Operations research: an introduction
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Upper Saddle River, NJ
Prentice Hall
1997
|
| Edition: | 6. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 916 S. graph. Darst. 1 Diskette ; 3,5" |
| ISBN: | 0132729156 |
Staff View
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| 245 | 1 | 0 | |a Operations research |b an introduction |c Hamdy A. Taha |
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| 264 | 1 | |a Upper Saddle River, NJ |b Prentice Hall |c 1997 | |
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| adam_text | Contents
CHAPTER 1: OVERVIEW OF OPERATIONS RESEARCH 1
1.1 Mathematical Operations Research Models 1
1.2 Operations Research Techniques 3
1.3 Simulation Modeling 4
1.4 Art of Modeling 5
1.5 About this Book 6
Selected References 7
Part I: Deterministic Models 9
CHAPTER 2: INTRODUCTION TO LINEAR PROGRAMMING 11
2.1 Introduction 11
2.2 Construction of the LP model 11
2.3 Graphical LP Solution 14
2.3.1 Solution of a Maximization Model 15
2.3.2 Solution of a Minimization Model 18
2.3.3 Slack, Surplus, and Unrestricted Variables 20
2.4 Graphical Sensitivity Analysis 22
2.4.1 Changes in the Objective Function Coefficients 23
2.4.2 Unit Worth of a Resource 27
2.5 Computer Solution of LP Problems 33
2.6 Analysis of Selected LP models 39
vii
viii Contents
2.7 Summary 62
Selected References 62
Comprehensive Problems 62
CHAPTER 3: THE SIMPLEX METHOD 67
3.1 Introduction 67
3.2 Standard LP Form and Its Basic Solutions 67
3.2.1 Standard LP Form 67
3.2.2 Determination of Basic Solutions 70
3.2.3 Unrestricted Variables and Basic Solutions 72
3.3 The Simplex Algorithm 74
3.4 Artificial Starting Solution 86
3.4.1 TheM Method 86
3.4.2 The Two Phase Method 92
3.5 Special Cases in Simplex Method Application 97
3.5.1 Degeneracy 97
3.5.2 Alternative Optima 101
3.5.3 Unbounded Solutions 103
3.5.4 Infeasible Solution 106
3.6 Summary 108
Selected References 108
Comprehensive Problems 108
CHAPTER 4: DUALITY AND SENSITIVITY ANALYSIS 111
4.1 Introduction 111
4.2 Definition of the Dual Problem 111
4.3 Relationship between the Optimal Primal and Dual
Solutions 117
4.4 Economic Interpretation of Duality 122
4.4.1 Economic Interpretation of Dual Variables 123
4.4.2 Economic Interpretation of Dual Constraints 125
4.5 Dual Simplex Method 128
4.6 Primal Dual Computations 135
4.7 Postoptimal or Sensitivity Analysis 143
Contents ix
4.7.1 Changes Affecting Feasibility 144
4.7.2 Changes Affecting Optimality 155
4.8 Summary 161
Selected References 161
Comprehensive Problems 162
CHAPTER 5: TRANSPORTATION MODEL AND ITS VARIANTS 165
5.1 Definition of the Transportation Model 165
5.2 Nontraditional Transportation Models 174
5.3 The Transportations Algorithm 179
5.3.1 Determination of the Starting Solution 181
5.3.2 Iterative Computations of the Algorithm 185
5.3.3 Simplex Method Explanation of the Method
of Multipliers 193
5.4 The Assignment Model 194
5.4.1 The Hungarian Method 195
5.4.2 Simplex Explanation of the Hungarian Method 201
5.5 The Transshipment Model 202
5.6 Summary 207
Selected References 208
Comprehensive problems 208
CHAPTER 6: NETWORK MODELS 215
6.1 Scope of Network Applications 215
6.2 Network Definitions 216
6.3 Minimal Spanning Tree Algorithm 218
6.4 Shortest Route Problem 222
6.4.1 Examples of the Shortest Route Applications 222
6.4.2 Shortest Route Algorithms 227
6.5 Maximal Flow Model 237
6.5.1 Enumeration of Cuts 238
6.5.2 Maximal Flow Algorithm 239
6.6 Minimum Cost Capacitated Flow Problem 248
x Contents
6.6.1 Network Representation 248
6.6.2 Linear Programming Formulation 250
6.6.3 Capacitated Network Simplex Algorithm 256
6.7 CPM and PERT 263
6.7.1 Network Representation 263
6.7.2 Critical Path Computations 270
