Copyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

Australia ● Brazil ● Mexico ● Singapore ● United Kingdom ● United States

David R. Anderson University of Cincinnati

Dennis J. Sweeney University of Cincinnati

Thomas A. Williams Rochester Institute of Technology

Jeffrey D. Camm University of Cincinnati

James J. Cochran

University of Alabama

Michael J. Fry University of Cincinnati

Jeffrey W. Ohlmann

University of Iowa

14e

An Introduction to Management Science: Quantitative Approaches

to Decision Making

This is an electronic version of the print textbook. Due to electronic rights restrictions, some third party content may be suppressed. Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. The publisher reserves the right to

remove content from this title at any time if subsequent rights restrictions require it. For valuable information on pricing, previous editions, changes to current editions, and alternate formats, please visit www.cengage.com/highered to search by

ISBN#, author, title, or keyword for materials in your areas of interest.

WCN: 02-200-203

ALL RIGHTS RESERVED. No part of this work covered by the copyright herein may be reproduced, transmitted, stored, or used in any form or by any means graphic, electronic, or mechanical, including but not limited to photocopying, recording, scanning, digitizing, taping, Web distribution, information networks, or information storage and retrieval systems, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the publisher.

Unless otherwise noted, all items © Cengage Learning®

Library of Congress Control Number: 2014947009

ISBN: 978-1-111-82361-0

Cengage Learning 20 Channel Center Street Boston, MA 02210 USA

Cengage Learning is a leading provider of customized learning solutions with office locations around the globe, including Singapore, the United Kingdom, Australia, Mexico, Brazil, and Japan. Locate your local office at: www.cengage.com/global

Cengage Learning products are represented in Canada by Nelson Education, Ltd.

To learn more about Cengage Learning Solutions, visit www.cengage.com

Purchase any of our products at your local college store or at our preferred online store www.cengagebrain.com

An Introduction to Management Science: Quantitative Approaches to Decision Making, Fourteenth Edition David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann

Vice President, General Manager, Science, Math and Quantitative Business: Balraj Kalsi

Product Director: Joe Sabatino

Product Manager: Aaron Arnsparger

Sr. Content Developer: Maggie Kubale

Content Coordinator: Eileen Corcoran

Sr. Product Assistant: Brad Sullender

Marketing Manager: Heather Mooney

Content Project Manager: Jana Lewis

Media Developer: Chris Valentine

Manufacturing Planner: Ron Montgomery

Production Service: MPS Limited

Sr. Art Director: Stacy Shirley

Internal Designer: Mike Stratton/Chris Miller Design

Cover Designer: Beckmeyer Design

Cover Image: iStockphoto.com/alienforce

Intellectual Property

Analyst: Christina Ciaramella

Project Manager: Betsy Hathaway

For product information and technology assistance, contact us at Cengage Learning Customer & Sales Support, 1-800-354-9706

For permission to use material from this text or product, submit all requests online at www.cengage.com/permissions

Further permissions questions can be emailed to permissionrequest@cengage.com

Printed in the United States of America Print Number: 01 Print Year: 2014

Dedication

To My Parents Ray and Ilene Anderson

DRA

To My Parents James and Gladys Sweeney

DJS

To My Parents Phil and Ann Williams

TAW

To My Parents Randall and Jeannine Camm

JDC

To My Wife Teresa

JJC

To My Parents Mike and Cynthia Fry

MJF

To My Parents Willis and Phyllis Ohlmann

JWO

Brief Contents

Preface xxi About the Authors xxv Chapter 1 Introduction 1 Chapter 2 An Introduction to Linear Programming 30 Chapter 3 Linear Programming: Sensitivity Analysis

and Interpretation of Solution 94 Chapter 4 Linear Programming Applications in Marketing,

Finance, and Operations Management 154 Chapter 5 Advanced Linear Programming Applications 216 Chapter 6 Distribution and Network Models 258 Chapter 7 Integer Linear Programming 320 Chapter 8 Nonlinear Optimization Models 369 Chapter 9 Project Scheduling: PERT/CPM 418 Chapter 10 Inventory Models 457 Chapter 11 Waiting Line Models 506 Chapter 12 Simulation 547 Chapter 13 Decision Analysis 610 Chapter 14 Multicriteria Decisions 689 Chapter 15 Time Series Analysis and Forecasting 733 Chapter 16 Markov Processes On Website Chapter 17 Linear Programming: Simplex Method On Website Chapter 18 Simplex-Based Sensitivity Analysis and Duality

