Chapter 1

INTRODUCTION

1.1 Business and Management Science

1.2 What Is Management Science?

1.3 Brief History of Management Science

1.4 Management Science Applications

1.5 What This Text Is All About

1.6 Organization of the Text

Chapter 2

THE MANAGEMENT SCIENCE PROCESS

2.1 Mathematical Modeling and the Management Science Process

2.2 The Management Science Process--Step 1: Defining the Problem

2.3 The Management Science Process--Step 2: Building a Mathematical Model

2.4 The Management Science Process--Step 3: Solving a Mathematical Model

2.5 The Management Science Process--Step 4: Communicating/Monitoring the Results

2.6 Writing Business Reports/Memos

2.7 Summary

Problems

Case

Chapter 3

LINEAR PROGRAMMING

3.1 Introduction to Linear Programming

3.2 A Linear Programming Model--A Prototype Example

3.3 Limiting Assumptions of Linear Programming Models

3.4 The Set of Feasible Solutions for Linear Programs

3.5 Solving Graphically for an Optimal Solution

3.6 The Role of Sensitivity Analysis of the Optimal Solution

3.7 Sensitivity Analysis of Objective Function Coefficients

3.8 Sensitivity Analysis of Right-Hand Side Values

3.9 Other Post-Optimality Changes

3.10 Models without Optimal Solutions--Infeasibility and Unboundedness

3.11 A Minimization Problem

3.12 Computer Solution of Linear Programs with Any Number of Decision Variables

3.13 Summary

Appendix 3.1 WINQSB Input for the Galaxy Industries Model

Appendix 3.2 Excel Input for the Galaxy Industries Model

Appendix 3.3 LINDO Input for the Galaxy Industries Model

Problems

Cases

Chapter 4

LINEAR PROGRAMMING APPLICATIONS

4.1 Building Good Linear Models

4.2 Linear Programming Models

4.3 Galaxy Industries--An Expansion Plan

4.4 Jones Investment Service

4.5 St. Joseph Public Utility Commission

4.6 Euromerica Liquors

4.7 Vertex Software, Inc.

4.8 United Oil Company

4.9 The Powers Group

4.10 Mobile Cabinet Company

4.11 Applications of Linear Models in Business and Government

4.12 Summary

Appendix 4.1 Excel Spreadsheet for the Powers Group Model

Problems

Cases

Chapter 5

INTEGER LINEAR PROGRAMMING

5.1 Introduction to Integer Linear Programming (ILP)

5.2 Complexities of ILPs

5.3 Sensitivity in ILP

5.4 Mixed Integer Linear Programming (MILP)

5.5 Solving Integer Programming Models

5.6 A Personnel Scheduling Problem--An Example of a Computer Solution

5.7 Binary Integer Linear Programming (BILP)

5.8 Fixed Charge/Facility Location Problems

5.9 Summary

Appendix 5.1 Computer Input for MILPs

Problems

Cases

Chapter 6

NETWORK MODELS

6.1 Introduction to Networks

6.2 The Transportation Problem

6.3 The Assignment Problem

6.4 The Traveling Salesman Problem

6.5 The Shortest Path Problem

6.6 The Minimal Spanning Tree Problem

6.7 The Maximal Flow Problem

6.8 Summary

Appendix 6.1 WINQSB Input for Network Problems

Appendix 6.2 Excel Solution for Transportation Problems

Problems

Cases

Chapter 7

PROJECT SCHEDULING

7.1 Introduction to Project Scheduling

7.2 Identifying the Activities of a Project

7.3 Gantt Charts

