简介
Employing state-of-the art quantitative models and case studies, Location Theory and Decision Analysis provides the methodologies behind the siting of such facilities as transportation terminals, warehouses, housing, landfills, state parks and industrial plants. Through its extensive methodological review, the book serves as a primer for more advanced texts on spatial analysis, including the monograph on Location, Transport and Land-Use by the same author. Given the rapid changes over the last decade, the Second Edition includes new analytic contributions as well as software survey of analytics and spatial information technology.聽 While the First Edition served the professional community well, the Second Edition has substantially expanded its emphasis for classroom use of the volume. Extensive pedagogic materials have been added, going from the fundamental principles to open-ended exercises, including solutions to selected problems. The text is of value to engineering and business programs that offer courses in Decision and Risk Analysis, Muticriteria Decision-Making, and Facility Location and Layout. It should also be of interest to public policy programs that use geographic Information Systems and satellite imagery to support their analyses.
目录
Contents 3
Dedication 14
Preface to the Second Edition 15
MOTIVATION FOR A SECOND EDITION 16
PEDAGOGY 17
STATE-OF-THE-ART 19
SCIENTIFIC COMPUTING 19
INFORMATION TECHNOLOGY 21
USE OF THIS BOOK 21
ACKNOWLEDGEMENTS 23
Preface 24
ORGANIZATION OF THE BOOK 25
SOFTWARE 26
ACKNOWLEDGEMENTS 27
ABOUT THE COVER 30
REFERENCES 30
1 Introduction 31
I. OBJECTIVES 31
II. DETERMINANTS OF LOCATION 33
A. Technological Factors 33
B. Economic and Geographic Factors 34
C. Political Factors 34
D. Social Factors 34
III. THE ROLE OF ANALYSIS 35
A. Airport Example 35
B. Manufacturing Plant Example 36
C. A Combined Example 37
IV. ANALYTICAL TECHNIQUES 39
V. CONCLUDING REMARKS 42
VI. EXERCISES Self-Instructional Module: EMPIRICAL MODELING 43
Problem 1: Further Discussions on Table 1.1 43
Problem 2: Further Discussions on Airport Location 44
ENDNOTE 45
REFERENCES 45
2 Economic Methods of Analysis 47
I. ECONOMIC CONSTRUCTS FOR ACTIVITY ALLOCATION AND FORECASTING 47
A. Economic-Base Theory 48
B. Location Theory 50
C. Input-Output Models 53
II. ECONOMETRIC MODELING: INTERREGIONAL DEMOGRAPHIC PROJECTIONS 55
A. Population Projection Models 55
B. Interregional Growth and Distribution 60
C. Interregional Components of Change Model 62
III. ECONOMIC CONSTRUCTS FOR COST-BENEFIT ESTIMATION 63
A. Shift-Share Analysis 64
B. Theory of Land Values 66
C. Consumers\u2019 Surplus 68
IV. UTILITY THEORY 70
A. Estimating Bid-Rent via Utility Function 73
B. Minimum-Cost Residential Location 76
V. THE LOCATION DECISION 77
A. Bid-Rent Curves 78
B. Industrial Location 78
C. Residential Location Models 80
VI. SCALE AND NUMBER OF PUBLIC FACILITIES 81
A. Static Short-Run Equilibrium 81
B. Dynamic Long-Run Equilibrium 85
VII. SPATIAL LOCATION OF A FACILITY 87
A. Center of a Network 88
B. Median of a Network 89
C. Competitive Location and Games 92
D. Imperfect Information 94
VIII. ECONOMIC BASIS OF THE GRAVITY-BASED SPATIAL ALLOCATION MODEL 96
A. The Singly Constrained Model 96
B. The Doubly Constrained Model 102
C. The Unconstrained Model 103
D. The Intervening Opportunity Model 104
IX. CONCLUDING REMARKS 107
X. EXERCISES Self-Instructional Module: PROBABILITY 107
Problem 1: Gravity Model 108
Problem 2: Further Discussions on Forecasting 109
ENDNOTES 111
REFERENCES 111
3 Descriptive Tools for Analysis 113
I. AN EXAMPLE 113
II. DESCRIPTIVE TECHNIQUES: ANOTHER EXAMPLE 115
III. SIMULATION 117
