Optimal control theory: applications to management science and economics
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Boston [u.a.]
Kluwer
2000
|
| Ausgabe: | 2. ed. |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009124527&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XVII, 504 S. graph. Darst. |
| ISBN: | 0792386086 |
Internformat
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| 245 | 1 | 0 | |a Optimal control theory |b applications to management science and economics |c Suresh P. Sethi ; Gerald L. Thompson |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Boston [u.a.] |b Kluwer |c 2000 | |
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| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Control theory | |
| 650 | 4 | |a Management |x Mathematical models | |
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Datensatz im Suchindex
| _version_ | 1819326173049520128 |
|---|---|
| adam_text | i
i
Contents
s
Preface to First Edition xiii
I
Preface to Second Edition xv
1 What is Optimal Control Theory? 1
1.1 Basic Concepts and Definitions 2
i 1.2 Formulation of Simple Control Models 4
1.3 History of Optimal Control Theory 7
1.4 Notation and Concepts Used 10
2 The Maximum Principle: Continuous Time 23
2.1 Statement of the Problem 23
2.1.1 The Mathematical Model 24
2.1.2 Constraints 24
2.1.3 The Objective Function 25
2.1.4 The Optimal Control Problem 25
2.2 Dynamic Programming and the Maximum Principle ... 27
2.2.1 The Hamilton Jacobi Bellman Equation 27
2.2.2 Derivation of the Adjoint Equation 31
2.2.3 The Maximum Principle 33
2.2.4 Economic Interpretations of the Maximum
Principle 34
2.3 Elementary Examples 36
2.4 Sufficiency Conditions 44
2.5 Solving a TPBVP by Using Spreadsheet Software 48
3 The Maximum Principle: Mixed Inequality Constraints 57
3.1 A Maximum Principle for Problems with Mixed Inequality
Constraints 58
3.2 Sufficiency Conditions 64
viii Contents
3.3 Current Value Formulation 65
3.4 Terminal Conditions 69
3.4.1 Examples Illustrating Terminal Conditions .... 74
3.5 Infinite Horizon and Stationarity 80
3.6 Model Types 83
4 The Maximum Principle: General Inequality
Constraints 97
4.1 Pure State Variable Inequality Constraints: Indirect Method 98
4.1.1 Jump Conditions 103
4.2 A Maximum Principle: Indirect Method 104
4.3 Current Value Maximum Principle: Indirect Method ... Ill
4.4 Sufficiency Conditions 113
5 Applications to Finance 119
5.1 The Simple Cash Balance Problem 120
5.1.1 The Model 120
5.1.2 Solution by the Maximum Principle 121
5.1.3 An Extension Disallowing Overdraft and
Short Selling 124
5.2 Optimal Financing Model 129
5.2.1 The Model 129
5.2.2 Application of the Maximum Principle 131
5.2.3 Synthesis of Optimal Control Paths 133
5.2.4 Solution for the Infinite Horizon Problem 144
6 Applications to Production and Inventory 153
6.1 A Production Inventory System 154
6.1.1 The Production Inventory Model 154
6.1.2 Solution by the Maximum Principle 156
6.1.3 The Infinite Horizon Solution 159
6.1.4 A Complete Analysis of the Constant Positive S
Case with Infinite Horizon 160
6.1.5 Special Cases of Time Varying Demands 162
6.2 Continuous Wheat Trading Model 164
6.2.1 The Model 165
6.2.2 Solution by the Maximum Principle 166
6.2.3 Complete Solution of a Special Case 167
6.2.4 The Wheat Trading Model with No Short Selling . 170
6.3 Decision Horizons and Forecast Horizons 173
Contents ix
I 6.3.1 Horizons for the Wheat Trading Model 174
6.3.2 Horizons for the Wheat Trading Model with
Warehousing Constraint 175
! 7 Applications to Marketing 185
7.1 The Nerlove Arrow Advertising Model 186
7.1.1 The Model 186
7.1.2 Solution by the Maximum Principle 188
7.1.3 A Nonlinear Extension 191
7.2 The Vidale Wolfe Advertising Model 194
7.2.1 Optimal Control Formulation for the Vidale Wolfe
Model 195
7.2.2 Solution Using Green s Theorem when Q is Large 196
7.2.3 Solution When Q Is Small 205
7.2.4 Solution When T Is Infinite 206
f 8 The Maximum Principle: Discrete Time 217
8.1 Nonlinear Programming Problems 217