6.7.3 Construction of the Time Schedule 274
6.8 Summary 278
Selected References 278
Comprehensive Problems 278
CHAPTER 7: ADVANCED LINEAR PROGRAMMING 281
7.1 Introduction 281
7.2 Vectors and Bases 281
7.2.1 Standard LP in Matrix Form 281
7.2.2 Vector Representation of a Basis 284
7.2.3 Basic Solutions 285
7.3 Validity Proofs of the Simplex Method 287
7.3.1 Definition of Convex Sets 287
7.3.2 Optimality of the Simplex Algorithm 288
1A Generalized Simplex Tableau in Matrix Form 291
7.5 Efficient Computational Algorithms 297
7.5.7 Revised Simplex Method 297
7.5.2 Bounded Variables Algorithm 305
7.5.3 Decomposition Algorithm 313
7.6 Duality 323
7.6.1 Matrix Definition of the Dual Problem 324
7.6.2 Optimal Dual Solution 324
7.7 Parametric Linear Programming 329
7.7.1 Parametric Changes in C 330
7.7.2 Parametric Changes in b 333
7.8 Karmarkar Interior Point Algorithm 336
7.8.1 Basic Idea of the Interior Point Algorithm 336
7.8.2 Interior Point Algorithm 338
7.9 Summary 346
References 346
Comprehensive Problems 346
Contents xi
CHAPTER 8: GOAL PROGRAMMING 349
8.1 Single Objective Versus Multiple Goals 349
8.2 A Goal Programming Formulation 349
8.3 Goal Programming Algorithms 354
8.3.1 The Weighting Method 355
8.3.2 The Preemptive Method 356
8.4 Summary 363
References 363
Comprehensive Problems 363
CHAPTER 9: INTEGER LINEAR PROGRAMMING 367
9.1 Introduction 367
9.2 Illustrative Applications 367
9.3 Integer Programming Solution Algorithms 384
9.3.1 Branch and Bound (B B) Algorithm 385
9.3.2 Zero One Implicit Enumeration Algorithm 391
9.3.3 Cutting Plane Algorithm 398
9.4 Summary 404
Selected References 405
Comprehensive Problems 405
CHAPTER 10: DETERMINISTIC DYNAMIC PROGRAMMING 409
10.1 Introduction 409
10.2 Recursive Nature of Computations in DP 409
10.3 Forward and Backward Recursion 413
10.4 Selected DP Applications 414
10.4.1 Cargo Loading Model 415
10.4.2 Work Force Size Model 421
10.4.3 Equipment Replacement Model 425
10.4.4 Investment Model 429
10.4.5 Inventory Models 433
10.5 Problem of Dimensionality 433
10.6 Summary 436
Selected References 436
xii Contents
Comprehensive Problems 436
CHAPTER 11: DETERMINISTIC INVENTORY MODELS 439
11.1 Introduction 439
11.2 General Inventory Model 439
11.3 Static EOQ Models 440
11.3.1 Classic EOQ Model 440
11.3.2 EOQ with Price Breaks 445
11.3.3 Multi Item EOQ with Storage Limitation 449
11A Dynamic EOQ models 452
11.4.1 No Setup Model 454
11.4.2 Setup Model 459
11.5 Summary 471
Selected References 471
Comprehensive Problems 471
Part II: Probabilistic Models 475
CHAPTER 12: REVIEW OF BASIC PROBABILITY 477
12.1 Introduction 477
12.2 Laws of Probability 477
12.2.1 Addition Law of Probability 478
12.2.2 Conditional Law of Probability 479
12.3 Random Variables and Probability
Distributions 481
12.4 Expectation of a Random Variable 483
12.4.1 Mean and Variance of a Random Variable 484
12.4.2 Mean and Variance of Joint Random Variables 486
12.5 Four Common Probability Distributions 489
12.5.1 Binomial Distribution 489
12.5.2 Poisson Distribution 491
12.5.3 Negative Exponential Distribution 492
12.5.4 Normal Distribution 493
12.6 Empirical Distribution 496
12.7 Summary 503
Selected References 503
Contents xiii
CHAPTER 13: FORECASTING MODELS 505
13.1 Introduction 505
13.2 Moving Average Technique 505
13.3 Exponential Smoothing 510
13.4 Regression 512
13.5 Summary 517
Selected References 517
Comprehensive Problem 517
CHAPTER 14: DECISION ANALYSIS AND GAMES 519
14.1 Decision Environments 519
14.2 Decision Making under Certainty 519
14.2.1 Analytical Hierarchy Approach 520
14.3 Decision Making under Risk 530
14.3.1 Expected Value Criterion 531
14.3.2 Variations of the Expected Value Criterion 539
14.4 Decision under Uncertainty 548
14.5 Game Theory 554
14.5.1 Optimal Solution of Two Person Zero Sum
