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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