IV. STOCHASTIC SIMULATION 122
V. DISCRETE EVENT SIMULATION 126
A. Stochastic Process 126
B. Simulation 130
VI. INVENTORY CONTROL USING MARGINAL ANALYSIS 132
VII. BAYESIAN ANALYSIS 135
A. Bayesian Update 136
B. Bayesian Decisions 137
C. Decision Tree 138
D. Influence Diagram 140
E. Bayesian Classifier 142
VIII. ECONOMETRIC APPROACH 145
A. Arrow Diagram and Path Analysis 146
B. Econometric Models 147
IX. CALIBRATION 149
A. Ordinary Least Squares 150
B. Two-Stage Least Squares 151
C. Example of Two-Stage Least Squares 152
D. Maximum Likelihood 154
X. AGGREGATE VERSUS DISAGGREGATE MODELING 156
XI. THE GRAVITY MODEL REVISITED 158
A. Singly Constrained Gravity Model 158
B. Doubly Constrained Model 161
XII. SPATIAL INTERACTION 164
A. Information Theory 164
B. Entropy 167
XIII. QUALITY OF A MODEL CALIBRATION 171
A. Chi-Square Test 171
B. Variance Reduction 172
XIV. CONCLUDING REMARKS 173
XV. EXERCISES Self-Instructional Module: PROBABILITY DISTRIBUTION AND QUEUING 174
Problem 1: Decision Tree 174
Problem 2: Simulation 177
ENDNOTES 179
REFERENCES 179
4 Prescriptive Tools for Analysis 182
I. A TYPICAL PRESCRIPTIVE MODEL 182
A. Goals and Objectives 183
B. Representation of the System 183
C. A Prescriptive Formulation of the Economic-Base Concept 184
II. HEURISTIC SOLUTION TECHNIQUES 185
A. Manual Approach 185
B. Enumerative Method 186
C. Direct Search Technique 190
D. The Golden Section Algorithm 191
E. Fibonacci Search Procedure 193
III. ANALYTICAL SOLUTION TECHNIQUES 196
A. Calculus 196
B. Linear Programming 198
C. Primal and Dual Linear Programs 201
D. Solution of Linear Programs 202
E. Nonlinear Programming 207
F. Solution of a Nonlinear Program 209
IV. INTEGER OR MIXED-INTEGER PROGRAMMING 213
A. Total Unimodularity 215
B. Network Software 216
C. Network with Gains 218
V. DECOMPOSITION METHODS IN FACILITY LOCATION 221
A. Resource Directive Decomposition 222
B. Price Directive Decomposition 224
VI. SPATIAL INTERACTIONS: THE QUADRATIC ASSIGNMENT PROBLEM 225
A. Nonlinear Formation 226
B. Linear Formulation 226
C. Comments 227
VII. PRESCRIPTIVE ANALYSIS IN FACILITY LOCATION: DATA ENVELOPMENT ANALYSIS 228
VIII. PRESCRIPTIVE TECHNIQUES IN LAND USE 232
A. Entropy Maximization Model 233
B. Relationship to the Allocation Model 234
C. Optimal Control Models of Spatial Interaction 235
IX. CONCLUDING REMARKS 235
X. EXERCISES Self-Instructional Module: GRAPH OPTIMIZATION 236
Problem 1: Properties of a Facility-Location Model 236
Problem 2: Maximal-Coverage Facility-Location Model 237
ENDNOTES 239
REFERENCES 239
5 Multicriteria Decision Making 242
I. PREFERENCE STRUCTURE 243
A. The Importance of Preference Structure 243
B. Paired versus Simultaneous Comparison 245
II. SIMPLE ORDERING 247
III. EXPLORING THE EFFICIENT FRONTIER 249
IV. MULTICRITERIA SIMPLEX (MC-SIMPLEX) 252
A. The MC-Simplex Algorithm 252
B. Nonlinear and Integer Programming 257
C. An Interactive Frank-Wolfe Example 258
D. Comments 262
V. GOAL SETTING 263
A. Compromise Programming 263
B. Deviational Measures 264
C. Goal-Setting Example 265
VI. VALUE FUNCTIONS 266
A. Additive versus Multiplicative Form 266
B. Univariate Utility Function Construction 267
C. Independence Among Criterion Functions 271
D. Summary 272
VII. VALUE-FUNCTION MEASUREMENT STEPS 274
A. Preferential, Utility and Additive Independence 275
B. Examples of Utility Function Calibration 279
C. Validation 285
VIII. MULTICRITERIA DECISION MAKING AND FACILITY LOCATION 289
A. The X, Y', and Z' Spaces in Facility Location 289
B. Multi-Attribute Utility and Optimization 290
IX. A TAXONOMY OF METHODS 293
A. Prior Articulation of Alternatives 293
B. Prior Articulation of Preferences 294
