGMRE rWRWDORIYLUWXDOYRWHVUHFHLYHGE\WKHVHOHFWHGMRE ZKHUH IREM LV WKH SD\RII UHFHLYHG E\ WKH VHOHFWHG MRE 2QH VWUDWHJ\ PD\ EH JLYH WKH KLJKHVW FUHGLW WR D FRQVLVWHQW UXOH VRPHZKDW ORZHU IRU WKH DFWLYH EXW LQFRQVLVWHQW UXOH DQG WKH ORZHVW IRU WKH LQDFWLYH UXOH %HORZ LV DQ H[DPSOH RI WKLV VWUDWHJ\ LI 5_ LV FRQVLVWHQW LI 5 LV DFWLYH EXW QRW FRQVLVWHQW M LI 5 LV LQDFWLYH M

PAGE 182

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f XVHG LQ HTXDWLRQ f 7KH VHFRQG GLJLW VKRZV WLPHV WKH FURVVRYHU UDWH XVHG 7KH WKLUG DQG WKH IRXUWK GLJLW KROGV WLPHV WKH PXWDWLRQ UDWH XVHG 7KH GLJLW DIWHU WKH GRW KROGV WLPHV WKH FRQVWDQW N GHVFULEHG LQ HTXDWLRQ f 7KH ILUVW VHW RI FKDUDFWHUV H[SODLQ ZKHWKHU LQWHUPHGLDWH HYDOXDWLRQ SRLQWV DQG D FHUWDLQ YRWLQJ VFKHPH LV XVHG RU QRW 7KH VHFRQG VHW RI FKDUDFWHUV H[SODLQ LI WKH GHJHQHUDWH UXOHV ZHUH UHPRYHG LH D G LV SUHVHQWf DQG LI ILWQHVV EDVHG YRWLQJ LV XVHG LH D S LV SUHVHQWf ([SHULPHQW 6HW 2QH ,Q WKLV VHW RI H[SHULPHQWV ZH KDYH ORRNHG DW D WZR PDFKLQH IORZVKRS ZKHUH MREV DUULYH DFFRUGLQJ WR 3RLVVRQ SURFHVV ZLWK PHDQ 7KH SURFHVVLQJ WLPHV RI MREV DUH GUDZQ IURP D XQLIRUP GLVWULEXWLRQ EHWZHHQ DQG IRU 0DFKLQH DQG EHWZHHQ

