ContentsCHAPTER ONE Introduction

F Answers to Even-Numbered Problems F-

E References and Bibliography E-

D Matnx Notation and Operations D-

C Values of e-λC-

B Random Digits B-

Appendixes A-

G Solutions to Self-Test Problems G-

A Areas for the Standard Normal Distribution A-

1.1 Problem Sotving and Decision Making

1.2 Quantitative Analvsis and Decision Making

1.3 Guantitative Analysis

Model Development

Data Preparation

Model Solution

Report Generation

A Note Regarding Implementation

Revenue and Volume Models

Cost and Volume Models

1.4 Models of Cost,Revenue,and Profit

Profit and Volume Models

Break-Even Analysis

1.5 Management Science in Practice

Management Science Techniques

Methods Used Most Frequently

Glossary

Summary

Problems

Appendix 1.1 Spreadsheets for Management Science

Appendix 1.2 The Management Scientist Software Package

Management Science in Practice:Mead Corporation

CHAPTER TWO Linear Programming:The Graphical Method

2.1 A Simple Maximization Problem

The Objective Function

The Constraints

Mathematical Statement of the Par,Inc.,Problem

2.2 Graphical Solution

A Note on Graphing Lines

Summary of the Graphical Solution Procedure for Maximization Problems

Slack Variables

2.3 Extreme Points and the Optimal Solution

2.4 A Simple Minimization Problem

Surplus Variables

Summary of the Graphical Solution Procedure for Minimization Problems

Alternative Optimal Solutions

2.5 Special Cases

Infeasibility

Unbounded

2.6 Introduction to Sensitivity Analysis

Obiective Function Coefficients

2.7 Graphical Sensitivity Analysis

Right-Hand Sides

Glossary

Summary

Problems

Case Problem:Production Strategy

Case Problem:Advertising Strategy

CHAPTER THREE Linear Programming:Formulation,Computer Solution,and Interpretation

3.1 Computer Solution of Linear Programs

Interpretation of Computer Output

Simultaneous Changes

Interpretation of Computer Output—A Second Example

Cautionary Note on the Interpretation of Dual Prices

3.2 More Than Two Decision Variables

The Modified Par,Inc.,Problem

The Bluegrass Farms Problem

Formulation of the Bluegrass Farms Problem

Computer Solution and Interpretation for the Bluegrass Farms Problem

Guidelines for Model Formulation

3.3 Modeling

Management Science in Action:An Optimal Wood Procurement Policy

The Electronic Communications Problem

Formulation of the Electronic Communications Problem

Computer Solution and Interpretation for the Electronic Communications Problem

Management Science in Action:Using Linear Programming for Traffic Control

Glossary

Summary

Problems

case Problem:Product Mix

Case Problem:Truck Leasing Strategy

Appendix 3.2:Solving Linear Programs with LINDO/PC

Appendix 3.1:Solving Linear Programs with The Management Scientist

Appendix 3.3:Spreadsheet Solution of Linear Programs

Management Science in Practice:Eastman Kodak

CHAPTER FOUR Linear Programming Applications

4.1 Marketing Applications

Media Selection

Marketing Research

Portfolio Selection

4.2 Financial Applications

Financial Planning

Management Science in Action:Using Linear Programming for Optimal Lease Structuring