C. Progressive Articulation of Alternatives 294
D. Progressive Articulation of Preferences 294
X. DOMINATION STRUCTURES 295
XI. COLLECTIVE DECISION MAKING 296
A. Arrow\u2019s Paradox 297
B. Game Theory 298
C. Recommended Procedure 300
XII. CONCLUDING REMARKS 301
XIII. EXERCISES Self-Instructional Module: RISK ASSESSMENT 303
Problem 1: Multicriteria Optimization 304
Problem 2: Multi-attribute Decision Analysis 304
ENDNOTES 306
REFERENCES 306
6 Remote Sensing and Geographic Information Systems 310
I. DATA IN SPATIAL-TEMPORAL ANALYSIS 310
A. Resource Requirement 312
B. Assembly of Data Sources 312
C. Use and Display of Information 313
II. GEOGRAPHIC CODING SYSTEMS 316
A. Central Place Theory 316
B. Concentric Zone, Sector, and Multi-Nuclei City Structures 316
C. Dual Independent Map Encoding System 317
D. Topologically Integrated Geographic Encoding and Referencing 319
E. Other Data Sources 320
III. GEOGRAPHIC INFORMATION SYSTEMS (GIS) 322
A. Data Organization and Structure 322
B. Location Reference System and Data Structure 329
C. Geospatial Metadata 331
IV. REMOTE SENSING SYSTEMS 332
A. Interface between Remote Sensing Data and GIS 333
B. An Assessment 334
C. Remote Sensing Technology 336
V. DIGITAL IMAGE PROCESSING 338
A. Image Rectification and Restoration 338
B. Image Enhancement 343
C. Image Classification 345
D. Data Merging 347
VI. DIGITAL IMAGE PROCESSING SOFTWARE AND HARDWARE 350
VII. APPLICATIONS OF REMOTE SENSING 351
VIII. SPECTRAL VERSUS SPATIAL PATTERN RECOGNITION 355
A. Spectral Pattern Recognition 355
B. Contextual Allocation of Pixels 357
IX. A DISTRICT CLUSTERING MODEL 362
A. A Single Subregion Model 362
B. Multiple Subregion Model 366
C. Demand Equity 370
D. Extensions 371
X. CASE STUDY OF IMAGE CLASSIFICATION 372
A. Digital Image Data 372
B. Image Classification 374
C. Lessons Learned 377
XI. REMOTE SENSING, GIS, AND SPATIAL ANALYSIS 378
XII. CONCLUDING REMARKS 381
XIII. EXERCISES Self-Instructional Module: LINEAR PROGRAMMING PART 1: MODEL FORMULATION 383
Problem 1: Bayesian and Contextual Classification 384
Problem 2: TS-IP Image-Processing Software 384
ENDNOTES 386
REFERENCES 387
7 Analytics and Spatial Information Technology: Retrospect and Prospects 392
I. ANALYTICS 393
A. Statistical Modeling 393
B. Optimization 394
C. Multicriteria Decision-Making 394
D. Location-Based Analysis 395
II. SPATIAL ANALYTICS 396
A. Spatial Association 397
B. Spatial Clustering 398
C. Facility or Site Location 400
D. Routing 401
III. SOFTWARE 402
A. Commercial/Licensed Software 403
B. Developmental Geospatial Software in the Public Domain 423
C. Selecting a Software: The Case of GIS 428
IV. SPATIAL INFORMATION TECHNOLOGY: LOOKING AHEAD 430
A. Spatial Information Technology 431
B. Going Beyond 433
V. EXERCISES Self-Instructional Module: LINEAR PROGRAMMING PART 2 SOLUTION ALGORITHM 435
ENDNOTES 435
REFERENCES 436
8 A Software Survey of Analytics and Spatial Information Technology 439
I. GENERAL ANALYTIC SOFTWARE 440
A. Spreadsheet Modeling 440
B. Applied Mathematics 441
C. Statistics 444
D. Simulation 446
E. Optimization 451
F. Decision Analysis 456
II. SPATIAL ANALYTICS SOFTWARE 457
A. GIS 458
B. Image Processing 461
C. Routing 464
III. CONCLUDING COMMENTS 465
ENDNOTES 466
REFERENCES 468
Synthesis Exercises and Problems 469
I. REMOTE SENSING AND GEOGRAPHIC INFORMATION SYSTEMS 469
A. Bayesian Classifier 470
B. Iterative Conditional Mode Algorithm 471
C. Weighted Iterative Conditional Mode Algorithm 471
D. District Clustering Model 471
E. Combined Classification Scheme 472
F. Histogram Processing 473
II. FACILITY LOCATION 475
A. Nodal Optimality Conditions 475