PAGE 183

DQG IRU PDFKLQH WZR 7KH LQLWLDO NQRZOHGJH EDVH KDG UXOHV DQG FRQMXQFWV SHU UXOH FUHDWHG UDQGRPO\ 7KH REMHFWLYH IXQFWLRQ ZH WULHG WR PD[LPL]H ZDV WKH SHUFHQWDJH RI WLPH D MRE VSHQGV IRU VHUYLFH KHQFH PLQLPL]LQJ WKH SHUFHQWDJH RI WLPH LW VSHQGV ZDLWLQJ (DFK OHDUQLQJ HSLVRGH ZDV UXQ ZLWK DQ DYHUDJH RI WKRXVDQG MREV 7KH VLPXODWLRQ ZDV UXQ IRU KXQGUHG DQG ILIW\ OHDUQLQJ HSLVRGHV 7R FRPSDUH WKH HIIHFW RI OHDUQLQJ WKH V\VWHP ZDV DOVR UXQ E\ XVLQJ VLPSOH GLVSDWFKLQJ UXOHV LQFOXGLQJ )&)6 637 ('' DQG 51'0 )LJXUH GLVSOD\V WKH SHUIRUPDQFH RI WKH OHDUQLQJ V\VWHP FRPSDUHG WR WKH V\VWHPV ZLWK RQO\ VLPSOH GLVSDWFKLQJ UXOHV )LJXUH FOHDUO\ VKRZV WKDW WKH OHDUQLQJ V\VWHP LV SHUIRUPLQJ EHWWHU WKDQ )&)6 DQG DV JRRG DV 637 6R WKLV VXJJHVWV WKDW WKH UHVXOWLQJ NQRZOHGJH EDVH VKRXOG EH GRPLQDWHG E\ 637 RU HTXLYDOHQW UXOHV 2Q WKH FRQWUDU\ WKH UHVXOWLQJ NQRZOHGJH EDVH KDV FRQYHUJHG WR /37 DQG /537 7KH H[SODQDWLRQ LV TXLWH LQWHUHVWLQJ 2QH ZD\ WR PD[LPL]H WKH SHUFHQWDJH RI WLPH VSHQW IRU VHUYLFH LV WKDW WKH V\VWHP VKRXOG XVH 637 VR WKDW WKH UHPDLQLQJ MREV ZDLW OHVV DQG WKHLU ZDLWLQJ WLPHV DUH VKRUWHU ZKHQ FRPSDUHG WR XVLQJ /37 %XW WKLV UHTXLUHV D PRUH WKDQ RQH VWHS GHGXFWLRQ ZKLFK WKH V\VWHP LV XQDEOH WR GR \HW ,QVWHDG WKH V\VWHP VLQFH LW LV HYDOXDWHG RQ D SHU MRE EDVLV VHOHFWV WKH MRE WKDW KDV WKH ORQJHVW SURFHVVLQJ WLPH VR WKDW LW FDQ PD[LPL]H WKH SHUFHQWDJH RI WLPH LW VSHQW LQ WKH TXHXH $IWHU DOO LW LV EHLQJ HYDOXDWHG RQO\ RQ WKDW MRE FKRRVLQJ 637 ZLOO DFWXDOO\ PLQLPL]H WKH WLPH LW KDV VSHQW IRU SURFHVVLQJ %DVLFDOO\ WKLV REMHFWLYH IXQFWLRQ FDQ EH LQWHUSUHWHG DV PD[LPL]LQJ WKH GROODU YDOXH RI D MRE VLQFH PRVW RI WKH WLPH MREV WKDW UHTXLUH PRUH UHVRXUFHV ZLOO KDYH PRUH GROODU YDOXH IURP D FRVW DFFRXQWLQJ SRLQW RI YLHZ 6R WKH V\VWHP GRHV WKH ULJKW WKLQJ DQG FKRRVHV WKH MREV ZLWK WKH KLJKHVW GROODU YDOXH ILUVW

PAGE 184

7KLV LV FRQVLVWHQW ZLWK WKH UHVXOWV SUHVHQWHG LQ %ODFNVWRQH 3KLOOLSV DQG +RJJ f WKDW WKH YDOXH UHODWHG GLVSDWFKLQJ LV EDVLFDOO\ XVLQJ /37 RU /537 DQG ZLOO UHVXOW LQ KLJK :,3 DQG UHGXFHG WKURXJKSXW ([SHULPHQW 6HW 7ZR 7KH ILUVW VHW RI H[SHULPHQWV UHYHDOHG WKH IDFW WKDW ZKHQ WKH NQRZOHGJH EDVH FRQYHUJHG PRVW RI WKH UXOHV FRQVLVWHG RI PXOWLSOH FRSLHV RI WKH VDPH FRQMXQFWV DQG KDG VKRUW OHQJWKV LH QXPEHU RI FRQMXQFWV SHU UXOH ZHUH DURXQG WZR RU WKUHHf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c LV WKH IORZ WLPH RI MRE L DQG Q LV WKH QXPEHU RI MREV GLVSDWFKHG 7KH LGHD ZDV WR PLQLPL]H WKH DYHUDJH IORZ WLPH RI MREV SHU OHDUQLQJ HSLVRGH (DFK OHDUQLQJ HSLVRGH FRQVLVWHG RI DQ DYHUDJH RI WKRXVDQG MREV 7KH VLPXODWLRQ ZDV UXQ IRU WZR KXQGUHG