7.4 Building PERT/CPM Networks

7.5 The PERT/CPM Approach for Project Scheduling

7.6 Resource Leveling/Resource Allocation

7.7 PERT--The Probabilistic Approach to Project Scheduling

7.8 Computer Solution of PERT/CPM Networks

7.9 Cost Analyses Using the Expected Value Approach

7.10 The Critical Path Method (CPM)

7.11 PERT/Cost

7.12 Summary

Appendix 7.1 WINQSB Input for PERT/CPM

Problems

Cases

Chapter 8

DECISION ANALYSIS

8.1 Introduction to Decision Analysis

8.2 Payoff Table Analysis

8.3 Decision-Making Criteria

8.4 Expected Value of Perfect Information

8.5 Bayesian Analyses--Decision Making with Imperfect Information

8.6 Decision Trees

8.7 Decision Making and Utility

Game Theory

Summary

Notational Summary

Appendix 8.1 Using WINQSB to Solve Decision Problems

Problems

Cases

Chapter 9

FORECASTING

9.1 Introduction to Time Series Forecasting

9.2 Stationary Forecasting Models

9.3 Evaluating the Performance of Forecasting Techniques

9.4 Forecasting Time Series that Have Linear Trend

9.5 Time Series with Trend, Seasonal, and Cyclical Variation

9.6 Other Forecasting Techniques

9.7 Summary

Notational Summary

Appendix 9.1 Using WINQSB to Evaluate Forecasting Models

Problems

Cases

Chapter 10

INVENTORY MODELS BASED ON STATIONARY DEMAND

10.1 Overview of Inventory Issues

10.2 Economic Order Quantity Model

10.3 EOQ Models with Quantity Discounts

10.4 Production Lot Size Model

10.5 Planned Shortage Model

10.6 Determining Safety Stock Levels

10.7 Review Systems

10.8 Summary

Notational Summary

Appendix 10.1 Using WINQSB to Solve Inventory Models

Based on StationaryDemand

Problems

Cases

Chapter 11

INVENTORY MODELS BASED ON NONSTATIONARY

DEMAND

11.1 Single-Period Inventory Model

11.2 Material Requirements Planning

11.3 Inventory Models with Time Varying Demand

11.4 Current Trends in Inventory Control

11.5 Summary

Notational Summary

Appendix 11.1 Using WINQSB to Solve Inventory Models

Based on NonstationaryDemand

Problems

Cases

Chapter 12

QUEUING THEORY

12.1 Introduction

12.2 Elements of the Queuing Process

12.3 Measures of Queuing System Performance

12.4 M/M/I Queuing Systems

12.5 M/M/k Queuing Systems

12.6 M/G/1 Queuing Systems

12.7 M/M/k/F Queuing Systems with Finite Queue Length

12.8 M/M/1//m Queuing Systems (Finite Customer Population)

12.9 Economic Analysis of Queuing Systems

12.10 Tandem Queuing Systems

12.11 Assembly Line Balancing--An Application of Tandem Queues

12.12Summary

Notational Summary

Appendix 12.1 Using WINQSB and Excel to Solve Queuing Problems

Problems

Cases

Chapter 13

SIMULATION

13.1 Overview of Simulation

13.2 Monte Carlo Simulation

13.3 Random Number Mappings for Continuous Random Variables

13.4 Simulation of a Queuing System

13.5 Simulation Modeling of Inventory Systems

13.6 Tests for Comparing Simulation Results

13.7 Advantages and Disadvantages of Simulation

13.8 Summary

Notational Summary

Appendix 13.1 Using WINQSB and Excel to Perform Simulations

Problems

Cases

APPENDICES

Appendix A Standard Normal Distribution P(0 ;lt Z ;lt z)