B. Solid Waste Facility 475
C. Quadratic Assignment Problem 476
III. LOCATION-ROUTING 476
A. Districting 477
B. Minkowski\u2019s Metric 478
IV. ACTIVITY DERIVATION, ALLOCATION AND COMPETITION 479
A. Multicriteria Game 479
B. Gravity versus Transportation Model 480
C. Calibration of a Doubly Constrained Model 481
V. LAND USE MODELS 481
A. Economic-Base and Activity Allocation 481
B. Forecasting Airbase Housing Requirements 483
VI. SPATIAL-TEMPORAL INFORMATION 483
A. Cohort Survival Method 485
VII. TERM PROJECT 487
REFERENCES 490
Appendix 1 Control, Dynamics, and System Stability 493
I. CONTROL THEORY 493
II. CALCULUS OF VARIATIONS 496
III. VARIATIONAL INEQUALITY 497
A. Fundamentals 498
B. Existence and Uniqueness 499
IV. CATASTROPHE THEORY 501
A. Basic Concepts 502
B. Elementary Catastrophes 504
C. The Fold Catastrophe as an Example 506
D. Higher Order Catastrophes 507
E. Remarks 508
V. COMPARTMENTAL MODELS 509
A. Basics 509
B. Stochastic Models 511
C. Deterministic Models 514
D. Deterministic Example 516
E. Stochastic Example 518
F. Discrete Time Models 519
G. Example of a Quasi-Deterministic Analysis 520
VI. SYSTEM STABILITY 522
A. Basic Types of Trajectory 522
B. Bifurcation Theory 524
C. Comments 527
VII. CONCLUDING REMARKS 528
ENDNOTES 528
REFERENCES 529
Appendix 2 Review of Some Pertinent Statistical Tools 531
I. STATISTICAL ANALYSIS: BASIC CONCEPTS 531
II. GOODNESS-OF-FIT MEASURES 533
III. LINEAR REGRESSION 534
IV. ANALYSIS OF VARIANCE 538
V. USING THE REGRESSION EQUATION 539
A. Confidence Interval 540
B. Prediction Interval 540
C. Summary 541
VI. STEPWISE REGRESSION 543
A. Backward and Forward Regression 543
B. Goodness-of-Fit Parameters for Stepwise Regression 545
VII. MATRIX APPROACH TO LINEAR REGRESSION 549
VIII. NONLINEAR REGRESSION 550
IX. CONCLUDING REMARKS 552
ENDNOTES 553
REFERENCES 553
Appendix 3 Review of Pertinent Markovian Processes 554
I. POISSON PROCESS 554
A. State Transition Equations 554
B. Solution to Random Process 556
II. FIELD DATA FROM AIR TERMINAL 556
A. Exponential Distribution 557
B. Poisson Distribution 557
III. M/M/1 QUEUE 560
IV. QUEUING SYSTEMS 561
A. Basic Theory 562
B. Queuing Formulas 563
C. Choosing a Queuing Discipline 566
V. MARKOVIAN PROPERTIES 568
VI. MARKOVIAN PROPERTIES OF DYNAMIC PROGRAMMING 569
A. Vehicle Dispatching Example 569
B. Principle of Optimality 574
VII. MARKOVIAN DECISION PROCESSES 575
A. Policy Iteration 575
B. Reward Per Period 578
VIII. RECURSIVE PROGRAMMING 579
A. Existence of Solutions 580
B. Phase Solutions 581
IX. CONCLUDING REMARKS 582
ENDNOTES 583
REFERENCES 583
Appendix 4 Review of Some Pertinent Optimization Schemes 584
I. LINEAR PROGRAMMING 584
A. Simplex Algorithm 584
B. Some Other Key Concepts 587
C. Theory of Simplex 589
II. NETWORK-WITH-SIDE-CONSTRAINTS 590
A. Multicommodity-Flow Problem 591
B. The Network-with-Side-Constraints Algorithm 593
III. LAGRANGIAN RELAXATION 603
A. Illustration of Basic Concepts 603
B. Underlying Theory 604
C. Subgradient Optimization 607
D. Branch-and-Bound (B&B) Solution 608
IV. BENDERS\u2019 DECOMPOSITION 610
A. Example 611
B. Convergence 613
C. Extension 613
V. ALGORITHMS AND COMPLEXITY 614
VI. CONCLUDING REMARKS 616
ENDNOTES 617
REFERENCES 617
Appendix 5 Discussion of Technical Concepts 619
Appendix 6 Abbreviation and Mathematical Symbols 646
List of Symbols 651
Solutions to Exercises and Problems 681
I. SOLUTIONS TO SELF-INSTRUCTIONAL MODULES 681
A. Empirical Modeling Module: Answers to Illustrative Exercises 682
B. Probability Module: Answers to Illustrative Exercises 684
C. Probability Distribution & Queuing Module: Answers to Illustrative Exercises 686
