CHAPTER 1 Introduction

1.1 The Origins of Operations Research

1.2 The Nature of Operations Research

1.3 The Impact of Operations Research

1.4 Algorithms and OR Courseware

Problems

CHAPTER 2 Overview of the Operations Research Modeling Approach

2.1 Defining the Problem and Gathering Data

2.2 Formulating a Mathematical Model

2.3 Deriving Solutions from the Model

2.4 Testing the Model

2.5 Preparing to Apply the Model

2.6 Implementation

2.7 Conclusions

Selected References

Problems

CHAPTER 3 Introduction to Linear Programming

3.1 Prototype Example

3.2 The Linear Programming Model

3.3 Assumptions of Linear Programming

3.4 Additional Examples

3.5 Some Case Studies

3.6 Displaying and Solving Linear Programming Models on a Spreadsheet

3.7 Formulating Very Large Linear Programming Models

3.8 Conclusions

Appendix 3.1 The LINGO Modeling Language

Selected References

Learning Aids for This Chapter in Your OR Courseware

Problems

Case 3.1 Auto Assembly

Case 3.2 Cutting Cafeteria Costs

Case 3.3 Staffing a Call Center

CHAPTER 4 Solving Linear Programming Problems：The Simplex Method

4.1 The Essence of the Simplex Method

4.2 Setting Up the Simplex Method

4.3 The Algebra of the Simplex Method

4.4 The Simplex Method in Tabular Form

4.5 Tie Breaking in the Simplex Method

4.6 Adapting to Other Model Forms

4.7 Postoptimality Analysis

4.8 Computer Implementation

4.9 The Interior-Point Approach to Solving Linear Programming Problems

4.10 Conclusions

Appendix 4.1 An Introduction to Using LINDO

Selected References

Learning Aids for This Chapter in Your OR Courseware

Problems

Case 4.1 Fabrics and Fall Fashions

Case 4.2 New Frontiers

Case 4.3 Assigning Students to Schools

CHAPTER 5 The Theory of the Simplex Method

5.1 Foundations of the Simplex Method

5.2 The Revised Simplex Method

5.3 A Fundamental Insight

5.4 Conclusions

Selected References

Learning Aids for This Chapter in Your OR Courseware

Problems

CHAPTER 6 Duality Theory and Sensitivity Analysis

6.1 The Essence of Duality Theory

6.2 Economic Interpretation of Duality

6.3 Primal-Dual Relationships

6.4 Adapting to Other Primal Forms

6.5 The Role of Duality Theory in Sensitivity Analysis

6.6 The Essence of Sensitivity Analysis

6.7 Applying Sensitivity Analysis

6.8 Conclusions

Selected References

Learning Aids for This Chapter in Your OR Courseware

Problems

Case 6.1 Controlling Air Pollution

Case 6.2 Farm Management

Case 6.3 Assigning Students to Schools（Revisited）

CHAPTER 7 Other Algorithms for Linear Programming

7.1 The Dual Simplex Method

7.2 Parametric Linear Programming

7.3 The Upper Bound Technique

7.4 An Interior-Point Algorithm

7.5 Linear Goal Programming and Its Solution Procedures

7.6 Conclusions

Selected References

Learning Aids for This Chapter in Your OR Courseware

Problems

Case 7.1 A Cure for Cuba

CHAPTER 8 The Transportation and Assignment Problems

8.1 The Transportation Problem

8.2 A Streamlined Simplex Method for the Transportation Problem

8.3 The Assignment Problem

8.4 Conclusions

Selected References

Learning Aids for This Chapter in Your OR Courseware

Problems

Case 8.1 Shipping Wood to Market

Case 8.2 Project Pickings

CHAPTER 9 Network Optimization Models

9.1 Prototype Example

9.2 The Terminology of Networks

9.3 The Shortest-Path Problem

9.4 The Minimum Spanning Tree Problem

9.5 The Maximum Flow Problem

9.6 The Minimum Cost Flow Problem

9.7 The Network Simplex Method

9.8 Conclusions

Selected References

Learning Aids for This Chapter in Your OR Courseware

Problems

Case 9.1 Aiding Allies

Case 9.2 Money in Motion

CHAPTER 10 Project Management with PERT/CPM

10.1 A Prototype Example—The Reliable Construction Co.Project

10.2 Using a Network to Visually Display a Project

10.3 Scheduling a Project with PERT/CPM

10.4 Dealing with Uncertain Activity Durations

10.5 Considering Time-Cost Trade-Offs

10.6 Scheduling and Controlling Project Costs

10.7 An Evaluation of PERT/CPM

10.8 Conclusions

Selected References

Learning Aids for This Chapter in Your OR Courseware

Problems

Case 10.1 Steps to Success

Case 10.2 “School’s out forever！！”

