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CHAPTER 1 Introduction1

1.1 The Origins of Operations Research1

1.2 The Nature of Operations Research2

1.3 The Impact of Operations Research3

1.4 Algorithms and OR Courseware5

Problems6

CHAPTER 2 Overview of the Operations Research Modeling Approach7

2.1 Defining the Problem and Gathering Data7

2.2 Formulating a Mathematical Model10

2.3 Deriving Solutions from the Model14

2.4 Testing the Model16

2.5 Preparing to Apply the Model18

2.6 Implementation20

2.7 Conclusions21

Selected References22

Problems22

CHAPTER 3 Introduction to Linear Programming24

3.1 Prototype Example25

3.2 The Linear Programming Model31

3.3 Assumptions of Linear Programming36

3.4 Additional Examples44

3.5 Some Case Studies61

3.6 Displaying and Solving Linear Programming Models on a Spreadsheet67

3.7 Formulating Very Large Linear Programming Models73

3.8 Conclusions79

Appendix 3.1 The LINGO Modeling Language79

Selected References89

Learning Aids for This Chapter in Your OR Courseware90

Problems90

Case 3.1 Auto Assembly103

Case 3.2 Cutting Cafeteria Costs104

Case 3.3 Staffing a Call Center106

CHAPTER 4 Solving Linear Programming Problems：The Simplex Method109

4.1 The Essence of the Simplex Method109

4.2 Setting Up the Simplex Method114

4.3 The Algebra of the Simplex Method118

4.4 The Simplex Method in Tabular Form123

4.5 Tie Breaking in the Simplex Method128

4.6 Adapting to Other Model Forms132

4.7 Postoptimality Analysis152

4.8 Computer Implementation160

4.9 The Interior-Point Approach to Solving Linear Programming Problems163

4.10 Conclusions168

Appendix 4.1 An Introduction to Using LINDO169

Selected References171

Learning Aids for This Chapter in Your OR Courseware172

Problems172

Case 4.1 Fabrics and Fall Fashions182

Case 4.2 New Frontiers185

Case 4.3 Assigning Students to Schools188

CHAPTER 5 The Theory of the Simplex Method190

5.1 Foundations of the Simplex Method190

5.2 The Revised Simplex Method202

5.3 A Fundamental Insight212

5.4 Conclusions220

Selected References220

Learning Aids for This Chapter in Your OR Courseware221

Problems221

CHAPTER 6 Duality Theory and Sensitivity Analysis230

6.1 The Essence of Duality Theory231

6.2 Economic Interpretation of Duality239

6.3 Primal-Dual Relationships242

6.4 Adapting to Other Primal Forms247

6.5 The Role of Duality Theory in Sensitivity Analysis252

6.6 The Essence of Sensitivity Analysis254

6.7 Applying Sensitivity Analysis262

6.8 Conclusions284

Selected References284

Learning Aids for This Chapter in Your OR Courseware285

Problems285

Case 6.1 Controlling Air Pollution302

Case 6.2 Farm Management304

Case 6.3 Assigning Students to Schools（Revisited）307

CHAPTER 7 Other Algorithms for Linear Programming309

7.1 The Dual Simplex Method309

7.2 Parametric Linear Programming312

7.3 The Upper Bound Technique317

7.4 An Interior-Point Algorithm320

7.5 Linear Goal Programming and Its Solution Procedures332

7.6 Conclusions339

Selected References340

Learning Aids for This Chapter in Your OR Courseware340

Problems341

Case 7.1 A Cure for Cuba347

CHAPTER 8 The Transportation and Assignment Problems350

8.1 The Transportation Problem351

8.2 A Streamlined Simplex Method for the Transportation Problem365

8.3 The Assignment Problem381

8.4 Conclusions391

Selected References391

Learning Aids for This Chapter in Your OR Courseware392

Problems392

Case 8.1 Shipping Wood to Market401

Case 8.2 Project Pickings402

CHAPTER 9 Network Optimization Models405

9.1 Prototype Example406

9.2 The Terminology of Networks407

9.3 The Shortest-Path Problem411

