1 Introduction 1
1-1 The Beginning and Progress of Operations Research 1
1-2 Classification of Problems in Operations Research 3
1-3 Mathematical Modeling in Operations Research 5
Part One Deterministic Operations Research Models 11
2 Dynamic Programming 11
2-1 Introduction 11
2-2 Investment Problem 12
2-3 Dynamic Programming Solution of the General Allocation Problem 18
2-4 Stagecoach Problem 27
2-5 Production Scheduling 38
2-6 Equipment Replacement 50
2-7 Summary 63
3 Linear Programming 68
3-1 Introduction 68
3-2 Formulation of Linear Programming Models 69
3-3 Graphic Solution of Linear Programming Models 74
3-4 Maximization with Less-than-or-equal-to Constraints 78
3-5 Equalities and Greater-than-or-equal-to Constraints 86
3-6 Minimization of the Objective Function 88
3-7 The Simplex Method 90
3-8 Example to Illustrate Simplex Algorithm 95
3-9 Computer Program for Algorithm 3.1 100
3-10 Properties of the Simplex Method 106
3-11 Transportation Problem 107
3-12 Assignment Problem 110
4 Integer Programming 129
4-1 Introduction 129
4-2 Implicit Enumeration 130
4-3 Cutting-Plane Technique 164
5 Branch-and-Bound Technique 193
5-1 Introduction 193
5-2 Branch-and-Bound Algorithm for Assignment Problem 194
5-3 Branch-and-Bound Algorithms for Traveling Salesman Problem 202
5-4 Branch-and-Bound Algorithm for Integer Programming 211
5-5 Branch-and-Bound Algorithm for Backpack-loading Problem 217
5-6 Algorithm 5.4—General Algorithm for the Branch-and-Bound Technique 233
6 Deterministic Inventory Models 242
6-1 Introduction 242
6-2 Infinite Delivery Rate with No Backordering 244
6-3 Finite Delivery Rate with No Backordering 250
6-4 Infinite Delivery Rate with Backordering 253
6-5 Finite Delivery Rate with Backordering 257
6-6 Summary 259
7 Sequencing Problems 262
7-1 Introduction 262
7-2 Two-Machine Sequencing Problem 263
7-3 N-Job，Three-Machine Sequencing Problem 278
Part Two Probabilistic Operations Research Models 293
8 Basic Probability and-Statistical Concepts 293
8-1 Introduction 293
8-2 Basic Probability 293
8-3 Random Variables 299
8-4 Discrete Random Variables 300
8-5 Continuous Random Variables 308
8-6 Selecting the Appropriate Distribution 317
9 Regression Analysis 326
9-1 Introduction 326
9-2 Polynomial Regression 329
9-3 Simple Linear Regression 348
9-4 Summary 379
10 Decision Theory 383
10-1 Introduction 383
10-2 Minimax Decision Procedure 385
10-3 Bayes Decision Procedure without Data 386
10-4 Bayes Decision Procedure with Data 388
10-5 Regret Function vs.Loss Function 398
11 Game Theory 402
11-1 Introduction 402
11-2 Minimax-Maximin Pure Strategies 403
11-3 Mixed Strategies and Expected Payoff 406
11-4 Solution of 2×2 Games 409
11-5 Relevant Rows and Columns 411
11-6 Dominance 412
11-7 Solution of 2×n Games 415
11-8 Solution of m×2 Games 423
11-9 Brown’s Algorithm 425
12 PERT 434
12-1 Introduction 434
12-2 PERT Network 435
12-3 Time Estimates for Activities（ET） 437
12-4 Earliest Expected Completion Time of Events（TE） 439
12-5 Latest Allowable Event Completion Time（TL） 440
12-6 Event Slack Times（SE） 442
12-7 Critical Path 442
12-8 Probability of Completing Events on Schedule 443
12-9 Computer Program for PERT Analysis 446
13 Queueing Theory 454
13-1 Introduction 454
13-2 Notation and Assumptions 455
13-3 Queueing Models with Poisson Input-Exponential Service 459
13-4 Queueing Models with Poisson Input—Arbitrary Service Time 486
13-5 Summary 494
14 Simulation 497
14-1 Introduction 497
14-2 Simulation of a Single-Queue，Single-Server Queueing System 499
14-3 Generation of Random Variates 516
14-4 Simulation Languages 523
15 Probabilistic Inventory Models 528
15-1 Introduction 528
15-2 Single-Period Models 529
15-3 Multiperiod Models 544
15-4 Summary 561
16 Markov Chains 564
16-1 Introduction 564
16-2 Formulation of Markov Chains 565
16-3 First-Passage Time 580
16-4 Computer Program for Markov Analysis 584
16-5 Summary 590
Appendixes 593
Appendix A Tables 593
Table A.1 Cumulative Normal Distribution Function 593
Table A.2 Critical Values for Chi-Square Test 594
Table A.3 Critical Values of Din the Kolmogorov-Smirnov One-Sample Test 595
Table A.4 Critical Values for F Test with α＝0.05 596
Table A.5 Critical Values for F Test with α＝0.01 597
Appendix B Derivation of Queueing Formulas 598
Appendix C Gauss-Jordan Method for Solving a System of Linear Equations 603
Index 607