On Website Chapter 19 Solution Procedures for Transportation and

Assignment Problems On Website Chapter 20 Minimal Spanning Tree On Website Chapter 21 Dynamic Programming On Website Appendixes 787 Appendix A Building Spreadsheet Models 788 Appendix B Areas for the Standard Normal Distribution 815 Appendix C Values of e2l 817 Appendix D References and Bibliography 819 Appendix E Self-Test Solutions and Answers

to Even-Numbered Problems 821 Index 863

Preface xxi About the Authors xxv

Chapter 1 Introduction 1 1.1 Problem Solving and Decision Making 3 1.2 Quantitative Analysis and Decision Making 5 1.3 Quantitative Analysis 7

Model Development 7 Data Preparation 10 Model Solution 11 Report Generation 12 A Note Regarding Implementation 13

1.4 Models of Cost, Revenue, and Profit 14 Cost and Volume Models 14 Revenue and Volume Models 15 Profit and Volume Models 15 Breakeven Analysis 15

1.5 Management Science Techniques 17 Methods Used Most Frequently 18

Summary 19 Glossary 19 Problems 20 Case Problem Scheduling a Golf League 25 Appendix 1.1 Using Excel for Breakeven Analysis 26

Chapter 2 An Introduction to Linear Programming 30 2.1 A Simple Maximization Problem 32

Problem Formulation 33 Mathematical Statement of the Par, Inc., Problem 35

2.2 Graphical Solution Procedure 37 A Note on Graphing Lines 46 Summary of the Graphical Solution Procedure

for Maximization Problems 48 Slack Variables 49

2.3 Extreme Points and the Optimal Solution 50 2.4 Computer Solution of the Par, Inc., Problem 52

Interpretation of Computer Output 53

Contents

x Contents

2.5 A Simple Minimization Problem 54 Summary of the Graphical Solution Procedure

for Minimization Problems 56 Surplus Variables 57 Computer Solution of the M&D Chemicals Problem 58

2.6 Special Cases 59 Alternative Optimal Solutions 59 Infeasibility 60 Unbounded 62

2.7 General Linear Programming Notation 64 Summary 66 Glossary 67 Problems 68 Case Problem 1 Workload Balancing 84 Case Problem 2 Production Strategy 85 Case Problem 3 Hart Venture Capital 86 Appendix 2.1 Solving Linear Programs with LINGO 87 Appendix 2.2 Solving Linear Programs with Excel Solver 89

Chapter 3 Linear Programming: Sensitivity Analysis and Interpretation of Solution 94

3.1 Introduction to Sensitivity Analysis 96 3.2 Graphical Sensitivity Analysis 97

Objective Function Coefficients 97 Right-Hand Sides 102

3.3 Sensitivity Analysis: Computer Solution 105 Interpretation of Computer Output 105 Cautionary Note on the Interpretation of Dual Values 108 The Modified Par, Inc., Problem 108

3.4 Limitations of Classical Sensitivity Analysis 112 Simultaneous Changes 113 Changes in Constraint Coefficients 114 Nonintuitive Dual Values 114

3.5 The Electronic Communications Problem 118 Problem Formulation 119 Computer Solution and Interpretation 120

Summary 123 Glossary 124 Problems 125 Case Problem 1 Product Mix 146 Case Problem 2 Investment Strategy 147 Case Problem 3 TRUCK LEASING STRATEGY 148 Appendix 3.1 Sensitivity Analysis with Excel Solver 149 Appendix 3.2 Sensitivity Analysis with LINGO 151

Contents xi

Chapter 4 Linear Programming Applications in Marketing, Finance, and Operations Management 154

4.1 Marketing Applications 155 Media Selection 156 Marketing Research 159

4.2 Financial Applications 162 Portfolio Selection 162 Financial Planning 165

4.3 Operations Management Applications 169 A Make-or-Buy Decision 169 Production Scheduling 173 Workforce Assignment 180 Blending Problems 184