9.4 The Minimum Spanning Tree Problem415

9.5 The Maximum Flow Problem420

9.6 The Minimum Cost Flow Problem429

9.7 The Network Simplex Method438

9.8 Conclusions448

Selected References449

Learning Aids for This Chapter in Your OR Courseware449

Problems450

Case 9.1 Aiding Allies458

Case 9.2 Money in Motion464

CHAPTER 10 Project Management with PERT/CPM468

10.1 A Prototype Example—The Reliable Construction Co.Project469

10.2 Using a Network to Visually Display a Project470

10.3 Scheduling a Project with PERT/CPM475

10.4 Dealing with Uncertain Activity Durations485

10.5 Considering Time-Cost Trade-Offs492

10.6 Scheduling and Controlling Project Costs502

10.7 An Evaluation of PERT/CPM508

10.8 Conclusions512

Selected References513

Learning Aids for This Chapter in Your OR Courseware514

Problems514

Case 10.1 Steps to Success524

Case 10.2 “School’s out forever！！”527

CHAPTER 11 Dynamic Programming533

11.1 A Prototype Example for Dynamic Programming533

11.2 Characteristics of Dynamic Programming Problems538

11.3 Deterministic Dynamic Programming541

11.4 Probabilistic Dynamic Programming562

11.5 Conclusions568

Selected References568

Learning Aids for This Chapter in Your OR Courseware568

Problems569

CHAPTER 12Integer Programming576

12.1 Prototype Example577

12.2 Some BIP Applications580

12.3 Innovative Uses of Binary Variables in Model Formulation585

12.4 Some Formulation Examples591

12.5 Some Perspectives on Solving Integer Programming Problems600

12.6 The Branch-and-Bound Technique and Its Application to Binary Integer Programming604

12.7 A Branch-and-Bound Algorithm for Mixed Integer Programming616

12.8 Other Developments in Solving BIP Problems622

12.9 Conclusions630

Selected References631

Learning Aids for This Chapter in Your OR Courseware631

Problems632

Case 12.1 Capacity Concerns642

Case 12.2 Assigning Art645

Case 12.3 Stocking Sets649

Case 12.4 Assigning Students to Schools（Revisited Again）653

CHAPTER 13 Nonlinear Programming654

13.1 Sample Applications655

13.2 Graphical Illustration of Nonlinear Programming Problems659

13.3 Types of Nonlinear Programming Problems664

13.4 One-Variable Unconstrained Optimization670

13.5 Multivariable Unconstrained Optimization673

13.6 The Karush-Kuhn-Tucker （KKT） Conditions for Constrained Optimization679

13.7 Quadratic Programming683

13.8 Separable Programming690

13.9 Convex Programming697

13.10 Nonconvex Programming702

13.11 Conclusions706

Selected References706

Learning Aids for This Chapter in Your OR Courseware707

Problems708

Case 13.1 Savvy Stock Selection720

CHAPTER 14 Game Theory726

14.1 The Formulation of Two-Person，Zero-Sum Games726

14.2 Solving Simple Games—A Prototype Example728

14.3 Games with Mixed Strategies733

14.4 Graphical Solution Procedure735

14.5 Solving by Linear Programming738

14.6 Extensions741

14.7 Conclusions742

Selected References743

Learning Aids for This Chapter in Your OR Courseware743

Problems743

CHAPTER 15 Decision Analysis749

15.1 A Prototype Example750

15.2 Decision Making without Experimentation751

15.3 Decision Making with Experimentation758

15.4 Decision Trees764

15.5 Utility Theory770

15.6 The Practical Application of Decision Analysis778

15.7 Conclusions781

Selected References781

Learning Aids for This Chapter in Your OR Courseware782

Problems782

Case 15.1 Brainy Business795

Case 15.2 Smart Steering Support798

CHAPTER 16 Markov Chains802

16.1 Stochastic Processes802

16.2 Markov Chains803

16.3 Chapman-Kolmogorov Equations808

16.4 Classification of States of a Markov Chain810

16.5 Long-Run Properties of Markov Chains812