PAGE 185

OHDUQLQJ HSLVRGHV 7R FRPSDUH WKH HIIHFW RI OHDUQLQJ WKH V\VWHP ZDV DOVR UXQ E\ XVLQJ VLPSOH GLVSDWFKLQJ UXOHV LQFOXGLQJ )&)6 637 ('' DQG 51'0 )LJXUH GLVSOD\V WKH SHUIRUPDQFH RI WKH OHDUQLQJ V\VWHP FRPSDUHG WR WKH V\VWHPV ZLWK RQO\ VLPSOH GLVSDWFKLQJ UXOHV 0HDQ ZDLWLQJ WLPH LQ 4XHXH DQG PHDQ ZDLWLQJ WLPH LQ 4XHXH DUH GLVSOD\HG LQ )LJXUHV DQG UHVSHFWLYHO\ ([SHULPHQW 6HW 7KUHH 5HDOL]LQJ WKDW GLIIHUHQFHV LQ WKH SHUIRUPDQFH RI WKH EHVW UXOH 637f DQG WKH ZRUVW )&)6 RU (''f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

PAGE 186

0DFKLQH DQG EHWZHHQ DQG IRU PDFKLQH WZR WKXV LQFUHDVLQJ WKH FRHIILFLHQW RI YDULDWLRQ RI WKH SURFHVVLQJ WLPHV DQG WKH WUDIILF LQWHQVLW\ IDFWRU 7KH LQLWLDO NQRZOHGJH EDVH KDG WZHQW\ UXOHV DQG WKUHH FRQMXQFWV SHU UXOH FUHDWHG UDQGRPO\ 7KH REMHFWLYH IXQFWLRQ ZH WULHG WR PD[LPL]H ZDV ZKHUH )c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

PAGE 187

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f EXW PRVW RI WKH WLPH LW FRQYHUJHV WR D NQRZOHGJH EDVH ZKLFK LV DFWXDOO\ LUUHOHYDQW WR WKH SHUIRUPDQFH PDMRU DQG XVXDOO\ GHJHQHUDWH

PAGE 188

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f \Q VUL &Mf ZKHUH Uc DQG Fc DUH WKH PHDQ YDOXHV RI WKH RXWSXWV IRU WKH H[SHULPHQWV OLVWHG LQ WKH LWK URZ DQG WKH MK FROXPQ RI WKH WDEOHV

PAGE 189

7DEOH 3DLUHG W 6WDWLVWLFV QDY DQY QDYGS IFIV VSW QDQYG QDY DQY QDYGS 7DEOH S 9DOXHV QDY DQY QDYGS IFIV VSW QDQYG ( ( ( ( QDY ( ( ( ( DQY ( ( ( QDYGS ( (

PAGE 190

)LJXUH $YHUDJH 2EMHFWLYHf§6HW

PAGE 191

HQ U HQ 2n + IIO LU K 2n f§ &1 1 &1 1 &1 HQ HQ HQ HQ 2Q HQ HQ LUM TQ f§ HQ mU U }Q Wa L LU P QDQY QDY IHIV L f fff rrf VSW PGP )LJXUH $YHUDJH 2EMHFWLYHf§6HW

PAGE 192

7UI6r F 2f SA D UUT 2f FWT + UWf R F 2f F 2f , P 2f KR A /L /L /O /O 2Q 2Q

PAGE 193

V 9} f f IW rf f fff ff fff p ff n rnf f f 9 \ 9 $ f \ 9 ‘Y LQ YR P R UA A 1 0 U 7M ,7 ,7 Y& 2&LUYF62nV2FQ2&AAI RF V V R f§f FQ FQ P } 1 2n ?F FQ 7MALULYRYRFARRR12Y QDQY IFIV VSW PGP QDQY )LJXUH $YHUDJH :DLWLQJ 7LPH LQ 4XHXH 6HW

PAGE 194

QR 2n 1 La 1 ; 1 UI 2 HQ HQ Q& 2Q 1 LU \U P [ mQ Q& 12 21 &1 RF RF 2&n 2n R 2n IFIV VSW PGP QDY PXL Y DQY )LJXUH $YHUDJH 2EMHFWLYHf§6HW

PAGE 195

)LJXUH $YHUDJH :DLWLQJ 7LPH LQ 4XHXH f§6HW

PAGE 196

V 8L A I IFIV VSW PGP QD Y QDQY 1 QR HQ &6 &6 &2 7I rQ P V U U RRAHVR1YSFQRWAAARRLULHVR1YRFQ 2A2Y2A&6&6H27I7WLU 12 Y2 21 2n )LJXUH $YHUDJH :DLWLQJ 7LPH LQ 4XHXH 6HW Q&