D. Graph Theory Module: Answers to Illustrative Exercises 689
E. Risk Assessment Module: Answers To Illustrstive Exercises 694
F. Linear Programming Module: Part 1 Modeling Answers To Illustrative Exercises 696
G. Linear Programming Module: Part 2 Solution Algorithm Answers To Illustrative Exercises 698
II. SOLUTIONS TO REGULAR PROBLEMS 700
III. SOLUTIONS TO SYNTHESIS EXERCISES AND PROBLEMS 700
A. Remote Sensing and Geographic Information Systems 700
B. Facility Location 705
C. Location-Routing 706
D. Activity Derivation, Competition and Allocation 710
E. Land-Use Models 713
F. Spatial-Temporal Information 714
REFERENCES 716
Index 717
Dedication 14
Preface to the Second Edition 15
MOTIVATION FOR A SECOND EDITION 16
PEDAGOGY 17
STATE-OF-THE-ART 19
SCIENTIFIC COMPUTING 19
INFORMATION TECHNOLOGY 21
USE OF THIS BOOK 21
ACKNOWLEDGEMENTS 23
Preface 24
ORGANIZATION OF THE BOOK 25
SOFTWARE 26
ACKNOWLEDGEMENTS 27
ABOUT THE COVER 30
REFERENCES 30
1 Introduction 31
I. OBJECTIVES 31
II. DETERMINANTS OF LOCATION 33
A. Technological Factors 33
B. Economic and Geographic Factors 34
C. Political Factors 34
D. Social Factors 34
III. THE ROLE OF ANALYSIS 35
A. Airport Example 35
B. Manufacturing Plant Example 36
C. A Combined Example 37
IV. ANALYTICAL TECHNIQUES 39
V. CONCLUDING REMARKS 42
VI. EXERCISES Self-Instructional Module: EMPIRICAL MODELING 43
Problem 1: Further Discussions on Table 1.1 43
Problem 2: Further Discussions on Airport Location 44
ENDNOTE 45
REFERENCES 45
2 Economic Methods of Analysis 47
I. ECONOMIC CONSTRUCTS FOR ACTIVITY ALLOCATION AND FORECASTING 47
A. Economic-Base Theory 48
B. Location Theory 50
C. Input-Output Models 53
II. ECONOMETRIC MODELING: INTERREGIONAL DEMOGRAPHIC PROJECTIONS 55
A. Population Projection Models 55
B. Interregional Growth and Distribution 60
C. Interregional Components of Change Model 62
III. ECONOMIC CONSTRUCTS FOR COST-BENEFIT ESTIMATION 63
A. Shift-Share Analysis 64
B. Theory of Land Values 66
C. Consumers\u2019 Surplus 68
IV. UTILITY THEORY 70
A. Estimating Bid-Rent via Utility Function 73
B. Minimum-Cost Residential Location 76
V. THE LOCATION DECISION 77
A. Bid-Rent Curves 78
B. Industrial Location 78
C. Residential Location Models 80
VI. SCALE AND NUMBER OF PUBLIC FACILITIES 81
A. Static Short-Run Equilibrium 81
B. Dynamic Long-Run Equilibrium 85
VII. SPATIAL LOCATION OF A FACILITY 87
A. Center of a Network 88
B. Median of a Network 89
C. Competitive Location and Games 92
D. Imperfect Information 94
VIII. ECONOMIC BASIS OF THE GRAVITY-BASED SPATIAL ALLOCATION MODEL 96
A. The Singly Constrained Model 96
B. The Doubly Constrained Model 102
C. The Unconstrained Model 103
D. The Intervening Opportunity Model 104
IX. CONCLUDING REMARKS 107
X. EXERCISES Self-Instructional Module: PROBABILITY 107
Problem 1: Gravity Model 108
Problem 2: Further Discussions on Forecasting 109
ENDNOTES 111
REFERENCES 111
3 Descriptive Tools for Analysis 113
I. AN EXAMPLE 113
II. DESCRIPTIVE TECHNIQUES: ANOTHER EXAMPLE 115
III. SIMULATION 117
IV. STOCHASTIC SIMULATION 122
V. DISCRETE EVENT SIMULATION 126
A. Stochastic Process 126
B. Simulation 130
VI. INVENTORY CONTROL USING MARGINAL ANALYSIS 132
VII. BAYESIAN ANALYSIS 135
A. Bayesian Update 136
B. Bayesian Decisions 137
C. Decision Tree 138
D. Influence Diagram 140
E. Bayesian Classifier 142
VIII. ECONOMETRIC APPROACH 145
A. Arrow Diagram and Path Analysis 146
B. Econometric Models 147
IX. CALIBRATION 149
A. Ordinary Least Squares 150
B. Two-Stage Least Squares 151
C. Example of Two-Stage Least Squares 152
D. Maximum Likelihood 154
X. AGGREGATE VERSUS DISAGGREGATE MODELING 156
XI. THE GRAVITY MODEL REVISITED 158
A. Singly Constrained Gravity Model 158