16.6 First Passage Times818

16.7 Absorbing States820

16.8 Continuous Time Markov Chains822

Selected References827

Learning Aids for This Chapter in Your OR Courseware828

Problems828

CHAPTER 17 Queueing Theory834

17.1 Prototype Example835

17.2 Basic Structure of Queueing Models835

17.3 Examples of Real Queueing Systems840

17.4 The Role of the Exponential Distribution841

17.5 The Birth-and-Death Process848

17.6 Queueing Models Based on the Birth-and-Death Process852

17.7 Queueing Models Involving Nonexponential Distributions871

17.8 Priority-Discipline Queueing Models879

17.9 Queueing Networks885

17.10 Conclusions889

Selected References890

Learning Aids for This Chapter in Your OR Courseware890

Problems891

Case 17.1 Reducing In-Process Inventory905

CHAPTER 18 The Application of Queueing Theory907

18.1 Examples907

18.2 Decision Making909

18.3 Formulation of Waiting-Cost Functions912

18.4 Decision Models917

18.5 Some Award-Winning Applications of Queueing Theory923

18.6 Conclusions926

Selected References926

Learning Aids for This Chapter in Your OR Courseware926

Problems927

Case 18.1 Queueing Quandary932

CHAPTER 19 Inventory Theory935

19.1 Examples936

19.2 Components of Inventory Models938

19.3 Deterministic Continuous-Review Models941

19.4 A Deterministic Periodic-Review Model951

19.5 A Stochastic Continuous-Review Model956

19.6 A Stochastic Single-Period Model for Perishable Products961

19.7 Stochastic Periodic-Review Models975

19.8 Larger Inventory Systems in Practice983

19.9 Conclusions987

Selected References987

Learning Aids for This Chapter in Your OR Courseware987

Problems988

Case 19.1 Brushing Up on Inventory Control1000

Case 19.2 TNT：Tackling Newsboy’s Teachings1002

Case 19.3 Jettisoning Surplus Stock1004

CHAPTER 20 Forecasting1009

20.1 Some Applications of Forecasting1010

20.2 Judgmental Forecasting Methods1013

20.3 Time Series1014

20.4 Forecasting Methods for a Constant-Level Model1016

20.5 Incorporating Seasonal Effects into Forecasting Methods1018

20.6 An Exponential Smoothing Method for a Linear Trend Model1021

20.7 Forecasting Errors1025

20.8 Box-Jenkins Method1026

20.9 Causal Forecasting with Linear Regression1028

20.10 Forecasting in Practice1036

20.11 Conclusions1038

Selected References1038

Learning Aids for This Chapter in Your OR Courseware1038

Problems1039

Case 20.1 Finagling the Forecasts1048

CHAPTER 21 Markov Decision Processes1053

21.1 A Prototype Example1053

21.2 A Model for Markov Decision Processes1056

21.3 Linear Programming and Optimal Policies1059

21.4 Policy Improvement Algorithm for Finding Optimal Policies1064

21.5 Discounted Cost Criterion1069

Selected References1077

Learning Aids for This Chapter in Your OR Courseware1078

Problems1078

CHAPTER 22 Simulation1084

22.1 The Essence of Simulation1084

22.2 Some Common Types of Applications of Simulation1097

22.3 Generation of Random Numbers1101

22.4 Generation of Random Observations from a Probability Distribution1105

22.5 Outline of a Major Simulation Study1110

22.6 Performing Simulations on Spreadsheets1115

22.7 Variance-Reducing Techniques1126

22.8 Regenerative Method of Statistical Analysis1131

22.9 Conclusions1138

Selected References1140

Learning Aids for This Chapter in Your OR Courseware1140

Problems1141

Case 22.1 Planning Planers1151

Case 22.2 Pricing under Pressure1153

APPENDIXES1156

1.Documentation for the OR Courseware1156

2.Convexity1159

3.Classical Optimization Methods1165

4.Matrices and Matrix Operations1169

5.Tables1174

PARTIAL ANSWERS TO SELECTED PROBLEMS1176

INDEXES1195

Author Index1195

Subject Index1199