Summary 189 Problems 190 Case Problem 1 Planning An Advertising Campaign 204 Case Problem 2 Schneider’s Sweet Shop 205 Case Problem 3 Textile Mill Scheduling 206 Case Problem 4 Workforce Scheduling 208 Case Problem 5 Duke Energy Coal Allocation 209 Appendix 4.1 Excel Solution of Hewlitt Corporation

Financial Planning Problem 212

Chapter 5 Advanced Linear Programming Applications 216 5.1 Data Envelopment Analysis 217

Evaluating the Performance of Hospitals 218 Overview of the DEA Approach 218 DEA Linear Programming Model 219 Summary of the DEA Approach 224

5.2 Revenue Management 225 5.3 Portfolio Models and Asset Allocation 231

A Portfolio of Mutual Funds 231 Conservative Portfolio 232 Moderate Risk Portfolio 234

5.4 Game Theory 238 Competing for Market Share 238 Identifying a Pure Strategy Solution 241 Identifying a Mixed Strategy Solution 242

Summary 250 Glossary 250 Problems 250

xii Contents

Chapter 6 Distribution and Network Models 258 6.1 Supply Chain Models 259

Transportation Problem 259 Problem Variations 262 A General Linear Programming Model 265 Transshipment Problem 266 Problem Variations 272 A General Linear Programming Model 272

6.2 Assignment Problem 274 Problem Variations 277 A General Linear Programming Model 277

6.3 Shortest-Route Problem 279 A General Linear Programming Model 282

6.4 Maximal Flow Problem 283 6.5 A Production and Inventory Application 287 Summary 290 Glossary 291 Problems 292 Case Problem 1 Solutions Plus 309 Case Problem 2 Supply Chain Design 311 Appendix 6.1 Excel Solution of Transportation, Transshipment,

and Assignment Problems 312

Chapter 7 Integer Linear Programming 320 7.1 Types of Integer Linear Programming Models 322 7.2 Graphical and Computer Solutions for an All-Integer

Linear Program 324 Graphical Solution of the LP Relaxation 325 Rounding to Obtain an Integer Solution 325 Graphical Solution of the All-Integer Problem 326 Using the LP Relaxation to Establish Bounds 326 Computer Solution 327

7.3 Applications Involving 0-1 Variables 328 Capital Budgeting 328 Fixed Cost 329 Distribution System Design 332 Bank Location 337 Product Design and Market Share Optimization 340

7.4 Modeling Flexibility Provided by 0-1 Integer Variables 344 Multiple-Choice and Mutually Exclusive Constraints 344 k out of n Alternatives Constraint 345 Conditional and Corequisite Constraints 345 A Cautionary Note About Sensitivity Analysis 347

Contents xiii

Summary 347 Glossary 348 Problems 349 Case Problem 1 Textbook Publishing 360 Case Problem 2 Yeager National Bank 361 Case Problem 3 Production Scheduling with Changeover Costs 362 Case Problem 4 Applecore Children’s Clothing 363 Appendix 7.1 Excel Solution of Integer Linear Programs 364 Appendix 7.2 LINGO Solution of Integer Linear Programs 368

Chapter 8 Nonlinear Optimization Models 369 8.1 A Production Application—Par, Inc., Revisited 371

An Unconstrained Problem 371 A Constrained Problem 372 Local and Global Optima 375 Dual Values 378

8.2 Constructing an Index Fund 378 8.3 Markowitz Portfolio Model 383 8.4 Blending: The Pooling Problem 386 8.5 Forecasting Adoption of a New Product 391 Summary 396 Glossary 396 Problems 397 Case Problem 1 Portfolio Optimization with Transaction Costs 407 Case Problem 2 Cafe Compliance in the Auto Industry 410 Appendix 8.1 Solving Nonlinear Problems with LINGO 412 Appendix 8.2 Solving Nonlinear Problems with Excel Solver 414

Chapter 9 Project Scheduling: PERT/CPM 418 9.1 Project Scheduling Based on Expected Activity Times 419

The Concept of a Critical Path 421 Determining the Critical Path 422 Contributions of PERT/CPM 427 Summary of the PERT/CPM Critical Path Procedure 427

9.2 Project Scheduling Considering Uncertain Activity Times 428 The Daugherty Porta-Vac Project 428 Uncertain Activity Times 430 The Critical Path 432 Variability in Project Completion Time 434

