Decision Analysis, Location Models, and Scheduling Problems

455 Pages·2004·11.835 MB·English

by  Prof. H. A. Eiselt, Prof. C.-L. Sandblom (auth.)

Decision Analysis, Location Models,
and Scheduling Problems
Springer-Verlag Berlin Heidelberg GmbH
H. A. Eiselt · C.-L. Sandbiom
Decision Analysis,
Location Models,
and Scheduling Problems
With Contributions by
J. Blazewicz, R. L. Church, A. Drexl,
G. Pinke, C. S. ReVelle
With 147 Figures
and 48 Tables
~Springer
Prof. H. A. Eiselt
University of New Brunswick
Faculty of Administration
P.O. Box 4400
Fredericton, NB E3B 5A3
Canada
Prof. C.-L. Sandblom
Dalhousie University
Department of Industrial Engineering
P.O. Box 1000
Halifax, B3J 2X4, Nova Scotia
Canada
ISBN 978-3-642-07315-1 ISBN 978-3-540-24722-7 (eBook)
DOI 10.1007/978-3-540-24722-7
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"How much, thought I, has each of these volumes, now thrust aside with such
indifference, cost some aching head! how many weary days; how many sleepless
nights! How have their authors buried themselves in the solitude of cells and
cloisters; shut themselves up from the face of man, and still more blessed face of
nature; and devoted themselves to painful research and intense reflection! And all
for what? to occupy an inch of dusty shelf--to have the title of their works read
now and then in a future age, by some drowsy churchman or casual straggler like
myself; and in another age to be lost, even to remembrance. Such is the amount of
this boasted immortality. A mere temporary rumour, a local sound; like the tone of
that bell which has just tolled among these towers, filling the ear for a
moment-lingering transiently in echcr-and then passing away like a thing that
was not!"
Washington lrving, (1783-1859) "The Mutability of Literature", in The Sketch
Book of Geoffrey Crayon, Gent, E.P. Dutton & Co., New York, 1906 (frrst
published in 1819).
PREFACE
The purpose of this book is to provide readers with an introduction to the fields of
decision making, location analysis, and project and machine scheduling. The
combination of these topics is not an accident: decision analysis can be used to
investigate decision seenarios in general, location analysis is one of the prime
examples of decision making on the strategic Ievel, project scheduling is typically
concemed with decision making on the tactical Ievel, and machine scheduling
deals with decision making on the operational Ievel. Some of the chapters were
originally contributed by different authors, and we have made every attempt to
unify the notation, style, and, most importantly, the Ievel of the exposition.
Similar to our book on Integer Programming and Network Models (Eiselt and
Sandblom, 2000), the emphasis of this volume is on models rather than solution
methods. This is particularly important in a book that purports to promote the
science of decision making. As such, advanced undergraduate and graduate
students, as weil as practitioners, will find this volume beneficial.
While different authors prefer different degrees of mathematical sophistication,
we have made every possible attempt to unify the approaches, provide clear
explanations, and make this volume accessible to as many readers as possible.
What is required in terms of prerequisites is collected in the introduction. Here,
we provide some basics of algorithms and computational complexity, matrix
algebra, graphs and networks, linear and integer optimization, and statistics. This
part is not meant as a substitute for a study of these fields, it is merely included
here as support methodology.
This is a truly international work: parts of the manuscript were written in Po land,
France, Germany, Sweden, the United States, and Canada, most editing was done
in New Brunswick and Nova Scotia, Canada, but parts were also completed in
Norrköping, Sweden and Cairo, Egypt.
