Mathematical programming methods for geographers and planners:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
Croom Helm
1983
|
| Schriftenreihe: | Croom Helm series in geography and environment
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 363 S. graph. Darst. |
| ISBN: | 0312501331 0709915128 |
Internformat
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| 650 | 4 | |a Programmation (Mathématiques) | |
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| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Industrial location |x Planning |x Mathematical models | |
| 650 | 4 | |a Land use |x Planning |x Mathematical models | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Programming (Mathematics) | |
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Datensatz im Suchindex
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| adam_text | Titel: Mathematical programming methods for geographers and planners
Autor: Killen, James E
Jahr: 1983
CONTENTS
LIST OF FIGURES
LIST OF TABLES
PREFACE
CHAPTER 1. INTRODUCTION I
1.1 MATHEMATICAL PROGRAMMING I
1.2 THE ROLE AND IMPORTANCE OF MATHEMATICAL PROGRAMMING h
1.3 OBJECTIVES AND PLAN OF BOOK 5
CHAPTER 2. NETWORK MODELS 9
2.1 INTRODUCTION 9
2.2 NETWORK DESIGN MODELS 3
2.2.1 Two Simple Network Design Models 9
2.2.2 The Optimal Network Problem Î1
2.2.3 Steiner Minima) Spanning Trees 14
2.3 SHORTEST ROUTE MODELS 17
2.3.1 Shortest Route Algorithm 1?
2.3.2 Some Appi i cat!oris 19
2.3.3 Second Shortest Route 22
2.4 NETWORK FLOW MODELS 24
2.4.1 Maximum Flow Problem 24
2.4.2 Least Cost Flow Problem With Capacity
Constraints 29
Page
CHAPTER 3. THE TRANSPORTATION AND RELATED PROBLEMS 33
3.1 INTRODUCTION 33
3.2 THE ASSIGNMENT PROBLEM 33
3.2.1 Formulation 33
3.2.2 Solution Method 35
3.2.3 Examples 37
3.2.4 The Assignment Problem Viewed as a Least
Cost Maximum Flow Problem 40
3.3 THE TRANSPORTATION PROBLEM 41
3.3.1 Formulation 41
3.3.2 Solution Method 43
3-3.3 Examples 48
3.3.4 An Alternative View of the Transportation
? rob 1 em 51
3.3.5 More Efficient Starting Solutions 58
3-3.6 Computational Difficulties 60
3-3.7 The Transportation Problem Viewed as a Least
Cost Maximum Flow Problem 65
3.4 THE TRANSHIPMENT PROBLEM 66
3.4.1 Formulation for One Intermediate Tranship¬
ment Point 66
3.4.2 Solution Methods 67
3.4.3 Examp1 e 67
3.4.4 Formulation With a Variable Number of
Intermediate Transhipment Points 68
3.4.5 Volume Change at Transhipment Points 69
3-4.6 Example 70
3.5 NETWORK DEVELOPMENT MODELS 74
CHAPTER 4. LINEAR PROGRAMMING : THE SIMPLEX METHOD 77
4.1 INTRODUCTION 77
4.2 SOME LINEAR PROGRAMMING FORMULATIONS 78
4.2.1 Urban Landuse Design 79
4.2.2 Regional and Interregional Development
Problems 82
4.2.3 Agriculture 87
4.2.4 Diet Composition 88
4.2.5 Transport 89
4.3 GRAPHICAL SOLUTION METHOD 91
4.4 PRELIMINARIES TO THE SIMPLEX METHOD 96
4.4.1 Standard Form Representation 96
Page
4.4.2 Solving Simultaneous Linear Equations 98
4.4.3 Change of Basis Operations 101
4.4.4 Algebraic Characteristics of a Linear
Programming Solution Space 103
4.5 THE SIMPLEX METHOD 106
4.6 GENERALISATION OF THE SIMPLEX METHOD 110
4.6.1 Greater Than or Equals Constraints 110
4.6.2 Equality Constraints 116
4.6.3 Minimisation Objective 116
4.7 SOME LINEAR PROGRAMMING STUDY RESULTS 119
4.7.1 Urban Landuse Design 119
4.7.2 Recreational Landuse 122
4.7.3 Agriculture 124
4.7-4 Diet 127
4.8 SOME RELATIONSHIPS BETWEEN THE NORTHWEST CORNER
STEPPING STONE METHOD FOR SOLVING THE TRANSPORT¬
ATION PROBLEM AND THE SIMPLEX METHOD 127
4.9 SPECIAL CASES 131
4.9-1 Alternative Optimal Solutions 131
4.9.2 Degeneracy 134
4.9-3 Constraint Contradiction 137
4-9.4 Infinite Solution Space 139
CHAPTER 5. LINEAR PROGRAMMING : SENSITIVITY ANALYSIS
AND THE DUAL 143
5.1 SENSITIVITY ANALYSIS 143
5.2 THREE MATHEMATICAL PROPERTIES 144
5.3 CHANGES IN RIGHT HAND SIDE COEFFICIENTS 148
5.4 CHANGES IN OBJECTIVE COEFFICIENTS 157
5.5 OTHER TYPES OF SENSITIVITY ANALYSIS 164
5-5.1 Changes in Constraint Coefficients 165
5.5-2 Addition of a New Decision Variable 167