Games 555
14.5.2 Solution of Mixed Strategy Games 559
14.6 Summary 567
Selected References 567
Comprehensive Problems 567
CHAPTER 15: PROBABILISTIC DYNAMIC PROGRAMMING 571
15.1 Introduction 571
15.2 A Game of Chance 571
15.3 Investment Problem 575
15.4 Maximization of the Event of
Achieving a Goal 580
Selected References 584
Comprehensive Problems 584
xiv Contents
CHAPTER 16: PROBABILISTIC INVENTORY MODELS 585
16.1 Introduction 585
16.2 Continuous Review Models 585
16.2.1 Probabilitized EOQ model 585
16.2.2 Probabilistic EOQ Model 588
16.3 Single Period Models 592
16.3.1 No Setup Model 593
16.3.2 Setup Model (s S Policy) 597
16.4 Multiperiod Model 600
16.5 Summary 603
Selected References 603
Comprehensive Problems 603
CHAPTER 17: QUEUEING SYSTEMS 607
17.1 Why Study Queues? 607
17.2 Elements of a Queueing Model 609
17.3 Role of Exponential Distribution 610
17.3.1 Forgetfulness Property 611
17.3.2 Derivation of the Exponential Distribution 612
VIA Pure Birth and Death Models (Relationship
between the Exponential and Poisson
Distributions) 615
17.4.1 Pure Birth Model 615
17.4.2 Pure Death Model 619
17.5 Generalized Poisson Queueing Model 621
17.6 Specialized Poisson Queues 627
77.6.2 Steady State Measures of Performance 628
17.6.2 Single Server Models 632
17.6.3 Multiple Server Models 642
17.6.4 Machine Servicing Model—
(M/M/R):(GD/K/K) 652
17.7 (M/G/l):(GD/oo/ *)_p0llaczek Khintchine (P K)
Formula 656
17.8 Other Queueing Models 658
17.9 Queueing Decision Models 659
17.9.1 Cost Models 659
17.9.2 Aspiration Level Model 665
Contents xv
17.10 Summary 667
Selected References 667
Comprehensive Problems 667
CHAPTER 18: SIMULATION MODELING 673
18.1 What Is Simulation? 673
18.2 Monte Carlo Simulation 674
18.3 Types of Simulation 679
18.4 Elements of Discrete Event Simulation 680
18.4.1 Generic Definition of Events 680
18.4.2 Sampling from Probability Distributions 682
18.5 Generation of Random Numbers 692
18.6 Mechanics of Discrete Simulation 693
18.7 Methods for Gathering Statistical Observations 699
18.7.1 Subinterval Method 700
18.7.2 Replication Method 702
18.7.3 Regenerative (Cycle) Method 702
18.8 Simulation Languages 705
18.9 Summary 709
Selected References 709
CHAPTER 19: MARKOVIAN DECISION PROCESS 711
19.1 Scope of the Markovian Decision Problem: The
Gardener Example 711
19.2 Finite Stage Dynamic Programming Model 713
19.3 Infinite Stage Model 718
19.3.1 Exhaustive Enumeration Method 719
19.3.2 Policy Iteration without Discounting 722
19.3.3 Policy Iteration with Discounting 726
19.4 Linear Programming Solution 729
19.5 Summary 733
19.6 Appendix: Review of Markov Chains 733
79.6./ Markov Processes 734
19.6.2 Markov Chains 734
Selected References 741
xvi Contents
Part III: Nonlinear Models 743
CHAPTER 20: CLASSICAL OPTIMIZATION THEORY 745
20.1 Introduction 745
20.2 Unconstrained Problems 745
20.2.7 Necessary and Sufficient Conditions 746
20.2.2 The Newton Raphson Method 751
20.3 Constrained Problems 753
20.3.1 Equality Constraints 753
20.3.2 Inequality Constraints 771
20.4 Summary 779
Selected References 779
CHAPTER 21: NONLINEAR PROGRAMMING ALGORITHMS 781
21.1 Unconstrained Nonlinear Algorithms 781
21.1.1 Direct Search Method 781
21.1.2 Gradient Method 783
21.2 Constrained Algorithms 787
21.2.1 Separable Programming 787
21.2.2 Quadratic Programming 797
21.2.3 Geometric Programming 801
21.2.4 Stochastic Programming 807
21.2.5 Linear Combinations Method 811
21.2.6 SUMTAlgorithm 813
21.3 Summary 814
Selected References 814
APPENDIX A: REVIEW OF MATRIX ALGEBRA 815
A.I Vectors 815
A.1.1 Definition of a Vector 815
A.1.2 Addition (Subtraction) of Vectors 815
A.1.3 Multiplication of a Vector by Scalars 816
A. 1.4 Linearly Independent Vectors 816
A.2 Matrices 816
A.2.1 Definition of a Matrix 816