A Make-or-Buy Decision

4.3 Production Management Applications

Production Scheduling

Management Science in Action:Libbey-Owens-Ford

Work-Force Assignment

4.4 Blending Problems

Evaluating the Performance of Hospitals

4.5 Data Envelopment Analvsis

An Overview of the DEA Approach

The DEA Linear Programming Model

Summary of the DEA Approach

Summary

Problems

Case Problem:Environmental Protection

Case Problem:Investment Strategy

Case Problem:Textile Mill Scheduling

Appendix 4.1 Spreadsheet Solution of Linear Programs

Management Science in Practice:Marathon Oil Company

CHAPTET FIVE Linear Programming:The Simplex Method

5.1 An Algebraic Overview of the Simplex Method

Management Science in Action:Fleet Assignment at Delta Air Lines

Algebraic Properties of the Simplex Method

Determining a Basic Solution

5.2 Tableau Form

Basic Feasible Solutions

5.3 Setting Up the Initial Simplex Tableau

5.4 Improving the Solution

5.5 Calculating the Next Tableau

Interpreting the Results of an Iteration

Moving toward a Better Solution

Interpreting the Optimal Solution

Summary of the Simplex Method

5.6 Tableau Form:The General Case

Greater-Than-or-Equal-to Constraints

Equality Constraints

Eliminating Negative Right-Hand-Side Values

Summary of the Steps to Create Tableau Form

5.7 Solving a Minimization Problem

5.8 Special Cases

Infeasibility

Unboundedness

Altemative Optimal Solutions

Degeneracy

Summary

Problems

Glossary

Objective Function Coefficients

6.1 Sensitivity Analysis with the Simplexrableau

CHAPTER SIX Simplex-Based Sensitivity Analysis and Duality

Right-Haod-Side Values

Simultaneous Changes

6.2 Duality

Economic Interpretation of the Dual Variables

Using the Dual to Identify the Primal Solution

Findingthe Dual of Anv Primal Problem

Glossary

Summary

Problems

Management Science in Practice:Performance Analysis Corporation

CHAPTER　SEVEN　Transportation,Assignment,and Transshipment Problems

7.1 The Transportation Problem:The Network Model and a Linear Programming Formulation

Problem Variations

A General Linear Programming Model of the Transportation Problem

7.2 The Assignment Problem:The Network Model and a Linear Programming Formulation

Management Science in Action:Marine Corps Mobilization

Problem Variations

Multiple Assignments

A General Linear Programming Model of the Assignment Problem

7.3 The Transshipment Problem:The Nelwork Model and a Linear Programming Formulation

Problem Variations

A General Linear Programming Model of the Transshipment Problem

7.4 A Production and Inventory Application

7.5 The Transportation Simplex Method:A Special-Purpose Solution Procedure(Optional)

Phase Ⅰ:Finding an Initial Feasible Solution

Phase Ⅱ:Iterating to the Optimal Solution

Summary of the Transportation Simplex Method

Problem Variations

7.6 The Assignment Problem:A Special-Purpose Solution Procedure(Optional)

Finding the Minimum Number of Lines

Problem Variations

Summary

Glossary

Problems

Case Problem:Assigning Umpire Crews

Case Problem:Distribution System Design

Management Science jn Practice:Procter Gamble

CHAPTER EIGHT Integer Linear Programming

Management Science in Action:Scheduling Employees at McDonald's Restaurant

8.1 Types of Integer Linear Programming Models

8.2 Graphicaland Computer Solution for an All-Integer Linear Program

Graphical Solution Procedure

Computer Solution

Management Science in Action:Cutting Photographic Color Paper Rolls

8.3 Applications

Capital Budgeting

Models Involving Fixed Costs

Distribution System Design

ABank Location Application

8.4 Modeling Flexibility Provided by 0-1 Integer Variables

Multiple-Choice and Mutually Exclusive Constraints

Management Science in Action:Analyzing Price Quotations Under Business Volume Discounts

k Out of n Alternatives Constraint

Conditional and Corequisite Constraints

Summary

A Cautionary Note on Sensitivity Analysis

Problems

Glossary

Case Problem:Textbook Publishing

Case Problem:Production Scheduling with Changeover Costs

Management Science in Practice:Ketron

CHAPTER NINE Network Models

9.1 The Shortest-Route Problem

A Shortest-Route Algorithm

A Minimal Spanning Tree Algorithm

9.2 The Minimal Spanning Tree Problem

9.3 The Maximal Flow Problem

A Maximal Flow Algorithm

Glossary

Problems

Summary

Case Problem:Ambulance Routing

Management Science in Practice:EDS

CHAPTER TEN Project Scheduling:PERT/CPM

10.1 Project Scheduling with Known Activity Times

The Concepts of a Critical Path

Determining the Critical Path

Contributions of PERT/CPM

Management Science in Action:Project Management on the PC

Summary of the PERT/CPM Critical Path Procedure

The Daugherty Porta-Vac Project

10.2 Project Scheduling with Uncertain Activity Times

Uncertain Activity Times

The Critical Path

Variability in Project Completion Time

10.3 Considering Time-Cost Trade-Offs

Crashing Activity Times

A Linear Programming Model for Crashing Decisions

Summary

Glossary

Problems

Case Problem:Warehouse Expansion

Management Science in Practice:Seasongood Mayer

CHAPTER ELEVEN Inventory Models

11.1 Economic Order Quantity(EOQ)Model　

The How-Much-to-Order Decision

The When-to-Order Decision

Sensitivity Analysis in the EOQ Model

The Manager's Use of the EOQ Model

A Summary of the EOQ Model Assumptions

How Has the EOQ Decision Model Helped?