Our thanks go to Springer-Verlag, and particularly Dr. Müller, whose patience and
support helped the project fmally come to fruition. W e wou1d like to express our
thanks to Zhijian Yin who provided us with many of the figures for the book, and
and #13, a.k.a. Kha1ed Abou-Zied, who prepared the index and the bibliography,
made last minute corrections, and acted as gofer. Many thanks are also due to Lisa
Shepard from #1 Copyediting Services for her meticulous work, particularly
considering the tight time frame. We are also grateful to colleagues and students
who have helped with the book.
H.A. Eiselt
C.-L. Sandbiom
CONTENTS
Introduction
Notation
Support Methodology 3
a. Algorithms and Computational Complexity 3
b. Matrix Algebra 5
c. Graphs and Networks 9
d. Linear and Integer Optirnization 11
e. Statistics 13
Part 1: Analysis of Decision Making 19
1 Multicriteria Decision Making 23
1.1 Vector Optimization 24
1.2 Basic Ideas ofMulticriteria Decision Making 29
1.3 Reference Point Methods 37
1.4 Data Envelopment Analysis 40
1.5 Preference Cones 43
1.6 Multiattribute Value Functions 46
1. 7 Outranking Methods 50
1.8 Methods Allowing Inconsistent Estimates 61
2 Games Against Nature 73
2.1 Elements of Games Against Nature 73
2.1.1 Basic Components 73
2.1.2 Lotteries and Certainty Equivalents 76
2.1.3 Visualizations of the Structure of Decision Problems 81
2.2 Rules for Decision Making Under Uncertainty and Risk 87
2.3 Multi-Stage Decisions and the Value oflnformation 99
X Contents
3 Game Theory 111
3.1 Features ofGame Theory 1I2
3 .1.1 Elements and Representations of Games 112
3 .1.2 Solution Concepts 1I6
3.2 Two-Person Zero-S um Games 122
3 .3 Extensions I33
3.3.1 Bimatrix Games 133
3.3.2 Multi-Stage Games 140
3.3.3 n-Person Games 143
Part II: Location and Layout Decisions 151
1 Fundamentals of Location and Layout Problems 153
I.l The Nature ofLocation Problems 153
I.2 The History ofLocation Models 155
I.3 The Major Elements of Location Problems I 57
1.4 Applications ofLocation Problems I64
2 Location Models on Networks I69
2.1 Covering Models I70
2.1.1 The Location Set Covering Problem 171
2.1.2 The Maximal Covering Location Problem 175
2.2 Center Problems I78
2.2.I I-Center Problems 179
2.2.2 p-Center Problems 186
2.3 Median Problems 188
2.3.1 Basic Results and Fonnutation ofthe Problem 189
2.3 .2 I-Median Problems 192
2.3.3 p-Medians Problems 194
2.4 Simple and Capacitated Plant Location Problems 205
2.5 An Application ofthe Capacitated Facility Location Problem 208
3 Continuous Location Models 211
3 .I Covering Problems 212
3.2 Single-FacilityMinimax Problems 214
3.3 Minisum Problems 220
3.3.1 Single-Facility Problems 220
3.3.2 Multi-Facility Problems 228
Contents XI
4 Other Location Models 237
4.1 The Location ofUndesirable Facilities 237
4.2 p-Dispersion Problems 243
4.3 Location Models with "Equity'' Objectives 244
4.4 Hub Location Problems 247
4.5 Competitive Location Problems 248
4.6 Locating Extensive Facilities and Routing in Irregular Spaces 252
5 Layout Models 255
5.1 Facility Layout Planning 256
5.2 Formulations ofthe BasicLayout Problem 260
5.3 Special Cases of the Quadratic Assignment Problem 266
5.3 .1 Triangulation Problems 267
5.3.2 Traveling Safesman Problems 268
5.3.3 Matehing Problems 269
5.4 Applications 270
5.4.1 Relay Team Running 270
5.4.2 Backboard Wiring 271
5.4.3 Building Layout Planning 272
5.4.5 Keyboard Design 273
5.5 Solution Methods 275
5.5.1 Exact Solution Methods 275
5.5.2 Heuristic Solution Methods 290
5.5.3 Solving General Facility Layout Problems 292
Part 111: Project Scheduling 295
1 Unconstrained Time Project Scheduling 297
1.1 Network Representations 297
1.2 The Critical Path Method 302
1.3 Project Aceeieration (Crashing) 309
1.4 Incorporating Uncertainties (PERT) 313
2 Project Scheduling with Resource Constraints 319
2.1. The Problemsand its Fonnutation 319
2.2 Exact Solution methods 326
2.3 Heuristic Methods 328