B. Doubly Constrained Model 161
XII. SPATIAL INTERACTION 164
A. Information Theory 164
B. Entropy 167
XIII. QUALITY OF A MODEL CALIBRATION 171
A. Chi-Square Test 171
B. Variance Reduction 172
XIV. CONCLUDING REMARKS 173
XV. EXERCISES Self-Instructional Module: PROBABILITY DISTRIBUTION AND QUEUING 174
Problem 1: Decision Tree 174
Problem 2: Simulation 177
ENDNOTES 179
REFERENCES 179
4 Prescriptive Tools for Analysis 182
I. A TYPICAL PRESCRIPTIVE MODEL 182
A. Goals and Objectives 183
B. Representation of the System 183
C. A Prescriptive Formulation of the Economic-Base Concept 184
II. HEURISTIC SOLUTION TECHNIQUES 185
A. Manual Approach 185
B. Enumerative Method 186
C. Direct Search Technique 190
D. The Golden Section Algorithm 191
E. Fibonacci Search Procedure 193
III. ANALYTICAL SOLUTION TECHNIQUES 196
A. Calculus 196
B. Linear Programming 198
C. Primal and Dual Linear Programs 201
D. Solution of Linear Programs 202
E. Nonlinear Programming 207
F. Solution of a Nonlinear Program 209
IV. INTEGER OR MIXED-INTEGER PROGRAMMING 213
A. Total Unimodularity 215
B. Network Software 216
C. Network with Gains 218
V. DECOMPOSITION METHODS IN FACILITY LOCATION 221
A. Resource Directive Decomposition 222
B. Price Directive Decomposition 224
VI. SPATIAL INTERACTIONS: THE QUADRATIC ASSIGNMENT PROBLEM 225
A. Nonlinear Formation 226
B. Linear Formulation 226
C. Comments 227
VII. PRESCRIPTIVE ANALYSIS IN FACILITY LOCATION: DATA ENVELOPMENT ANALYSIS 228
VIII. PRESCRIPTIVE TECHNIQUES IN LAND USE 232
A. Entropy Maximization Model 233
B. Relationship to the Allocation Model 234
C. Optimal Control Models of Spatial Interaction 235
IX. CONCLUDING REMARKS 235
X. EXERCISES Self-Instructional Module: GRAPH OPTIMIZATION 236
Problem 1: Properties of a Facility-Location Model 236
Problem 2: Maximal-Coverage Facility-Location Model 237
ENDNOTES 239
REFERENCES 239
5 Multicriteria Decision Making 242
I. PREFERENCE STRUCTURE 243
A. The Importance of Preference Structure 243
B. Paired versus Simultaneous Comparison 245
II. SIMPLE ORDERING 247
III. EXPLORING THE EFFICIENT FRONTIER 249
IV. MULTICRITERIA SIMPLEX (MC-SIMPLEX) 252
A. The MC-Simplex Algorithm 252
B. Nonlinear and Integer Programming 257
C. An Interactive Frank-Wolfe Example 258
D. Comments 262
V. GOAL SETTING 263
A. Compromise Programming 263
B. Deviational Measures 264
C. Goal-Setting Example 265
VI. VALUE FUNCTIONS 266
A. Additive versus Multiplicative Form 266
B. Univariate Utility Function Construction 267
C. Independence Among Criterion Functions 271
D. Summary 272
VII. VALUE-FUNCTION MEASUREMENT STEPS 274
A. Preferential, Utility and Additive Independence 275
B. Examples of Utility Function Calibration 279
C. Validation 285
VIII. MULTICRITERIA DECISION MAKING AND FACILITY LOCATION 289
A. The X, Y', and Z' Spaces in Facility Location 289
B. Multi-Attribute Utility and Optimization 290
IX. A TAXONOMY OF METHODS 293
A. Prior Articulation of Alternatives 293
B. Prior Articulation of Preferences 294
C. Progressive Articulation of Alternatives 294
D. Progressive Articulation of Preferences 294
X. DOMINATION STRUCTURES 295
XI. COLLECTIVE DECISION MAKING 296
A. Arrow\u2019s Paradox 297
B. Game Theory 298
C. Recommended Procedure 300
XII. CONCLUDING REMARKS 301
XIII. EXERCISES Self-Instructional Module: RISK ASSESSMENT 303
Problem 1: Multicriteria Optimization 304
Problem 2: Multi-attribute Decision Analysis 304
ENDNOTES 306
REFERENCES 306
6 Remote Sensing and Geographic Information Systems 310
I. DATA IN SPATIAL-TEMPORAL ANALYSIS 310
A. Resource Requirement 312
B. Assembly of Data Sources 312
C. Use and Display of Information 313
II. GEOGRAPHIC CODING SYSTEMS 316