CHAPTER 11 Dynamic Programming

11.1 A Prototype Example for Dynamic Programming

11.2 Characteristics of Dynamic Programming Problems

11.3 Deterministic Dynamic Programming

11.4 Probabilistic Dynamic Programming

11.5 Conclusions

Selected References

Learning Aids for This Chapter in Your OR Courseware

Problems

CHAPTER 12Integer Programming

12.1 Prototype Example

12.2 Some BIP Applications

12.3 Innovative Uses of Binary Variables in Model Formulation

12.4 Some Formulation Examples

12.5 Some Perspectives on Solving Integer Programming Problems

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

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

12.8 Other Developments in Solving BIP Problems

12.9 Conclusions

Selected References

Learning Aids for This Chapter in Your OR Courseware

Problems

Case 12.1 Capacity Concerns

Case 12.2 Assigning Art

Case 12.3 Stocking Sets

Case 12.4 Assigning Students to Schools（Revisited Again）

CHAPTER 13 Nonlinear Programming

13.1 Sample Applications

13.2 Graphical Illustration of Nonlinear Programming Problems

13.3 Types of Nonlinear Programming Problems

13.4 One-Variable Unconstrained Optimization

13.5 Multivariable Unconstrained Optimization

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

13.7 Quadratic Programming

13.8 Separable Programming

13.9 Convex Programming

13.10 Nonconvex Programming

13.11 Conclusions

Selected References

Learning Aids for This Chapter in Your OR Courseware

Problems

Case 13.1 Savvy Stock Selection

CHAPTER 14 Game Theory

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

14.2 Solving Simple Games—A Prototype Example

14.3 Games with Mixed Strategies

14.4 Graphical Solution Procedure

14.5 Solving by Linear Programming

14.6 Extensions

14.7 Conclusions

Selected References

Learning Aids for This Chapter in Your OR Courseware

Problems

CHAPTER 15 Decision Analysis

15.1 A Prototype Example

15.2 Decision Making without Experimentation

15.3 Decision Making with Experimentation

15.4 Decision Trees

15.5 Utility Theory

15.6 The Practical Application of Decision Analysis

15.7 Conclusions

Selected References

Learning Aids for This Chapter in Your OR Courseware

Problems

Case 15.1 Brainy Business

Case 15.2 Smart Steering Support

CHAPTER 16 Markov Chains

16.1 Stochastic Processes

16.2 Markov Chains

16.3 Chapman-Kolmogorov Equations

16.4 Classification of States of a Markov Chain

16.5 Long-Run Properties of Markov Chains

16.6 First Passage Times

16.7 Absorbing States

16.8 Continuous Time Markov Chains

Selected References

Learning Aids for This Chapter in Your OR Courseware

Problems

CHAPTER 17 Queueing Theory

17.1 Prototype Example

17.2 Basic Structure of Queueing Models

17.3 Examples of Real Queueing Systems

17.4 The Role of the Exponential Distribution

17.5 The Birth-and-Death Process

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

17.7 Queueing Models Involving Nonexponential Distributions

17.8 Priority-Discipline Queueing Models

17.9 Queueing Networks

17.10 Conclusions

Selected References

Learning Aids for This Chapter in Your OR Courseware

Problems

Case 17.1 Reducing In-Process Inventory

CHAPTER 18 The Application of Queueing Theory

18.1 Examples

18.2 Decision Making

18.3 Formulation of Waiting-Cost Functions

18.4 Decision Models

18.5 Some Award-Winning Applications of Queueing Theory

18.6 Conclusions

Selected References

Learning Aids for This Chapter in Your OR Courseware

Problems

Case 18.1 Queueing Quandary

CHAPTER 19 Inventory Theory

19.1 Examples

19.2 Components of Inventory Models

19.3 Deterministic Continuous-Review Models

19.4 A Deterministic Periodic-Review Model

19.5 A Stochastic Continuous-Review Model

19.6 A Stochastic Single-Period Model for Perishable Products

19.7 Stochastic Periodic-Review Models

19.8 Larger Inventory Systems in Practice

19.9 Conclusions

Selected References

Learning Aids for This Chapter in Your OR Courseware

Problems

Case 19.1 Brushing Up on Inventory Control

Case 19.2 TNT：Tackling Newsboy’s Teachings

Case 19.3 Jettisoning Surplus Stock

CHAPTER 20 Forecasting

20.1 Some Applications of Forecasting

20.2 Judgmental Forecasting Methods

20.3 Time Series

20.4 Forecasting Methods for a Constant-Level Model

20.5 Incorporating Seasonal Effects into Forecasting Methods

20.6 An Exponential Smoothing Method for a Linear Trend Model

20.7 Forecasting Errors

20.8 Box-Jenkins Method

20.9 Causal Forecasting with Linear Regression

20.10 Forecasting in Practice

20.11 Conclusions

Selected References

Learning Aids for This Chapter in Your OR Courseware

Problems

Case 20.1 Finagling the Forecasts

CHAPTER 21 Markov Decision Processes

21.1 A Prototype Example

21.2 A Model for Markov Decision Processes

21.3 Linear Programming and Optimal Policies

21.4 Policy Improvement Algorithm for Finding Optimal Policies

21.5 Discounted Cost Criterion

Selected References

Learning Aids for This Chapter in Your OR Courseware

Problems

CHAPTER 22 Simulation

22.1 The Essence of Simulation

22.2 Some Common Types of Applications of Simulation

22.3 Generation of Random Numbers

22.4 Generation of Random Observations from a Probability Distribution

22.5 Outline of a Major Simulation Study

22.6 Performing Simulations on Spreadsheets

22.7 Variance-Reducing Techniques

22.8 Regenerative Method of Statistical Analysis

22.9 Conclusions

Selected References

Learning Aids for This Chapter in Your OR Courseware

Problems

Case 22.1 Planning Planers

Case 22.2 Pricing under Pressure

APPENDIXES

1.Documentation for the OR Courseware

2.Convexity

3.Classical Optimization Methods

4.Matrices and Matrix Operations

5.Tables

PARTIAL ANSWERS TO SELECTED PROBLEMS

INDEXES

Author Index

Subject Index