8.1.1 Lagrange Multipliers 218
8.1.2 Inequality Constraints 220
8.1.3 Theorems from Nonlinear Programming 227
8.2 A Discrete Maximum Principle 228
8.2.1 A Discrete Time Optimal Control Problem .... 228
8.2.2 A Discrete Maximum Principle 229
; 8.2.3 Examples 231
8.3 A General Discrete Maximum Principle 234
9 Maintenance and Replacement 241
9.1 A Simple Maintenance and Replacement Model 242
9.1.1 The Model 242
9.1.2 Solution by the Maximum Principle 243
9.1.3 A Numerical Example 245
9.1.4 An Extension 247
9.2 Maintenance and Replacement for a Machine Subject to
Failure 248
9.2.1 The Model 249
9.2.2 Optimal Policy 251
9.2.3 Determination of the Sale Date 253
9.3 Chain of Machines 254
9.3.1 The Model 254
x Contents
9.3.2 Solution by the Discrete Maximum Principle . . . 256
9.3.3 Special Case of Bang Bang Control 257
9.3.4 Incorporation into the Wagner Whitm Framework
for a Complete Solution 258
9.3.5 A Numerical Example 259
10 Applications to Natural Resources 267
10.1 The Sole Owner Fishery Resource Model 268
10.1.1 The Dynamics of Fishery Models 268
10.1.2 The Sole Owner Model 269
10.1.3 Solution by Green s Theorem 270
10.2 An Optimal Forest Thinning Model 273
10.2.1 The Forestry Model 273
10.2.2 Determination of Optimal Thinning 274
10.2.3 A Chain of Forests Model 276
10.3 An Exhaustible Resource Model 279
10.3.1 Formulation of the Model 279
10.3.2 Solution by the Maximum Principle 282
11 Economic Applications 289
11.1 Models of Optimal Economic Growth 289
11.1.1 An Optimal Capital Accumulation Model 290
11.1.2 Solution by the Maximum Principle 290
11.1.3 A One Sector Model with a Growing Labor Force . 291
11.1.4 Solution by the Maximum Principle 292
11.2 A Model of Optimal Epidemic Control 295
11.2.1 Formulation of the Model 295
11.2.2 Solution by Green s Theorem 296
11.3 A Pollution Control Model 299
11.3.1 Model Formulation 299
11.3.2 Solution by the Maximum Principle 300
11.3.3 Phase Diagram Analysis 301
11.4 Miscellaneous Applications 303
12 Differential Games, Distributed Systems, and
Impulse Control 307
12.1 Differential Games 308
12.1.1 Two Person Zero Sum Differential Games 308
12.1.2 Nonzero Sum Differential Games 310
Contents xi
12.1.3 An Application to the Common Property Fishery
Resources 312
12.2 Distributed Parameter Systems 315
12.2.1 The Distributed Parameter Maximum Principle . . 317
l 12.2.2 The Cattle Ranching Problem 318
12.2.3 Interpretation of the Adjoint Function 322
12.3 Impulse Control 322
12.3.1 The Oil Driller s Problem 324
I 12.3.2 The Maximum Principle for Impulse Optimal
Control 325
12.3.3 Solution of the Oil Driller s Problem 327
12.3.4 Machine Maintenance and Replacement 331
! 12.3.5 Application of the Impulse Maximum Principle . . 332
13 Stochastic Optimal Control 339
13.1 The Kalman Filter 340
i 13.2 Stochastic Optimal Control 345
13.3 A Stochastic Production Planning Model 347
13.3.1 Solution for the Production Planning Problem . . 350
13.4 A Stochastic Advertising Problem 352
13.5 An Optimal Consumption Investment Problem 355
13.6 Concluding Remarks 360
A Solutions of Linear Differential Equations 363
; A.I Linear Differential Equations with Constant Coefficients . 363
A.2 Homogeneous Equations of Order One 364
A.3 Homogeneous Equations of Order Two 364
A.4 Homogeneous Equations of Order n 365
A.5 Particular Solutions of Linear D.E. with Constant
Coefficients 366
A.6 Integrating Factor 368
A.7 Reduction of Higher Order Linear Equations to
Systems of First Order Linear Equations 369
A.8 Solution of Linear Two Point Boundary Value Problems . 372
A.9 Homogeneous Partial Differential Equations 372
A. 10 Inhomogeneous Partial Differential Equations 374
A. 11 Solutions of Finite Difference Equations 375
A. 11.1 Changing Polynomials in Powers of k into Facto¬
rial Powers of A; 376
xii Contents
A.11.2 Changing Factorial Powers of k into Ordinary
Powers of k 377
B Calculus of Variations and Optimal Control Theory 379
B.I The Simplest Variational Problem 379
B.2 The Euler Equation 380
B.3 The Shortest Distance Between Two Points on the Plane 383