5.5.3 Imposition of an Additional Constraint I69
5.6 PARAMETRIC LINEAR PROGRAMMING 172
5-7 THE DUAL LINEAR PROGRAMMING PROBLEM 174
5.8 INTERPRETATION OF THE DUAL 179
5.8.1 The Dual of a Maximisation Problem 179
5.8.2 The Dual of a Minimisation Problem 185
Page
5.9 DUAL FORMULATIONS : FURTHER EXAMPLES I88
5.9.I Henderson (1968) I88
5.9·2 Herbert and Stevens (i960) 189
5.9.3 Miller (1963) 190
5.10 A FURTHER NOTE ON PRIMAL-DUAL INTERRELATIONSHIPS 192
5.11 THE DUAL OF THE TRANSPORTATION PROBLEM 193
CHAPTER 6. INTEGER PROGRAMMING 195
6.1 INTRODUCTION 195
6.2 CUTTING PLANE METHODS : THE FRACTIONAL ALGORITHM 197
6.3 BRANCH AND BOUND METHODS : DAKIN S ALGORITHM 203
CHAPTER 7. ZERO-ONE PROGRAMMING 209
7.1 INTRODUCTION 209
7.2 SOLUTION METHODS FOR ZERO-ONE PROGRAMMING PROBLEMS 210
7.3 THE TRAVELLING SALESMAN PROBLEM 218
7.4 THE TOTAL COVER PROBLEM 223
7.5 THE PARTIAL COVER PROBLEM 225
7.6 THE p-MEDIAN PROBLEM 227
7.7 DEVELOPMENTS OF THE p-MEDIAN PROBLEM 229
7.8 THE LOCATION-ALLOCATION PROBLEM 232
7.9 DEVELOPMENTS OF THE LOCATION-ALLOCATION PROBLEM 241
7.10 FURTHER EXAMPLES OF PROGRAMMING FORMULATIONS
INCORPORATING ZERO-ONE VARIABLES 243
7.10.1 Scheduling Planning Projects : Tourist
Development in Turkey 243
7.10.2 Plant Location and Air Quality Management 244
7.10.3 Some Network Development Models 246
CHAPTER 8. NONLINEAR PROGRAMMING 249
8.1 INTRODUCTION 249
8.1.1 Nonlinear Programming Models 249
8.1.2 Some Nonlinear Objectives 250
8.2 SOME POTENTIAL DIFFICULTIES IN SOLVING NONLINEAR
AS OPPOSED TO LINEAR PROGRAMMING PROBLEMS 253
8.3 UNCONSTRAINED OPTIMISATION 255
Page
8.3· 1 Quadratic Objective 255
8.3.2 Nan Quadratic Objectives 257
8.3.3 Optimising An Imprecisely Defined Non¬
linear Objective Whose General Form Is
Known : The Method of Golden Sections 257
8.4 OPTIMISING A NONLINEAR OBJECTIVE WITH LINEAR
EQUALITY CONSTRAINTS : THE METHOD OF LAGRANGE
MULTIPLIERS 261
8.5 TWO ENTROPY MAXIMISING MODELS 265
8.5.1 A Trip Distribution Model 266
8.5.2 The Herbert-Stevens Residential Landuse
Model Revisited 271
8.6 OPTIMISING A NONLINEAR OBJECTIVE WITH LINEAR
INEQUALITY CONSTRAINTS 272
8.6.1 Kuhn-Tucker Conditions 272
8.6.2 Example 275
8.7 SOME OTHER NONLINEAR PROGRAMMING SOLUTION
APPROACHES 276
8.7.1 Geometric Programming 276
8.7.2 Separable Programming 279
8.7·3 Direct Linearisation 283
CHAPTER 9. DYNAMIC PROGRAMMING 285
9.1 INTRODUCTION 285
9-2 THE SHORTEST ROUTE PROBLEH 286
9.3 GENERALISATION 291
9.4 EXAMPLES 293
9.4.1 A Network Development Problem 293
9.4.2 The Stepwise Location-Allocation Problem 296
9.4.3 The Optimal Allocation Problem 297
9.4.4 A Water Resources Problem 299
9.4.5 Decision Making Under Conditions of
Uncertainty : Maximisation of Expected
Value 302
9.4.6 A Multiplicative Objective Function 304
9.5 SOME ADVANCED TOPICS 305
9.5.1 Continuous Variable Problems 305
9.5.2 More Complex Decision Making Processes 307
9.5.3 The Nature of the Objective Function 308
Page
CHAPTER IO. GOAL PROGRAMMING AND RELATED TOPICS 309
10.1 GOAL PROGRAMMING : INTRODUCTION 309
10.2 GOAL PROGRAMMING : GENERAL FORMULATION 310
10.3 GOAL PROGRAMMING EXAMPLES 313
10.3.1 Recreational and Forest Landuse 313
10.3.2 Residential and Industrial Location 317
10.3.3 Goal Programming in the Context of the
Transportation Problem 322
10.4 MULTICRITERIA ANALYSIS 322
10.5 HIERARCHICAL OPTIMISATION 325
APPENDIX 327
A. 1 MATRIX ALGEBRA 327
A. 2 CALCULUS 329
REFERENCES 337
AUTHOR 1NDEX 355
SUBJECT INDEX 359
|
| any_adam_object | 1 |
| author | Killen, James E. |
| author_facet | Killen, James E. |
| author_role | aut |
| author_sort | Killen, James E. |
| author_variant | j e k je jek |
| building | Verbundindex |
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| callnumber-first | H - Social Science |
| callnumber-label | HD108 |
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| dewey-ones | 658 - General management |
| dewey-raw | 658.4/033 |
| dewey-search | 658.4/033 |
| dewey-sort | 3658.4 233 |
| dewey-tens | 650 - Management and auxiliary services |