PAGE 197

U 1 1 1 U R FQ P WMr WM 9& 2n 1 LU [ W 7I LW P P YR U R P n22n1LU[W 21 21 2n QDYGS QDY DQY QDQYG )LJXUH $YHUDJH 2EMHFWLYHf§(IIHFWV RI 'HJHQHUDF\ DQG )LWQHVV %DVHG 9RWLQJ 6HW

PAGE 198

)LJXUH $YHUDJH :DLWLQJ 7LPH LQ 4XHXH f§(IIHFWV RI 'HJHQHUDF\ DQG )LWQHVV %DVHG 9RWLQJ 6HW

PAGE 199

e

PAGE 200

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

PAGE 201

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n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f DUH VHHQ DW OHDVW RQFH ZLWK VSHFLILHG SUREDELOLWLHV 7KLV

PAGE 202

ZRXOG QRW QHFHVVLWDWH VHHLQJ DOO SRSXODWLRQV ZLWK VSHFLILHG SUREDELOLW\ DQG KHQFH VKRXOG SURYLGH D EHWWHU ERXQG $SSOLHG 5HVHDUFK 5HVXOWV DQG )XWXUH 5HVHDUFK 7KH SUHOLPLQDU\ VWXG\ GHVFULEHG LQ &KDSWHU KDG FOHDUO\ GHPRQVWUDWHG WKH DELOLW\ RI WKH V\VWHP WR LPSURYH LWV SHUIRUPDQFH XVLQJ *$ EDVHG OHDUQLQJ PHWKRGV 7KH OHDUQLQJ FRPSRQHQW ZDV DEOH WR LPSURYH WKH VLPXODWLRQf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

PAGE 203

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

PAGE 204

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

PAGE 205

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f Ef GLVFXVVHV WKH XVH RI :DOVK FRHIILFLHQWV WR FDOFXODWH WKH DYHUDJH VFKHPD ILWQHVVHV ZKLFK LV YHU\ KDUG WR FRPSXWH GLUHFWO\ 6XFK D VFKHPH FDQ EH XWLOL]HG IRU FRPSXWDWLRQDO HIILFLHQF\ :H GR QRW \HW NQRZ LI DQ RSWLPDO VHW RI SDUDPHWHUV H[LVW IRU DQ\ JLYHQ OHDUQLQJ SUREOHP ,W ZRXOG EH D ELJ FRQWULEXWLRQ WR ILQG RXW ZKDW SDUDPHWHU UDQJHV \LHOG WKH EHVW SHUIRUPDQFH 7KLV ZRXOG PDNH WKLV DSSURDFK DV JHQHUDO DV LW FRXOG EH DQG UHGXFH WKH FRPSXWDWLRQDO EXUGHQ RQ VHDUFKLQJ IRU WKH EHVW SDUDPHWHU VHWWLQJV

PAGE 206

5()(5(1&(6 $GDFKL 7 7DODYDJH DQG &/ 0RRGLH $ 5XOH %DVHG &RQWURO 0HWKRG IRU D 0XOWLn ORRS 3URGXFWLRQ 6\VWHP $UWLILFLDO ,QWHOOLJHQFH LQ (QJLQHHULQJ 1R SS $OSDU 3 DQG .1 6ULNDQWK $ &RPSDULVRQ RI $QDO\WLF DQG .QRZOHGJH%DVHG $SSURDFKHV WR &ORVHG6KRS 6FKHGXOLQJ $QQDOV RI 2SHUDWLRQV 5HVHDUFK D SS $OSDU 3 DQG .1 6ULNDQWK &ORVHG6KRS 6FKHGXOLQJ ZLWK ([SHUW 6\VWHP 7HFKQLTXHV .QRZOHGJHEDVHG 6\VWHPV LQ 0DQXIDFWXULQJ E (G $ .XVLDN 1HZ
PAGE 207

%HQ$ULHK .QRZOHGJH%DVHG &RQWURO 6\VWHP IRU $XWRPDWHG 3URGXFWLRQ DQG $VVHPEO\ 0RGHOOLQJ DQG 'HVLJQ RI )OH[LEOH 0DQXIDFWXULQJ 6\VWHPV (G $ .XVLDN 1HZ
PAGE 208