B.4 The Brachistochrone Problem 384
B.5 The Weierstrass Erdmann Corner Conditions 386
B.6 Legendre s Conditions: The Second Variation 388
B.7 Necessary Condition for a Strong Maximum 389
B.8 Relation to the Optimal Control Theory 390
C An Alternative Derivation of the Maximum Principle 393
C.I Needle Shaped Variation 394
C.2 Derivation of the Adjoint Equation and the Maximum
Principle 396
D Special Topics in Optimal Control 401
D.I Linear Quadratic Problems 401
D.I.I Certainty Equivalence or Separation Principle . . . 403
D.2 Second Order Variations 405
D.3 Singular Control 407
E Answers to Selected Exercises 409
Bibliography 417
Index 483
List of Figures 501
List of Tables 505
|
| any_adam_object | 1 |
| author | Sethi, Suresh P. 1945- Thompson, Gerald Luther 1923- |
| author_GND | (DE-588)123987202 (DE-588)135869943 |
| author_facet | Sethi, Suresh P. 1945- Thompson, Gerald Luther 1923- |
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| callnumber-subject | HD - Industries, Land Use, Labor |
| classification_rvk | SK 880 |
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| dewey-full | 658.4/033 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| 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 | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV013377583 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T10:46:10Z |
| institution | BVB |
| isbn | 0792386086 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009124527 |
| oclc_num | 44110402 |
| open_access_boolean | |
| owner | DE-703 DE-29T DE-573 DE-634 DE-11 |
| owner_facet | DE-703 DE-29T DE-573 DE-634 DE-11 |
| physical | XVII, 504 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Kluwer |
| record_format | marc |
| spellingShingle | Sethi, Suresh P. 1945- Thompson, Gerald Luther 1923- Optimal control theory applications to management science and economics Management gtt Operations research gtt Wiskundige modellen gtt Mathematisches Modell Control theory Management Mathematical models Operations research Unternehmensleitung (DE-588)4233771-9 gnd Operations Research (DE-588)4043586-6 gnd Kontrolltheorie (DE-588)4032317-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd Stochastische optimale Kontrolle (DE-588)4207850-7 gnd |
| subject_GND | (DE-588)4233771-9 (DE-588)4043586-6 (DE-588)4032317-1 (DE-588)4114528-8 (DE-588)4207850-7 |
| title | Optimal control theory applications to management science and economics |
| title_auth | Optimal control theory applications to management science and economics |
| title_exact_search | Optimal control theory applications to management science and economics |
| title_full | Optimal control theory applications to management science and economics Suresh P. Sethi ; Gerald L. Thompson |
| title_fullStr | Optimal control theory applications to management science and economics Suresh P. Sethi ; Gerald L. Thompson |
| title_full_unstemmed | Optimal control theory applications to management science and economics Suresh P. Sethi ; Gerald L. Thompson |
| title_short | Optimal control theory |
| title_sort | optimal control theory applications to management science and economics |
| title_sub | applications to management science and economics |
| topic | Management gtt Operations research gtt Wiskundige modellen gtt Mathematisches Modell Control theory Management Mathematical models Operations research Unternehmensleitung (DE-588)4233771-9 gnd Operations Research (DE-588)4043586-6 gnd Kontrolltheorie (DE-588)4032317-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd Stochastische optimale Kontrolle (DE-588)4207850-7 gnd |
| topic_facet | Management Operations research Wiskundige modellen Mathematisches Modell Control theory Management Mathematical models Unternehmensleitung Operations Research Kontrolltheorie Stochastische optimale Kontrolle |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009124527&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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