A.2.2 Types of Matrices 816
A.2.3 Matrix Arithmetic Operations 817
A.2.4 Determinant of a Square Matrix 819
Contents xvii
A.2.5 Nonsingular Matrix 820
A.2.6 Inverse of a Matrix 821
A.2.7 Methods of Computing the Inverse 822
A.3 Quadratic Forms 825
A.4 Convex and Concave Functions 826
Selected References 826
Problems 826
APPENDIX B: INTRODUCTION TO SIMNET II 829
B.I Modeling Framework 829
B.2 Statement Representation 830
B.2.1 Source Node 830
B.2.2 Queue Node 832
B.2.3 Facility Node 833
B.2.4 Auxiliary Node 835
B.2.5 Basic Rules for the Operation of Nodes 836
B.3 SIMNET II Mathematical Expressions 838
B.4 A SIMNET II Model Example 840
B.5 Transaction Routing in SIMNET II 842
B.5.1 Select Routing 843
B.5.2 GOTO Routing (*T field) 845
B.6 Branches in SIMNET II 847
B.7 Statistical Variables 853
B.8 Logic Switches 855
B.9 Special Assignments 858
B.9.1 Source Activation and Deactivation 859
B.9.2 Statistical Variables Collection 859
B.9.3 File Manipulation Assignments 860
B.10 Initial Data 865
ft 10.1 Initial File Entries 865
B.I0.2 Discrete and Discretized Continuous Density
Functions 866
B.10.3 Table Look Up Functions 867
B.10.4 Initialization of Array Elements 868
B.11 Summary 870
Reference 870
xviii Contents
APPENDIX C: TORA AND SIMNET II INSTALLATION AND
EXECUTION 871
C.1 Installation and Execution 871
APPENDIX D: STATISTICAL TABLES 873
APPENDIX E: ANSWERS TO ODD NUMBERED PROBLEMS 877
INDEX 909
|
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| discipline | Informatik Mathematik Wirtschaftswissenschaften |
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| publisher | Prentice Hall |
| record_format | marc |
| spelling | Taha, Hamdy A. 1937- Verfasser (DE-588)133779432 aut Operations research an introduction Hamdy A. Taha 6. ed. Upper Saddle River, NJ Prentice Hall 1997 XX, 916 S. graph. Darst. 1 Diskette ; 3,5" txt rdacontent n rdamedia nc rdacarrier Investigación operacional Pesquisa operacional larpcal Programación (Matemáticas) Operations research Programming (Mathematics) Verhaltensforschung (DE-588)4062862-0 gnd rswk-swf Operations Research (DE-588)4043586-6 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Operations Research (DE-588)4043586-6 s DE-604 Verhaltensforschung (DE-588)4062862-0 s 2\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008161600&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Taha, Hamdy A. 1937- Operations research an introduction Investigación operacional Pesquisa operacional larpcal Programación (Matemáticas) Operations research Programming (Mathematics) Verhaltensforschung (DE-588)4062862-0 gnd Operations Research (DE-588)4043586-6 gnd |
| subject_GND | (DE-588)4062862-0 (DE-588)4043586-6 (DE-588)4151278-9 |
| title | Operations research an introduction |
| title_auth | Operations research an introduction |
| title_exact_search | Operations research an introduction |
| title_full | Operations research an introduction Hamdy A. Taha |
| title_fullStr | Operations research an introduction Hamdy A. Taha |
| title_full_unstemmed | Operations research an introduction Hamdy A. Taha |
| title_short | Operations research |
| title_sort | operations research an introduction |
| title_sub | an introduction |
| topic | Investigación operacional Pesquisa operacional larpcal Programación (Matemáticas) Operations research Programming (Mathematics) Verhaltensforschung (DE-588)4062862-0 gnd Operations Research (DE-588)4043586-6 gnd |
| topic_facet | Investigación operacional Pesquisa operacional Programación (Matemáticas) Operations research Programming (Mathematics) Verhaltensforschung Operations Research Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008161600&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT tahahamdya operationsresearchanintroduction |