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
PAGE 209

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f $ .QRZOHGJH%DVHG $SSURDFK WR '\QDPLF -RE6KRS 6FKHGXOLQJ ,QWHUQDWLRQDO -RXUQDO RI &RPSXWHU ,QWHJUDWHG 0DQXIDFWXULQJ 1R SS )ODQQ 1 6 DQG 7 'LHWWHULFK $ 6WXG\ RI ([SODQDWLRQ%DVHG 0HWKRGV IRU ,QGXFWLYH /HDUQLQJ 0DFKLQH /HDUQLQJ SS )R[ %5 DQG .* .HPSI 5HDVRQLQJ $ERXW 2SSRUWXQLVWLF 6FKHGXOHV ,((( SS )R[ 06 &RQVWUDLQW 'LUHFWHG 6HDUFK $ &DVH 6WXG\ RI -RE6KRS 6FKHGXOLQJf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nV WK $QQXDO 0HHWLQJ DQG 7HFKQLFDO &RQIHUHQFH &OHDUZDWHU %HDFK )/ 1RYHPEHU D SS

PAGE 210

)R[ 06 DQG 6) 6PLWK ,6,6$ .QRZOHGJH%DVHG 6\VWHP IRU )DFWRU\ 6FKHGXOLQJ ([SHUW 6\VWHPV E 1R SS )R[ 0 6 DQG .3 6\FDUD 2YHUYLHZ RI &257(6 $ &RQVWUDLQW %DVHG $SSURDFK WR 3URGXFWLRQ 3ODQQLQJ 6FKHGXOLQJ DQG &RQWURO 3URFHHGLQJV RI WKH )RXUWK ,QWHUQDWLRQDO &RQIHUHQFH RQ ([SHUW 6\VWHPV LQ 3URGXFWLRQ DQG 2SHUDWLRQV 0DQDJHPHQW +LOWRQ +HDG 0D\ SS )UH\ 3 : DQG 6ODWH /HWWHU 5HFRJQLWLRQ XVLQJ +ROODQG6W\OH $GDSWLYH &ODVVLILHUV 0DFKLQH /HDUQLQJ 1R SS *DU\ 0 5 DQG 6 -RKQVRQ &RPSXWHUV DQG ,QWUDFWDELOLW\ $ *XLGH WR WKH 7KHRU\ RI 13&RPSOHWHQHVV 1HZ
PAGE 211

*UHIHQVWHWWH &UHGLW $VVLJQPHQW LQ 5XOH 'LVFRYHU\ 6\VWHPV %DVHG RQ *HQHWLF $OJRULWKPV 0DFKLQH /HDUQLQJ SS *UHIHQVWHWWH ,QFUHPHQWDO /HDUQLQJ RI &RQWURO 6WUDWHJLHV ZLWK *HQHWLF $OJRULWKPV 3URFHHGLQJV RI WKH 6L[WK ,QWHUQDWLRQDO &RQIHUHQFH RQ 0DFKLQH /HDUQLQJ &RUQHOO 8QLYHUVLW\ ,WKDFD 1< 6HJUH $ 0 (GLWRU 6DQ 0DWHR &$ 0RUJDQ .DXIPDQQ 3XEOLVKHUV ,QF SS +DXVVOHU $SSO\LQJ 9DOLDQWfV /HDUQLQJ )UDPHZRUN WR $, &RQFHSW /HDUQLQJ 3UREOHPV 3DSHU 8&6&&5/ %DVNLQ &HQWHU IRU &RPSXWHU (QJLQHHULQJ DQG ,QIRUPDWLRQ 6FLHQFHV 8QLYHUVLW\ RI &DOLIRUQLD 6DQWD &UX] +DXVVOHU 4XDQWLI\LQJ ,QGXFWLYH %LDV $, /HDUQLQJ $OJRULWKPV DQG 9DOLDQWf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
PAGE 212