9.3 Considering Time–Cost Trade-Offs 437 Crashing Activity Times 438 Linear Programming Model for Crashing 441

xiv Contents

Summary 443 Glossary 443 Problems 444 Case Problem 1 R. C. Coleman 454 Appendix 9.1 Finding Cumulative Probabilities for Normally

Distributed Random Variables 455

Chapter 10 Inventory Models 457 10.1 Economic Order Quantity (EOQ) Model 459

The How-Much-to-Order Decision 463 The When-to-Order Decision 464 Sensitivity Analysis for the EOQ Model 465 Excel Solution of the EOQ Model 466 Summary of the EOQ Model Assumptions 467

10.2 Economic Production Lot Size Model 468 Total Cost Model 469 Economic Production Lot Size 471

10.3 Inventory Model with Planned Shortages 471 10.4 Quantity Discounts for the EOQ Model 476 10.5 Single-Period Inventory Model with Probabilistic Demand 478

Neiman Marcus 479 Nationwide Car Rental 482

10.6 Order-Quantity, Reorder Point Model with Probabilistic Demand 484 The How-Much-to-Order Decision 485 The When-to-Order Decision 486

10.7 Periodic Review Model with Probabilistic Demand 488 More Complex Periodic Review Models 491

Summary 492 Glossary 492 Problems 493 Case Problem 1 Wagner Fabricating Company 501 Case Problem 2 River City Fire Department 503 Appendix 10.1 Development of the Optimal Order Quantity (Q)

Formula for the EOQ Model 504 Appendix 10.2 Development of the Optimal Lot Size (Q*) Formula for

the Production Lot Size Model 504

Chapter 11 Waiting Line Models 506 11.1 Structure of a Waiting Line System 508

Single-Server Waiting Line 508 Distribution of Arrivals 508 Distribution of Service Times 510

Contents xv

Queue Discipline 511 Steady-State Operation 511

11.2 Single-Server Waiting Line Model with Poisson Arrivals and Exponential Service Times 511 Operating Characteristics 511 Operating Characteristics for the Burger Dome Problem 513 Managers’ Use of Waiting Line Models 514 Improving the Waiting Line Operation 514 Excel Solution of Waiting Line Model 515

11.3 Multiple-Server Waiting Line Model with Poisson Arrivals and Exponential Service Times 516 Operating Characteristics 517 Operating Characteristics for the Burger Dome Problem 518

11.4 Some General Relationships for Waiting Line Models 521 11.5 Economic Analysis of Waiting Lines 523 11.6 Other Waiting Line Models 525 11.7 Single-Server Waiting Line Model with Poisson Arrivals and Arbitrary

Service Times 525 Operating Characteristics for the M/G/1 Model 526 Constant Service Times 527

11.8 Multiple-Server Model with Poisson Arrivals, Arbitrary Service Times, and No Waiting Line 528 Operating Characteristics for the M/G/k Model with Blocked Customers

Cleared 528 11.9 Waiting Line Models with Finite Calling Populations 530

Operating Characteristics for the M/M/1 Model with a Finite Calling Population 531

Summary 533 Glossary 535 Problems 535 Case Problem 1 Regional Airlines 543 Case Problem 2 Office Equipment, Inc. 544

Chapter 12 Simulation 547 12.1 Risk Analysis 550

PortaCom Project 550 What-If Analysis 550 Simulation 552 Simulation of the PortaCom Project 560

12.2 Inventory Simulation 563 Simulation of the Butler Inventory Problem 566

12.3 Waiting Line Simulation 568 Black Sheep Scarves 569

xvi Contents

Customer (Scarf) Arrival Times 569 Customer (Scarf) Service Times 570 Simulation Model 571 Simulation of Black Sheep Scarves 574 Simulation with Two Quality Inspectors 576 Simulation Results with Two Quality Inspectors 577

12.4 Other Simulation Issues 579 Computer Implementation 579 Verification and Validation 580 Advantages and Disadvantages of Using Simulation 581

Summary 581 Glossary 582 Problems 583 Case Problem 1 Tri-State Corporation 592 Case Problem 2 Harbor Dunes Golf Course 593 Case Problem 3 County Beverage Drive-Thru 595 Appendix 12.1 Simulation with Excel 597 Appendix 12.2 Simulation Using Analytic Solver Platform 603