Appendix B Partial Expectations of the Standard Normal Distribution

Appendix C Pseudorandom Numbers

Appendix D t Distribution

Appendix E Chi-Square Distribution

Appendix F F Distribution

Appendix G Constants for Quality Control Charts

Appendix H Critical Values of Spearman's Rank Correlation

Coefficient

Glossary

Answers to Selected Problems

Index

CD-ROM Contents

Chapter 14

QUALITY MANAGEMENT

14.1 Overview of Quality

14.2 Managerial Issues in Quality Control

14.3 Control Charts Based on Multi-Item Sampling of Quantitative Data

14.4 Control Charts Based on a Single-Item Sampling of Quantitative Data

14.5 Quality Control Based on Attributes

14.6 Economic Issues in Achieving Quality

14.7 Summary

Notational Summary

Appendix 14.1 Using WINQSB to Set Up Control Charts

Appendix 14.2 Testing for Normality of Data Using Probability Plots

Problems

Cases

Chapter 15

MARKOV PROCESSES

15.1 Basic Concepts of Markov Processes

15.2 Transition Matrices for Processes with no Absorbing States

15.3 Transition Matrices for Processes with Absorbing States

15.4 Determining a State Vector

15.5 Determining Limiting (Steady State) Behavior for Markov Processes without Absorbing States

15.6 Determining Limiting (Steady State) Behavior for Markov Processes with Absorbing States

15.7 Using Markov Processes in Economic Analyses

15.8 Applying Markov Processes to Gambling Situations

15.9 Summary

Notational Summary

Appendix 15.1 Using WINQSB to Evaluate Markov Processes

Appendix 15.2 Matrix Algebra

Appendix 15.3 Determining the Inverse of a Matrix

Problems

Cases

Chapter 16

NONLINEAR MODELS: DYNAMIC, GOAL, AND NONLINEAR PROGRAMMING

16.1 Introduction to Nonlinear Programming

16.2 Dynamic Programming

16.3 Computational Properties of Dynamic Programming

16.4 Dynamic Programming Examples

16.5 Goal Programming Nonlinear Programming Concepts

16.7 Unconstrained Nonlinear Programming

16.8 Constrained Nonlinear Programming Problems

16.9 Summary

Appendix 16.1 WINQSB Input for Dynamic Programming

Appendix 16.2 WINQSB Input for Goal Programming

Appendix 16.3 WINQSB Input for Quadratic Programming

Appendix 16.4 Solving Nonlinear Models by Excel

Appendix 16.5 The Golden Search Technique for Finding the Optimal Solution to a Unimodal Problem with One Variable

Appendix 16.6 Tests for Concavity and Convexity

Appendix 16.7 The Method of Steepest Ascent for Finding Optimal Solutions for Unconstrained Problems with More Than One Variable

Appendix 16.8 The Modified Simplex Approach for

Solving Quadratic Programming Models

Problems

Cases

Supplement CD1

REVIEW OF PROBABILITY AND STATISTICS CONCEPTS

Descriptive Statistics

Probability

Random Variables

The Central Limit Theorem

Confidence Intervals and Hypothesis Tests for ;gm

Regression

Supplement CD2

DUALITY

Constructing a Dual Linear Program

Duality Theorems

Economic Interpretation of the Dual Problem

Supplement CD3

THE SIMPLEX METHOD

Standard and Canonical Form

Tableaus for Maximization Problems When All Functional

Constraints Are ì<î Constraints

The Simplex Algorithm

Geometric Interpretation of the Simplex Algorithm

The Simplex Method When Some Functional Constraints

Are Not ì<'' Constraints

Simplex Algorithm--Special Cases

Sensitivity Analysis Using the Simplex Method

The Dual Simplex Method

Duality and Tableaus

Problems

Supplement CD4

BRANCH AND BOUND ALGORITHMS FOR INTEGER PROGRAMMING MODELS

A Branch and Bound Approach for Solving Mixed Integer or All Integer Linear

Programming Models

A Branch and Bound Algorithm for Solving Binary Integer

Linear Programs

Supplement CD5

ALGORITHMS FOR NETWORK MODELS

The Transportation Problem--The Transportation Algorithm

The Capacitated Transshipment Problem--The Out-of-Kilter Algorithm

The Assignment Problem--The Hungarian Algorithm

A Traveling Salesman Algorithm

The Shortest Path Problem--The Dijkstra Algorithm

The Minimal Spanning Tree Problem--The Greedy Algorithm

The Maximal Flow Problem--The Maximal Flow Algorithm

Appendix 9.2 Daniel's Test for Trend

Appendix 9.3 Tests for Autocorrelation

Appendix 9.3 Forecasting Based on Taking First Differences

Appendix 10.2 Mathematical Formulas for Inventory Models

Appendix 10.3 Determining the Reorder Point, R, Corresponding to a

Unit Service Level

Appendix 10.4 Determining the Optimal Order Quantity Under an

Incremental Discount Schedule

Appendix 10.5 Derivation of the Planned Shortage Model

Appendix 11.2 Single-Period Inventory Model

Appendix 11.3 Calculating Costs of Satisfying k Periods Worth of

Demand for Inventory Models with Time Varying Demand

Appendix 12.2 Goodness of Fit Testing to Determine the Appropriate Probability Distribution for the Arrival and Service Processes

Appendix 12.3 The Erlangian Distribution

Appendix 12.4 Derivation of Performance Measures for M/M/1 Queues Using BalanceEquations

Appendix 12.5 Derivation of Performance Measures for M/M/k Queues Using BalanceEquations

Appendix 12.6 Transition Diagram for an M/M/k/F Queuing System

Appendix 12.7 Transition Diagram for an M/M/1//m Queuing System

Appendix 13.2 Generating Pseudo-Random Numbers Using the Linear Congruential Method

Appendix 13.3 BASIC Program Listing for Jewel Vending Simulation

Appendix 13.4 Interpolation Method for Generating Random Variable Inputs

Appendix 13.5 Variance Reduction Techniques

Problems/Cases Additional Problems and Cases

Software WINQSB Software Package