.RHKOHU $ 3URRI RI WKH 9RVH/LHSLQV &RQMHFWXUH ZRUNLQJ SDSHU 'HFLVLRQ DQG ,QIRUPDWLRQ 6FLHQFHV %86 8QLYHUVLW\ RI )ORULGD *DLQHVYLOOH )/ .RWRQ 3 60$57SODQ $ &DVH%DVHG 5HVRXUFH $OORFDWLRQ DQG 6FKHGXOLQJ 6\VWHP 3URFHHGLQJV RI WKH '$53$ :RUNVKRS RQ &DVH%DVHG 5HDVRQLQJ 3HQVDFROD %HDFK )/ ; (G .DXIPDQQ 0 +DPPRQG SS ; .XVLDN $ DQG 0 &KHQ ([SHUW 6\VWHPV )RU 3ODQQLQJ DQG 6FKHGXOLQJ 0DQXIDFWXULQJ 6\VWHPV (XURSHDQ -RXUQDO RI 2SHUDWLRQV 5HVHDUFK ;; SS /DJHZHJ % -f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

PAGE 213

/LHSLQV ( DQG 0 9RVH'HFHSWLYHQHVV DQG *HQHWLF $OJRULWKP '\QDPLFV )RXQGDWLRQV RI *HQHWLF $OJRULWKPV (G 5DZOLQV D 6DQ 0DWHR &$ 0RUJDQ .DXIPDQ 3XEOLVKHUV /LHSLQV ( DQG 0 9RVH 3RO\QRPLDOV %DVLV 6HWV DQG 'HFHSWLYHQHVV LQ *HQHWLF $OJRULWKPV &RPSOH[ 6\VWHPV E 1RO SS /LHSLQV (f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f /* 9DUJDV 5'Hf 6$ 6ORWQLFN 7( 0RUWRQ ': 3HQWLFR DQG *7DWDU 0XOWH[ $Q ,QWHJUDWHG $,25 6\VWHP )RU )DFWRU\ 6FKHGXOLQJ 3URFHHGLQJV RI WKH 1RUWKHDVW '6, &RQIHUHQFH $SULO 3LWWVEXUJK 0H .D\ .1 -$ %X]DFRWW 1 &KDUQHVV DQG )5 6DID\HQL 7KH 6FKHGXOHUf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
PAGE 214

0LQJHUV $Q (PSLULFDO &RPSDULVRQ RI 3UXQLQJ 0HWKRGV IRU 'HFLVLRQ 7UHH ,QGXFWLRQ 0DFKLQH /HDUQLQJ E SS 0LWFKHOO 7 0 5 0 .HOOHU DQG 6 7 .HGDU&DEHOOL ([SODQDWLRQ%DVHG *HQHUDOL]DWLRQ $ 8QLI\LQJ 9LHZ 0DFKLQH /HDUQLQJ SS 0RKDQ 6 DQG &ODQF\ 6,65XOH %DVHG 6RIWZDUH IRU $XWRPDWLQJ -RE 'LVSDWFK RQ WKH )DFWRU\ )ORRU 3URFHHGLQJV IURP WKH 7KLUG ,QWHUQDWLRQDO &RQIHUHQFH RQ ([SHUW 6\VWHPV DQG WKH /HDGLQJ (GJH LQ 3URGXFWLRQ 3ODQQLQJ DQG &RQWURO 0XOOHU 0DOHNf + 'H 6DPEODQFN[ DQG 0DWWK\V 7KH ([SHUW 6\VWHP $SSURDFK DQG WKH )OH[LELOLW\&RPSOH[LW\ 3UREOHP LQ 6FKHGXOLQJ 3URGXFWLRQ 6\VWHPV ,QWHUQDWLRQDO -RXUQDO RI 3URGXFWLRQ 5HVHDUFK 1R SS 1DNDVXND 6 7
PAGE 215

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
PAGE 216

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f 1RQ1HJDWLYH 0DWULFHV /RQGRQ *HUJR $OOHQ t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

PAGE 217

6KHQ 6 DQG < &KDQJ $Q $, $SSURDFK WR 6FKHGXOH *HQHUDWLRQ LQ )OH[LEOH 0DQXIDFWXULQJ (GV .( 6WHFNH DQG 5 6XUL )OH[LEOH 0DQXIDFWXULQJ 6\VWHPV 2SHUDWLRQV 5HVHDUFK 0RGHOV DQG $SSOLFDWLRQV (OVHYLHU 1HZ
PAGE 218