| discipline | Wirtschaftswissenschaften Geographie |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T15:59:43Z |
| institution | BVB |
| isbn | 0312501331 0709915128 |
| language | English |
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| oclc_num | 9044552 |
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| physical | 363 S. graph. Darst. |
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| spelling | Killen, James E. Verfasser aut Mathematical programming methods for geographers and planners James Killen London [u.a.] Croom Helm 1983 363 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Croom Helm series in geography and environment Industrie - Localisation - Planification - Modèles mathématiques Optimisation mathématique Programmation (Mathématiques) Sol, Utilisation du - Planification - Modèles mathématiques Transport - Planification - Modèles mathématiques Mathematisches Modell Industrial location Planning Mathematical models Land use Planning Mathematical models Mathematical optimization Programming (Mathematics) Transportation Planning Mathematical models Datenverarbeitung (DE-588)4011152-0 gnd rswk-swf Geografie (DE-588)4020216-1 gnd rswk-swf Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Geografie (DE-588)4020216-1 s Mathematische Methode (DE-588)4155620-3 s DE-604 Datenverarbeitung (DE-588)4011152-0 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002166457&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Killen, James E. Mathematical programming methods for geographers and planners Industrie - Localisation - Planification - Modèles mathématiques Optimisation mathématique Programmation (Mathématiques) Sol, Utilisation du - Planification - Modèles mathématiques Transport - Planification - Modèles mathématiques Mathematisches Modell Industrial location Planning Mathematical models Land use Planning Mathematical models Mathematical optimization Programming (Mathematics) Transportation Planning Mathematical models Datenverarbeitung (DE-588)4011152-0 gnd Geografie (DE-588)4020216-1 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| subject_GND | (DE-588)4011152-0 (DE-588)4020216-1 (DE-588)4155620-3 |
| title | Mathematical programming methods for geographers and planners |
| title_auth | Mathematical programming methods for geographers and planners |
| title_exact_search | Mathematical programming methods for geographers and planners |
| title_full | Mathematical programming methods for geographers and planners James Killen |
| title_fullStr | Mathematical programming methods for geographers and planners James Killen |
| title_full_unstemmed | Mathematical programming methods for geographers and planners James Killen |
| title_short | Mathematical programming methods for geographers and planners |
| title_sort | mathematical programming methods for geographers and planners |
| topic | Industrie - Localisation - Planification - Modèles mathématiques Optimisation mathématique Programmation (Mathématiques) Sol, Utilisation du - Planification - Modèles mathématiques Transport - Planification - Modèles mathématiques Mathematisches Modell Industrial location Planning Mathematical models Land use Planning Mathematical models Mathematical optimization Programming (Mathematics) Transportation Planning Mathematical models Datenverarbeitung (DE-588)4011152-0 gnd Geografie (DE-588)4020216-1 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| topic_facet | Industrie - Localisation - Planification - Modèles mathématiques Optimisation mathématique Programmation (Mathématiques) Sol, Utilisation du - Planification - Modèles mathématiques Transport - Planification - Modèles mathématiques Mathematisches Modell Industrial location Planning Mathematical models Land use Planning Mathematical models Mathematical optimization Programming (Mathematics) Transportation Planning Mathematical models Datenverarbeitung Geografie Mathematische Methode |
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