Chapter 13 Decision Analysis 610 13.1 Problem Formulation 612

Influence Diagrams 613 Payoff Tables 613 Decision Trees 614

13.2 Decision Making Without Probabilities 615 Optimistic Approach 615 Conservative Approach 616 Minimax Regret Approach 616

13.3 Decision Making with Probabilities 618 Expected Value of Perfect Information 621

13.4 Risk Analysis and Sensitivity Analysis 622 Risk Analysis 622 Sensitivity Analysis 623

13.5 Decision Analysis with Sample Information 627 Influence Diagram 628 Decision Tree 629 Decision Strategy 632 Risk Profile 634 Expected Value of Sample Information 637 Efficiency of Sample Information 638

13.6 Computing Branch Probabilities with Bayes’ Theorem 638 13.7 Utility Theory 642

Utility and Decision Analysis 644

Contents xvii

Utility Functions 648 Exponential Utility Function 651

Summary 653 Glossary 653 Problems 655 Case Problem 1 Property Purchase Strategy 670 Case Problem 2 Lawsuit Defense Strategy 671 Appendix 13.1 Using Analytic Solver Platform to Create

Decision Trees 672 Appendix 13.2 Decision Analysis with TreePlan 683

Chapter 14 Multicriteria Decisions 689 14.1 Goal Programming: Formulation and Graphical Solution 690

Developing the Constraints and the Goal Equations 691 Developing an Objective Function with Preemptive Priorities 693 Graphical Solution Procedure 694 Goal Programming Model 697

14.2 Goal Programming: Solving More Complex Problems 698 Suncoast Office Supplies Problem 698 Formulating the Goal Equations 699 Formulating the Objective Function 700 Computer Solution 701

14.3 Scoring Models 704 14.4 Analytic Hierarchy Process 708

Developing the Hierarchy 709 14.5 Establishing Priorities Using AHP 709

Pairwise Comparisons 710 Pairwise Comparison Matrix 711 Synthesization 713 Consistency 714 Other Pairwise Comparisons for the Car Selection Problem 716

14.6 Using AHP to Develop an Overall Priority Ranking 717 Summary 719 Glossary 720 Problems 721 Case Problem 1 EZ Trailers, Inc. 730 Appendix 14.1 Scoring Models With Excel 731

Chapter 15 Time Series Analysis and Forecasting 733 15.1 Time Series Patterns 735

Horizontal Pattern 735 Trend Pattern 738

xviii Contents

Seasonal Pattern 740 Trend and Seasonal Pattern 741 Cyclical Pattern 741 Selecting a Forecasting Method 742

15.2 Forecast Accuracy 744 15.3 Moving Averages and Exponential Smoothing 749

Moving Averages 749 Weighted Moving Averages 752 Exponential Smoothing 753

15.4 Linear Trend Projection 757 15.5 Seasonality 761

Seasonality Without Trend 761 Seasonality with Trend 764 Models Based on Monthly Data 767

Summary 767 Glossary 768 Problems 768 Case Problem 1 Forecasting Food and Beverage Sales 776 Case Problem 2 Forecasting Lost Sales 777 Appendix 15.1 Forecasting with Excel Data Analysis Tools 778

Chapter 16 Markov Processes On Website 16.1 Market Share Analysis 16-3 16.2 Accounts Receivable Analysis 16-11

Fundamental Matrix and Associated Calculations 16-12 Establishing the Allowance for Doubtful Accounts 16-14

Summary 16-16 Glossary 16-17 Problems 16-17 Case Problem 1 Dealer’s Absorbing State Probabilities in

Blackjack 16-22 Appendix 16.1 Matrix Notation and Operations 16-23 Appendix 16.2 Matrix Inversion with Excel 16-26

Chapter 17 Linear Programming: Simplex Method On Website 17.1 An Algebraic Overview of the Simplex Method 17-2

Algebraic Properties of the Simplex Method 17-3 Determining a Basic Solution 17-3 Basic Feasible Solution 17-4

17.2 Tableau Form 17-5 17.3 Setting up the Initial Simplex Tableau 17-7 17.4 Improving the Solution 17-10

Contents xix

17.5 Calculating the Next Tableau 17-12 Interpreting the Results of an Iteration 17-15 Moving Toward a Better Solution 17-15 Summary of the Simplex Method 17-18

17.6 Tableau Form: The General Case 17-19 Greater-Than-or-Equal-to Constraints 17-19 Equality Constraints 17-23 Eliminating Negative Right-Hand-Side Values 17-24 Summary of the Steps to Create Tableau Form 17-25

17.7 Solving a Minimization Problem 17-26 17.8 Special Cases 17-28

Infeasibility 17-28 Unboundedness 17-30 Alternative Optimal Solutions 17-31 Degeneracy 17-32

Summary 17-34 Glossary 17-35 Problems 17-36

Chapter 18 Simplex-Based Sensitivity Analysis and Duality On Website

18.1 Sensitivity Analysis with the Simplex Tableau 18-2 Objective Function Coefficients 18-2 Right-Hand-Side Values 18-6

18.2 Duality 18-13 Economic Interpretation of the Dual Variables 18-16 Using the Dual to Identify the Primal Solution 18-17 Finding the Dual of Any Primal Problem 18-18

Summary 18-20 Glossary 18-20 Problems 18-21

Chapter 19 Solution Procedures for Transportation and Assignment Problems On Website

19.1 Transportation Simplex Method: A Special-Purpose Solution Procedure 19-2 Phase I: Finding an Initial Feasible Solution 19-2 Phase II: Iterating to the Optimal Solution 19-7 Summary of the Transportation Simplex Method 19-17 Problem Variations 19-17

19.2 Assignment Problem: A Special-Purpose Solution Procedure 19-18 Finding the Minimum Number of Lines 19-21 Problem Variations 19-21

xx Contents

Glossary 19-25 Problems 19-26

Chapter 20 Minimal Spanning Tree On Website 20.1 A Minimal Spanning Tree Algorithm 20-2 Glossary 20-5 Problems 20-5

Chapter 21 Dynamic Programming On Website 21.1 A Shortest-Route Problem 21-2 21.2 Dynamic Programming Notation 21-6 21.3 The Knapsack Problem 21-10 21.4 A Production and Inventory Control Problem 21-16 Summary 21-20 Glossary 21-21 Problems 21-22 Case Problem Process Design 21-26

Appendixes 787

Appendix A Building Spreadsheet Models 788

Appendix B Areas for the Standard Normal Distribution 815

Appendix C Values of e2l 817

Appendix D References and Bibliography 819

Appendix E Self-Test Solutions and Answers to Even-Numbered Problems 821

Index 863

Preface

We are very excited to publish the fourteenth edition of a text that has been a leader in the field for nearly 25 years. The purpose of this fourteenth edition, as with previous editions, is to provide undergraduate and graduate students with a sound conceptual understanding of the role that management science plays in the decision-making process. The text de- scribes many of the applications where management science is used successfully. Former users of this text have told us that the applications we describe have led them to find new ways to use management science in their organizations.

An Introduction to Management Science: Quantiative Approaches to Decision Mak- ing, 14e is applications oriented and continues to use the problem-scenario approach that is a hallmark of every edition of the text. Using the problem scenario approach, we describe a problem in conjunction with the management science model being introduced. The model is then solved to generate a solution and recommendation to management. We have found that this approach helps to motivate the student by demonstrating not only how the proce- dure works, but also how it contributes to the decision-making process.

From the first edition we have been committed to the challenge of writing a textbook that would help make the mathematical and technical concepts of management science un- derstandable and useful to students of business and economics. Judging from the responses from our teaching colleagues and thousands of students, we have successfully met the challenge. Indeed, it is the helpful comments and suggestions of many loyal users that have been a major reason why the text is so successful.

Throughout the text we have utilized generally accepted notation for the topic being covered so those students who pursue study beyond the level of this text should be comfort- able reading more advanced material. To assist in further study, a references and bibliog- raphy section is included at the back of the book.

CHANGES IN THE FOURTEENTH EDITION

We are very excited about the changes in the fourteenth edition of Management Science and want to explain them and why they were made. Many changes have been made throughout the text in response to suggestions from instructors and students. While we cannot list all these changes, we highlight the more significant revisions.

New Members of the ASW Team Prior to getting into the content changes, we want to announce that we have some changes in the ASW author team for Management Science. Previous author Kipp Martin decided to pursue other interests and will no longer be involved with this text. We thank Kipp for his previous contributions to this text. We have brought on board three new outstanding authors who we believe will be strong contributors and bring a thoughtful and fresh view as we move forward. The new authors are James Cochran, University of Alabama, Michael Fry of the University of Cincinnati, and Jeffrey Ohlmann, University of Iowa. You may read more about each of these authors in the brief bios which follow.

xxii Preface

Updated Chapter 9: Project Scheduling Within this chapter, the section on considering variability’s impact on project completion time has been significantly revised. The new discussion maintains the emphasis on the critical path in estimating the probability of completing a project by a specified deadline, but generalizes this calculation to also consider the other paths through the project network. Also, Appendix 9.1 has been added to show how to find a cumulative probability for a nor- mally distributed random variable; the normal distribution is commonly used to describe the completion time for sequences of activities.

Updated Chapter 6: Distribution and Network Models This chapter has been updated and rearranged to reflect the increased importance of supply chain applications for quantitative methods in business. Transportation and transshipment models are grouped into a single section on supply chain models. This chapter better rep- resents the current importance of supply chain models for business managers. All models in this chapter are presented as linear programs. In keeping with the theme of this book, we do not burden the student with solution algorithms in the chapter. Details on many of the solution algorithms used in this text can still be found in the Web chapters for this text.

Updated Chapter 13: Decision Analysis This chapter has been updated with a new section on Utility Theory to complement the previous material on decision analysis.

Updated Chapter 15: Time Series Analysis and Forecasting We have updated our discussion of trends and seasonality in Chapter 15. We now focus on the use of regression to estimate linear trends and seasonal effects. We have also added a discussion on using the Excel LINEST function to estimate linear trends and seasonal effects in Appendix 15.1 at the end of this chapter. These revisions better represent industry approaches to these important topics.

Management Science in Action The Management Science in Action vignettes describe how the material covered in a chap- ter is used in practice. Some of these are provided by practitioners. Others are based on articles from publications such as Interfaces and OR/MS Today. We updated the text with over 20 new Management Science in Action vignettes in this edition.

Cases and Problems The quality of the problems and case problems is an important feature of the text. In this edition we have added over 45 new problems and 3 new case problems.

COMPUTER SOFTWARE INTEGRATION

To make it easy for new users of LINGO or Excel Solver, we provide both LINGO and Excel files with the model formulation for every optimization problem that appears in the body of the text. The model files are well-documented and should make it easy for the user to understand the model formulation. Microsoft Excel 2010 and 2013 both use an updated version of Excel Solver that allows all problems in this book to be solved using the standard version of Excel Solver. LINGO 14.0 is the version used in the text.

Preface xxiii

In an Appendix 12.2 at the end of Chapter 12, we have replaced Crystal BallTM with Analytic Solver Platform to construct and solve simulation models. In Appendix 13.1 at the end of Chapter 13, we have replaced the TreePlan software with Analytic Solver Platform to create decision trees.

FEATURES AND PEDAGOGY

We have continued many of the features that appeared in previous editions. Some of the important ones are noted here.

Annotations Annotations that highlight key points and provide additional insights for the student are a continuing feature of this edition. These annotations, which appear in the margins, are designed to provide emphasis and enhance understanding of the terms and concepts being presented in the text.

Notes and Comments At the end of many sections, we provide Notes and Comments designed to give the student additional insights about the methodology and its application. Notes and Comments in- clude warnings about or limitations of the methodology, recommendations for application, brief descriptions of additional technical considerations, and other matters.

Self-Test Exercises Certain exercises are identified as self-test exercises. Completely worked-out solutions for those exercises are provided in an appendix at the end of the text. Students can attempt the self-test exercises and immediately check the solution to evaluate their understanding of the concepts presented in the chapter.

ANCILLARY TEACHING AND LEARNING MATERIALS

For Students Print and online resources are available to help the student work more efficiently.

● LINGO. A link to download an educational version of the LINGO software is available on the student website at www.cengagebrain.com.

● Analytic Solver Platform. Instructions to download an educational version of Frontline Systems’ (the makers of Excel Solver) Analytic Solver Platform are in- cluded with the purchase of this textbook. These instructions can be found within the inside front cover of the text.