11.2 Economic Production Lot Size Model

The Total Cost Model

Finding the Economic Production Lot Size

11.4 Quantity Discounts for the EOQ Model

11.3 An Inventory Model with Planned Shortages

11.5 A Single-Period lnventory Model with Probabilistic Demand

The Johnson Shoe Company Problem

The Kremer Chemical Company Problem

11.6 An Order-Quantity,Reorder-Point Model with Probabilistic Demand

The When-to-Order Decision

The How-Much-to-Order Decision

11.7 A Periodic-Review Model with Probabilistic Demand

Management Science in Action:Information from a Netherlands Supplier Lowers Inventory Cost

More Complex Periodic-Review Models

Management Science in Action:Inventory Model Helps Hewlett-Packard's Product Design for Worldwide Markets

11.8 Material Requirements Planning

Dependent Demand and the MRP Concept

Information System for MRP

MRP Calculations

11.9 The Just-in-Time Approach to Inventory Management

Summary

Glossary

Problems

Case Problem:A Make-or-Buy Analysis

Appendix 11.1:Inventory Models with Spreadsheets

Appendix 11.3 Development of the Optimal Lot Size(Q)Formula for the Production Lot Size Model

Appendix 11.2 Development of the Optimal Order-Quantity(Q)Formula for the EOQ Model

Appendix 11.4 Development of the Optimal Order-Quantity(Q)and Optimal Backorder(S)Formulas for the Planned Shortage Model

Management Science in Practice:SupeRx.Inc.

CHAPTER TWELVE Waiting Line Models

12.1 The Structure of a Waiting Line System

The Single-Channel Waiting Line

The Distribution of Arrivals

The Distribution of Service Times

Queue Discipline

Steady-State Operation

The Operating Characteristics

12.2 The Single-Channel Waiting Line Model with Poisson Arrivals and Exponential Service Times

Operating Characteristics for the Burger Dome Problem

The Manager's Use of Waiting Line Models

Improving the Waiting Line Operation

12.3 The Multiple-Channel Waiting Line Model with Poisson Arrivals and Exponential Service Times

The Operatinig Characteristics

Operating Characteristics for the Burger Dome Problem

Management Science in Action:Hospital Staffing Based on a Multiple-Channel Waiting Line Model

12.4 Some General Relationships for Waiting Line Models

12.5 Economic Analysis of Waiting Lines

12.6 Other Waiting Line Models

Operating Characteristics for the M/G/l Model

12.7 The Single-Channel Waiting Line Model with Poisson Arrivals and Arbitrary Service Times

Constant Service Times

12.8 A Multiple-Channel Model with Poisson Arrivals,Arbitrary Service Times,and No Waiting Line

The Operating Characteristics for the M/G/K Model with Blocked Customers Cleared

The Operating Characteristics for the M/M/l Model with a Finite Calling Population

12.9 Waiting Line Models with Finite Calling Populations

Summary

Management Science in Action:Improving Fire Department Productivity

Glossary

Problems

Case Problem:Airline Reservations

Appendix 12.1:Waiting Line Models with Spreadsheets

Management Science in Practice:CITIBANK

CHAPER THIRETTEN Simulation

13.1 Using Simulation for Risk Analysis

The PortaCom Project

The PortaCom Simulation Model

Random Numbers and Simulating Values of Random Variables

Using the Simulation Model

Risk Analysis Conclusions

Simulation Results

13.2 An Inventory Simulation Model

Some Simulation Terminology

13.3 A Waiting Line Simulation Model

The Hammondsport Savings and Loan Waiting Line

Customer Arrival Times

Customer Service Times

The Simulation Model

Simulation Results

Management Science in Action:Red Cross Uses Simulation to Improve Bloodmobile Services