7KHVHQ $ DQG / /HL $Q f([SHUWf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f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
PAGE 219


PAGE 220

%,2*5$3+,&$/ 6.(7&+ +DOGXQ $\WXJ UHFHLYHG KLV %DFKHORU RI 6FLHQFH GHJUHH LQ LQGXVWULDO HQJLQHHULQJ LQ -XO\ IURP %RJD]LFL 8QLYHUVLW\ ,VWDQEXO7XUNH\ +H VWDUWHG KLV JUDGXDWH VWXGLHV LQ GHFLVLRQ DQG LQIRUPDWLRQ VFLHQFHV DW WKH 8QLYHUVLW\ RI )ORULGD LQ $XJXVW 7KH DXWKRU KDV EHHQ D WHDFKLQJ DVVLVWDQW IRU WKH ,QWURGXFWLRQ WR 0DQDJHPHQW ,QIRUPDWLRQ 6\VWHPV FRXUVH IRU VHYHUDO VHPHVWHUV DQG KDV WDXJKW WKH 0DQDJHULDO 2SHUDWLRQV $QDO\VLV ,,, FRXUVH LQ 6SULQJ +H KDV SDUWLFLSDWHG LQ D SURMHFW ZLWK ,%0 &RUSRUDWLRQ RQ WKH DSSOLFDELOLW\ RI JHQHWLF DOJRULWKP EDVHG OHDUQLQJ RQ VFKHGXOLQJ +LV UHVHDUFK FRQFHQWUDWHV RQ PDFKLQH OHDUQLQJ DQG DUWLILFLDO LQWHOOLJHQFH DSSOLFDWLRQV LQ EXVLQHVV +H LV D PHPEHU RI %HWD *DPPD 6LJPD DQG $OSKD ,RWD 'HOWD KRQRUDU\ VRFLHWLHV DQG 7KH ,QVWLWXWH RI 0DQDJHPHQW 6FLHQFH

PAGE 221

, FHUWLI\ WKDW KDYH UHDG WKLV VWXG\ DQG WKDW LQ P\ RSLQLRQ LW FRQIRUPV WR DFFHSWDEOH VWDQGDUGV RI VFKRODUO\ SUHVHQWDWLRQ DQG LV IXOO\ DGHTXDWH LQ VFRSH DQG TXDOLW\ DV D GLVVHUWDWLRQ IRU WKH GHJUHH RI 'RFWRU RI 3KLORVRSK\ *DU\ .RHKOHU &KDLUPDQ 3URIHVVRU RI 'HFLVLRQ DQG ,QIRUPDWLRQ 6FLHQFHV FHUWLI\ WKDW KDYH UHDG WKLV VWXG\ DQG WKDW LQ P\ RSLQLRQ LW FRQIRUPV WR DFFHSWDEOH VWDQGDUGV RI VFKRODUO\ SUHVHQWDWLRQ DQG LV IXOO\ DGHTXDWH LQ VFRSH DQG TXDOLW\ DV D GLVVHUWDWLRQ IRU WKH GHJUHH RI 'RFWRU RI 3KLORVRSK\ &KXQJ
PAGE 222

7KLV GLVVHUWDWLRQ ZDV VXEPLWWHG WR WKH *UDGXDWH )DFXOW\ RI WKH 'HSDUWPHQW RI 'HFLVLRQ DQG ,QIRUPDWLRQ 6FLHQFHV LQ WKH &ROOHJH RI %XVLQHVV $GPLQLVWUDWLRQ DQG WR WKH *UDGXDWH 6FKRRO DQG ZDV DFFHSWHG DV SDUWLDO IXOILOOPHQW RI WKH UHTXLUHPHQWV IRU WKH GHJUHH RI 'RFWRU RI 3KLORVRSK\ $XJXVW 'HDQ *UDGXDWH 6FKRRO

PAGE 223

81,9(56,7< 2) )/25,'$


xml version 1.0 encoding UTF-8
REPORT xmlns http:www.fcla.edudlsmddaitss xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd
INGEST IEID E8Q1960T1_X9NOOA INGEST_TIME 2011-08-29T16:10:26Z PACKAGE AA00002073_00001
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES