Interactive operations research with maple: methods and models
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston, Mass. [u.a.]
Birkhäuser
2000
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 468 S. graph. Darst. |
| ISBN: | 3764341653 0817641653 |
Internformat
MARC
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| 100 | 1 | |a Parlar, Mahmut |d 1952- |e Verfasser |0 (DE-588)122351800 |4 aut | |
| 245 | 1 | 0 | |a Interactive operations research with maple |b methods and models |c Mahmut Parlar |
| 264 | 1 | |a Boston, Mass. [u.a.] |b Birkhäuser |c 2000 | |
| 300 | |a XIV, 468 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Dataprocessing |2 gtt | |
| 650 | 7 | |a Operations research |2 gtt | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Maple (Computer file) | |
| 650 | 4 | |a Operations research |x Data processing | |
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| 650 | 0 | 7 | |a Operations Research |0 (DE-588)4043586-6 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1822414677695528960 |
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Contents
Preface xi
1 Introduction to Operations Research 1
1.1 A Brief History 1
1.2 The Method of OR 2
1.3 About This Book 4
2 A Quick Tour of Maple 5
2.1 Introduction 5
2.2 Symbolics 6
2.2.1 Expanding, Factoring and Simplifications 6
2.2.2 Function Definitions Using " " and unapplyO . 8
2.2.3 Lists, Sets and Arrays 9
2.2.4 Additional Commands to Manipulate Expressions . 12
2.2.5 Solving Equations Analytically 14
2.3 Numerics 15
2.3.1 Solving Equations Numerically 16
2.3.2 Statistical Computations Using the stats Package. . 17
2.3.3 The simplex Package 19
2.4 Graphics 19
2.4.1 Two dimensional Plots 20
2.4.2 Three Dimensional Plots 24
2.5 Other Useful Commands and Packages 27
2.5.1 Thepiecewise () Command 27
vi Contents
2.5.2 The interface () Command 29
2.5.3 The inf olevel[ ] Command 30
2.5.4 Exporting to C, FORTRAN and LaTeX 31
2.5.5 Programming in Maple 32
2.5.6 The finance Package 33
2.6 Summary 35
2.7 Exercises 35
3 Maple and Mathematical Foundations of Operations Research 37
3.1 Introduction 37
3.2 Algebra 38
3.2.1 Solution of a Single Equation or Inequality 38
3.2.2 Solution of a System of Nonlinear Equations 41
3.3 Calculus 44
3.3.1 Limits 44
3.3.2 Derivatives 45
3.3.3 Integrals 49
3.3.4 Finite Sums and Infinite Series 54
3.4 Linear Algebra 55
3.4.1 Matrix Operations 55
3.4.2 Solution of Simultaneous Linear Equations 58
3.4.3 Eigenvalues, Eigenvectors and Diagonalization 61
3.4.4 Least Squares Fitting to Data 63
3.4.5 Special Matrices 66
3.4.6 Positive Definiteness 67
3.5 Differential Equations 68
3.5.1 Ordinary Differential Equations 69
3.5.2 Partial Differential Equations 77
3.5.3 Difference (Recurrence) Equations 79
3.6 Transform Methods 81
3.6.1 Laplace Transforms 81
3.6.2 Generating Functions 85
3.7 Probability 88
3.7.1 Continuous and Discrete Random Variables 88
3.7.2 Expectation 92
3.7.3 Jointly Distributed Random Variables 95
3.8 Summary 96
3.9 Exercises 96
4 Linear Programming 99
4.1 Introduction 99
4.2 Graphical Solution 100
4.3 The Simplex Method 104
4.3.1 Manual Solution of the Production Problem 107
4.3.2 Solution Using Maple's simplex Package 113
Contents vii
4.3.3 A Problem with Mixed Constraints 116
4.4 Special Cases and Difficulties 118
4.4.1 Infeasibility 118
4.4.2 Unbounded Solutions 119
4.4.3 Degeneracy 119
4.5 Other Examples 120
4.5.1 The Transportation Problem 121
4.5.2 Two Person Zero Sum Games 124
4.5.3 A Linear Program with Randomly Generated Data . 129
4.6 Sensitivity Analysis and Duality 130
4.6.1 Changes in the RHS Values and Dual Prices 130
4.6.2 Changes in the Objective Function Coefficients 133
4.6.3 Addition of a New Decision Variable 135
4.6.4 Duality 136
4.7 Integer Linear Programming 145
4.8 Summary 147
4.9 Exercises 148
5 Nonlinear Programming 153
5.1 Introduction 153
5.2 Convexity of Sets and Functions 154
5.2.1 Positive and Negative Definite Matrices 157
5.2.2 Convexity of a Function and Definiteness of its Hessian . 160
5.2.3 Examples of Definiteness/Convexity 160
5.2.4 Cholesky Factorization 164
5.3 Unconstrained Optimization 166
5.4 Inequality and Equality Constrained Optimization 170
5.4.1 Geometric Interpretation of Kuhn Tucker Conditions . 173
5.4.2 Constraint Qualification 174
5.4.3 An Equivalent Formulation Using the Lagrangian . 176
5.4.4 Economic Interpretation of the Lagrange Multipliers . 181
5.5 Lagrangian Duality 183
5.6 Summary 190
5.7 Exercises 190
6 Dynamic Programming 193
6.1 Introduction 193
6.2 Stagecoach Problem 197
6.3 Models with a Linear System and Quadratic Cost 201
6.3.1 The Infinite Stage Problem 207
6.4 Continuous Time Dynamic Programming 211
6.4.1 A Problem with Linear System and Quadratic Cost . . . .214
6.4.2 A Problem with Quadratic and Linear Costs 215
6.5 A Constrained Work Force Planning Model 219
6.6 A Gambling Model with Myopic Optimal Policy 224
viii Contents
6.7 Optimal Stopping Problems 228
6.7.1 The Infinite Stage Problem 230
6.8 Summary 233
6.9 Exercises 233
7 Stochastic Processes 237
7.1 Introduction 237
7.2 Exponential Distribution and Poisson Process 238
7.2.1 Memory less Property of the Exponential Distribution . . . 239
7.2.2 Hazard Rate Function 240
7.2.3 The Erlang Random Variable 241
7.2.4 Poisson Process 243
7.2.5 Interarrival Times of the Poisson Process 246
7.2.6 Density of the Erlang—An Equivalent Derivation . 246
7.2.7 Nonhomogeneous Poisson Process 247
7.2.8 Compound Poisson Process 251
7.3 Renewal Theory 256
7.3.1 Preliminaries 257
7.3.2 Distribution of N(t) 257
7.3.3 Renewal Function and Renewal Density 259
7.3.4 Renewal Equation and the Key Renewal Theorem 262
7.3.5 Renewal Reward Process 268
7.4 Discrete Time Markov Chains 271
7.4.1 Chapman Kolmogorov Equations 276
7.4.2 Limiting Probabilities and the Stationary Distribution . . 278
7.4.3 Classification of States 287
7.4.4 Imbedded Markov Chain Technique 293
7.4.5 Transient Behavior of Markov Chains 301
7.5 Continuous Time Markov Chains 305
7.5.1 Kolmogorov Differential Equations 308
7.5.2 Limiting Probabilities 318
7.6 Summary 327
7.7 Exercises 327
8 Inventory Models 331
8.1 Introduction 331
8.2 Classification of Inventory Models 332
8.3 Costs Associated with Inventory Models 334
8.3.1 Procurement Cost 334
8.3.2 Holding (or Carrying) Cost 334
8.3.3 Penalty Cost 334
8.4 Deterministic Inventory Models 335
8.4.1 The Basic EOQ Model 335
8.4.2 The EOQ Model with Planned Backorders 338
8.4.3 Analysis of Implied Backorder Costs 343
Contents ix
8.4.4 Quantity Discounts 346
8.5 Probabilistic Inventory Models 349
8.5.1 The Continuous Review Model: Approximate Formulation 349
8.5.2 The Continuous Review Model: Exact Formulation . 354
8.5.3 One Period (Newsvendor) Model with Random Demand . 358
8.5.4 Dynamic Inventory Models 361
8.5.5 Diversification Under Yield Randomness 366
8.6 Summary 371
8.7 Exercises 371
9 Queueing Systems 375
9.1 Introduction 375
9.2 Markovian Queueing Systems 377
9.2.1 Birth and Death Processes 377
9.2.2 M/M/l Queueing System 378
9.2.3 Finite Capacity Markovian Queue: M/M/l/K 382
9.2.4 Multiserver Queue M/M/c 383
9.2.5 Markovian Bulk Arrival System: Mx/M/\ 387
9.3 Transient Solutions 389
9.3.1 Finite Capacity M/M/l/K Queue with K = 1 389
9.3.2 Ample Server System M/M/oo 391
9.4 Queueing Networks 394
9.4.1 Serial Queue with Blocking 394
9.4.2 Jackson Networks 398
9.5 Optimization of Queueing Systems 401
9.5.1 A Transportation Queueing Process 402
9.5.2 An M/M/l System with Controlled Arrivals 404
9.5.3 Optimal Dynamic Service Rate Control 406
9.6 Summary 413
9.7 Exercises 413
10 Simulation 417
10.1 Introduction 417
10.2 Generating (Pseudo ) Random Numbers 423
10.2.1 Mixed Congruential Method 424
10.2.2 Maple's Uniform Random Number Generator 426
10.2.3 Kolmogorov Smirnov Test for Uniformity 426
10.3 Generating Random Variates from Other Distributions 428
10.3.1 Exponential Random Variates 429
10.3.2 Maple's Random Variate Generators 430
10.4 Monte Carlo Simulation 432
10.4.1 Numerical Evaluation of Definite Integrals 432
10.4.2 Simulation of a Static (Single Period) Problem 434
10.5 Dynamic Simulation Models 435
10.5.1 Simulation of an Inventory System with Random Yield . .436
x Contents
10.5.2 Simulation of a Non Markovian Queue 438
10.6 Optimization by Random Search 441
10.7 Summary 445
10.8 Exercises 446
References 449
Index 463 |
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| language | English |
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| spelling | Parlar, Mahmut 1952- Verfasser (DE-588)122351800 aut Interactive operations research with maple methods and models Mahmut Parlar Boston, Mass. [u.a.] Birkhäuser 2000 XIV, 468 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Dataprocessing gtt Operations research gtt Datenverarbeitung Maple (Computer file) Operations research Data processing Maple Programm (DE-588)4209397-1 gnd rswk-swf Operations Research (DE-588)4043586-6 gnd rswk-swf Operations Research (DE-588)4043586-6 s Maple Programm (DE-588)4209397-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009132799&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Parlar, Mahmut 1952- Interactive operations research with maple methods and models Dataprocessing gtt Operations research gtt Datenverarbeitung Maple (Computer file) Operations research Data processing Maple Programm (DE-588)4209397-1 gnd Operations Research (DE-588)4043586-6 gnd |
| subject_GND | (DE-588)4209397-1 (DE-588)4043586-6 |
| title | Interactive operations research with maple methods and models |
| title_auth | Interactive operations research with maple methods and models |
| title_exact_search | Interactive operations research with maple methods and models |
| title_full | Interactive operations research with maple methods and models Mahmut Parlar |
| title_fullStr | Interactive operations research with maple methods and models Mahmut Parlar |
| title_full_unstemmed | Interactive operations research with maple methods and models Mahmut Parlar |
| title_short | Interactive operations research with maple |
| title_sort | interactive operations research with maple methods and models |
| title_sub | methods and models |
| topic | Dataprocessing gtt Operations research gtt Datenverarbeitung Maple (Computer file) Operations research Data processing Maple Programm (DE-588)4209397-1 gnd Operations Research (DE-588)4043586-6 gnd |
| topic_facet | Dataprocessing Operations research Datenverarbeitung Maple (Computer file) Operations research Data processing Maple Programm Operations Research |
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