A. Central Place Theory 316
B. Concentric Zone, Sector, and Multi-Nuclei City Structures 316
C. Dual Independent Map Encoding System 317
D. Topologically Integrated Geographic Encoding and Referencing 319
E. Other Data Sources 320
III. GEOGRAPHIC INFORMATION SYSTEMS (GIS) 322
A. Data Organization and Structure 322
B. Location Reference System and Data Structure 329
C. Geospatial Metadata 331
IV. REMOTE SENSING SYSTEMS 332
A. Interface between Remote Sensing Data and GIS 333
B. An Assessment 334
C. Remote Sensing Technology 336
V. DIGITAL IMAGE PROCESSING 338
A. Image Rectification and Restoration 338
B. Image Enhancement 343
C. Image Classification 345
D. Data Merging 347
VI. DIGITAL IMAGE PROCESSING SOFTWARE AND HARDWARE 350
VII. APPLICATIONS OF REMOTE SENSING 351
VIII. SPECTRAL VERSUS SPATIAL PATTERN RECOGNITION 355
A. Spectral Pattern Recognition 355
B. Contextual Allocation of Pixels 357
IX. A DISTRICT CLUSTERING MODEL 362
A. A Single Subregion Model 362
B. Multiple Subregion Model 366
C. Demand Equity 370
D. Extensions 371
X. CASE STUDY OF IMAGE CLASSIFICATION 372
A. Digital Image Data 372
B. Image Classification 374
C. Lessons Learned 377
XI. REMOTE SENSING, GIS, AND SPATIAL ANALYSIS 378
XII. CONCLUDING REMARKS 381
XIII. EXERCISES Self-Instructional Module: LINEAR PROGRAMMING PART 1: MODEL FORMULATION 383
Problem 1: Bayesian and Contextual Classification 384
Problem 2: TS-IP Image-Processing Software 384
ENDNOTES 386
REFERENCES 387
7 Analytics and Spatial Information Technology: Retrospect and Prospects 392
I. ANALYTICS 393
A. Statistical Modeling 393
B. Optimization 394
C. Multicriteria Decision-Making 394
D. Location-Based Analysis 395
II. SPATIAL ANALYTICS 396
A. Spatial Association 397
B. Spatial Clustering 398
C. Facility or Site Location 400
D. Routing 401
III. SOFTWARE 402
A. Commercial/Licensed Software 403
B. Developmental Geospatial Software in the Public Domain 423
C. Selecting a Software: The Case of GIS 428
IV. SPATIAL INFORMATION TECHNOLOGY: LOOKING AHEAD 430
A. Spatial Information Technology 431
B. Going Beyond 433
V. EXERCISES Self-Instructional Module: LINEAR PROGRAMMING PART 2 SOLUTION ALGORITHM 435
ENDNOTES 435
REFERENCES 436
8 A Software Survey of Analytics and Spatial Information Technology 439
I. GENERAL ANALYTIC SOFTWARE 440
A. Spreadsheet Modeling 440
B. Applied Mathematics 441
C. Statistics 444
D. Simulation 446
E. Optimization 451
F. Decision Analysis 456
II. SPATIAL ANALYTICS SOFTWARE 457
A. GIS 458
B. Image Processing 461
C. Routing 464
III. CONCLUDING COMMENTS 465
ENDNOTES 466
REFERENCES 468
Synthesis Exercises and Problems 469
I. REMOTE SENSING AND GEOGRAPHIC INFORMATION SYSTEMS 469
A. Bayesian Classifier 470
B. Iterative Conditional Mode Algorithm 471
C. Weighted Iterative Conditional Mode Algorithm 471
D. District Clustering Model 471
E. Combined Classification Scheme 472
F. Histogram Processing 473
II. FACILITY LOCATION 475
A. Nodal Optimality Conditions 475
B. Solid Waste Facility 475
C. Quadratic Assignment Problem 476
III. LOCATION-ROUTING 476
A. Districting 477
B. Minkowski\u2019s Metric 478
IV. ACTIVITY DERIVATION, ALLOCATION AND COMPETITION 479
A. Multicriteria Game 479
B. Gravity versus Transportation Model 480
C. Calibration of a Doubly Constrained Model 481
V. LAND USE MODELS 481
A. Economic-Base and Activity Allocation 481
B. Forecasting Airbase Housing Requirements 483
VI. SPATIAL-TEMPORAL INFORMATION 483
A. Cohort Survival Method 485
VII. TERM PROJECT 487
REFERENCES 490
Appendix 1 Control, Dynamics, and System Stability 493
I. CONTROL THEORY 493
II. CALCULUS OF VARIATIONS 496
III. VARIATIONAL INEQUALITY 497