Selecting a Simulation Language

13.4 Other lssues

Verification and Validation

Keeping Track of Time

Advantages and Disadvantages

Management Science in Action:Simulation at Mexico's Vilpac Truck Company

Summary

Glossary

Problems

Case Problem:County Beverage Drive-Thru

Case Problem:Machine Repair

Appendix 13.1 Simulation with Spreadsheets

Management Science in Practice:The Upjohn Company

CHAPTER FOURTEEN Decision Analysis

Payoff Tables

14.1 Structuring the Decision Problem

Decision Trees

14.2 Decision Making Without Probabilities

Optimistic Approach

Conservative Approach

Minimax Regret Approach

14.3 Decision Making with Probabilities

14.4 Sensitivity Analvsis

Management Science in Action:Decision Analysis and the Selection of Home Mortgages

14.5 Expected Value of Perfect Information

14.6 Decision Analvsis with Sample Information

14.7 Developing a Decision Strategy

Computing Branch Probabilities

An Optimal Decision Strategy

Management Science in Action:Decision Analysis and Drug Testing for Student Athletes

14.8 Expected Value of Sample Information

Efficiency of Sample Information

The Meaning of Utility

14.9 Utility and Decision Making

Developing Utilities for Payoffs

The Expected Utility Approach

Glossary

Summary

Problems

Case Problem:Property Purchase Strategy

Appendix 14.1:Decision Analysis and Spreadsheets

Management Science in Practice:Ohio Edison Company

CHAPTET FIFTEEN Multicriteria Decision Problems

15.1 Goal Programming:Formulation and Graphical Solution

Developing the Constraints and the Goal Equations

Developing an Objective Function with Preemptive Priorities

The Graphical Solution Procedure

The Goal Programming Model

15.2 Goal Programming:Solving More Complex Problems

The Suncoast Office Supplies Problem

Formulating the Goal Equations

Formulating the Objective Function

Computer Solution

15.3 The Analytic Hierarchy Process

Management Science in Action:Using AHP and Goal Programming to Plan Facility Locations

Developing the Hierarchy

15.4 Establishing Priorities Using AHP

The Pairwise Comparison Matrix

Pairwise Comparisons

Procedure for Synthesizing Judgments

Synthesis

Consistency

Estimating the Consistency Ratio

Other Pairwise Comparisons for the Car-Selection Problem

15.5 Using AHP to Develop an Overall Priority Ranking

15.6 Using Expert Choice to Implement AHP

Summary

Glossary

Problems

Case Problem:Production Scheduling

CHAPTER XIXTEEN Forecasting

16.1 The Components of a Time Series

Trend Component

Cyclical Component

Seasonal Component

Irregular Component

16.2 Smoothing Methods

Moving Averages

Weighted Moving Averages

Exponential Smoothing

16.3 Trend Projection

16.4 Trend and Seasonal Components

The Multiplicative Model

Calculating the Seasonal Indexes

Deseasonalizing the Time Series

Using the Deseasonalized Time Series to Identify Trend

Seasonal Adjustments

Models Based on Monthy Data

Cyclical Component

16.5 Forecasting Using Regression Models

Management Science in Action:Spare Parts Forecasting at American Airlines

Using Regression Analysis When Time Series Data Are Not Available

Using Regression Analysis with Time Series Data

Delphi Method

16.6 Qualitative Approaches to Forecasting

Scenario Writing

Expert Judgment

Management Science in Action:The Business Week Industry Outlook 70lIntuitive Approaches

Summary

Glossary

Problems

Case Problem:Forecasting Sales

Case Problem:Forecasting Lost Sales

Appendix 16.1 Forecasting with Spreadsheets

Management Science in Practice:The Cincinnati Gas Electric Company

CHAPTER SEVENTEEN Markov Processes

17.1 Market Share Analysis

17.2 Accounts Receivable Analysis

The Fundamental Matrix and Associated Calculations

Establishing the Allowance for Doubtful Accounts

Problems

Glossary

Summary

Management Science in Practice:U.S.General Accounting Office

18.1 A Shortest-Route Problem

CHAPTER ELGHTEEN Dynamic Programming

18.2 Dynamic Programming Notation

18.3 The Knapsack Problem

18.4 A Production and Inventory Control Problem

Summary

Glossary

Problems

Management Science in Practice:The U.S.Environmental Protection Agency