A. Fundamentals 498
B. Existence and Uniqueness 499
IV. CATASTROPHE THEORY 501
A. Basic Concepts 502
B. Elementary Catastrophes 504
C. The Fold Catastrophe as an Example 506
D. Higher Order Catastrophes 507
E. Remarks 508
V. COMPARTMENTAL MODELS 509
A. Basics 509
B. Stochastic Models 511
C. Deterministic Models 514
D. Deterministic Example 516
E. Stochastic Example 518
F. Discrete Time Models 519
G. Example of a Quasi-Deterministic Analysis 520
VI. SYSTEM STABILITY 522
A. Basic Types of Trajectory 522
B. Bifurcation Theory 524
C. Comments 527
VII. CONCLUDING REMARKS 528
ENDNOTES 528
REFERENCES 529
Appendix 2 Review of Some Pertinent Statistical Tools 531
I. STATISTICAL ANALYSIS: BASIC CONCEPTS 531
II. GOODNESS-OF-FIT MEASURES 533
III. LINEAR REGRESSION 534
IV. ANALYSIS OF VARIANCE 538
V. USING THE REGRESSION EQUATION 539
A. Confidence Interval 540
B. Prediction Interval 540
C. Summary 541
VI. STEPWISE REGRESSION 543
A. Backward and Forward Regression 543
B. Goodness-of-Fit Parameters for Stepwise Regression 545
VII. MATRIX APPROACH TO LINEAR REGRESSION 549
VIII. NONLINEAR REGRESSION 550
IX. CONCLUDING REMARKS 552
ENDNOTES 553
REFERENCES 553
Appendix 3 Review of Pertinent Markovian Processes 554
I. POISSON PROCESS 554
A. State Transition Equations 554
B. Solution to Random Process 556
II. FIELD DATA FROM AIR TERMINAL 556
A. Exponential Distribution 557
B. Poisson Distribution 557
III. M/M/1 QUEUE 560
IV. QUEUING SYSTEMS 561
A. Basic Theory 562
B. Queuing Formulas 563
C. Choosing a Queuing Discipline 566
V. MARKOVIAN PROPERTIES 568
VI. MARKOVIAN PROPERTIES OF DYNAMIC PROGRAMMING 569
A. Vehicle Dispatching Example 569
B. Principle of Optimality 574
VII. MARKOVIAN DECISION PROCESSES 575
A. Policy Iteration 575
B. Reward Per Period 578
VIII. RECURSIVE PROGRAMMING 579
A. Existence of Solutions 580
B. Phase Solutions 581
IX. CONCLUDING REMARKS 582
ENDNOTES 583
REFERENCES 583
Appendix 4 Review of Some Pertinent Optimization Schemes 584
I. LINEAR PROGRAMMING 584
A. Simplex Algorithm 584
B. Some Other Key Concepts 587
C. Theory of Simplex 589
II. NETWORK-WITH-SIDE-CONSTRAINTS 590
A. Multicommodity-Flow Problem 591
B. The Network-with-Side-Constraints Algorithm 593
III. LAGRANGIAN RELAXATION 603
A. Illustration of Basic Concepts 603
B. Underlying Theory 604
C. Subgradient Optimization 607
D. Branch-and-Bound (B&B) Solution 608
IV. BENDERS\u2019 DECOMPOSITION 610
A. Example 611
B. Convergence 613
C. Extension 613
V. ALGORITHMS AND COMPLEXITY 614
VI. CONCLUDING REMARKS 616
ENDNOTES 617
REFERENCES 617
Appendix 5 Discussion of Technical Concepts 619
Appendix 6 Abbreviation and Mathematical Symbols 646
List of Symbols 651
Solutions to Exercises and Problems 681
I. SOLUTIONS TO SELF-INSTRUCTIONAL MODULES 681
A. Empirical Modeling Module: Answers to Illustrative Exercises 682
B. Probability Module: Answers to Illustrative Exercises 684
C. Probability Distribution & Queuing Module: Answers to Illustrative Exercises 686
D. Graph Theory Module: Answers to Illustrative Exercises 689
E. Risk Assessment Module: Answers To Illustrstive Exercises 694
F. Linear Programming Module: Part 1 Modeling Answers To Illustrative Exercises 696
G. Linear Programming Module: Part 2 Solution Algorithm Answers To Illustrative Exercises 698
II. SOLUTIONS TO REGULAR PROBLEMS 700
III. SOLUTIONS TO SYNTHESIS EXERCISES AND PROBLEMS 700
A. Remote Sensing and Geographic Information Systems 700
B. Facility Location 705
C. Location-Routing 706
D. Activity Derivation, Competition and Allocation 710
E. Land-Use Models 713
F. Spatial-Temporal Information 714
REFERENCES 716
Index 717
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