For Instructors Instructor support materials are available to adopters from the Cengage Learning customer ser- vice line at 800-423-0563 or through www.cengage.com. Instructor resources are available on the Instructor Companion Site, which can be found and accessed at login.cengage.com, including:

● Solutions Manual. The Solutions Manual, prepared by the authors, includes solu- tions for all problems in the text.

● Solutions to Case Problems. These are also prepared by the authors and contain solutions to all case problems presented in the text.

xxiv Preface

● PowerPoint Presentation Slides. Prepared by John Loucks of St. Edwards Univer- sity, the presentation slides contain a teaching outline that incorporates graphics to help instructors create more stimulating lectures.

● Test Bank. Cengage Learning Testing Powered by Cognero is a flexible, online system that allows you to:

● author, edit, and manage test bank content from multiple Cengage Learning solutions, ● create multiple test versions in an instant, ● deliver tests from your LMS, your classroom or wherever you want. The Test

Bank is also available in Microsoft Word.

CengageNOW CengageNOW™ is a powerful course management and online homework tool that provides robust instructor control and customization to optimize the learning experience and meet desired outcomes. CengageNOW™ features author-written homework from the textbook, integrated eBook, assessment options, and course management tools, including gradebook.

For more information about instructor resources, please contact your Cengage Learn- ing Consultant.

ACKNOWLEDGMENTS

We owe a debt to many of our colleagues and friends whose names appear below for their helpful comments and suggestions during the development of this and previous editions. Our associates from organizations who supplied several of the Management Science in Ac- tion vignettes make a major contribution to the text. These individuals are cited in a credit line associated with each vignette.

Art Adelberg CUNY Queens College

Joseph Bailey University of Maryland

Ike C. Ehie Kansas State University

John K. Fielding University of Northwestern Ohio

Subodha Kumar Mays Business School Texas A&M University

Dan Matthews Trine University

Avarind Narasipur Chennai Business School

Nicholas W. Twigg Coastal Carolina University

Julie Ann Stuart Williams University of West Florida

We are also indebted to our Product Director, Joe Sabatino; our Product Manager, Aaron Arnsparger; our Marketing Manager, Heather Mooney; our Sr. Content Developer, Maggie Kubale; our Media Developer, Chris Valentine; our Content Project Manager, Jana Lewis, and others at Cengage Learning for their counsel and support during the preparation of this text.

David R. Anderson Dennis J. Sweeney

Thomas A. Williams Jeffrey D. Camm

James J. Cochran Michael J. Fry

Jeffrey W. Ohlmann

About the Authors

David R. Anderson. David R. Anderson is Professor of Quantitative Analysis in the College of Business Administration at the University of Cincinnati. Born in Grand Forks, North Dakota, he earned his B.S., M.S., and Ph.D. degrees from Purdue University. Profes- sor Anderson has served as Head of the Department of Quantitative Analysis and Opera- tions Management and as Associate Dean of the College of Business Administration. In addition, he was the coordinator of the College’s first Executive Program.

At the University of Cincinnati, Professor Anderson has taught introductory statistics for business students as well as graduate-level courses in regression analysis, multivariate analysis, and management science. He has also taught statistical courses at the Department of Labor in Washington, D.C. He has been honored with nominations and awards for ex- cellence in teaching and excellence in service to student organizations.

Professor Anderson has coauthored 10 textbooks in the areas of statistics, management science, linear programming, and production and operations management. He is an active consultant in the field of sampling and statistical methods.

Dennis J. Sweeney. Dennis J. Sweeney is Professor of Quantitative Analysis and Founder of the Center for Productivity Improvement at the University of Cincinnati. Born in Des Moines, Iowa, he earned a B.S.B.A. degree from Drake University and his M.B.A. and D.B.A. degrees from Indiana University, where he was an NDEA Fellow. During 1978–79, Professor Sweeney worked in the management science group at Procter & Gamble; dur- ing 1981–82, he was a visiting professor at Duke University. Professor Sweeney served as Head of the Department of Quantitative Analysis and as Associate Dean of the College of Business Administration at the University of Cincinnati.

Professor Sweeney has published more than 30 articles and monographs in the area of management science and statistics. The National Science Foundation, IBM, Procter & Gamble, Federated Department Stores, Kroger, and Cincinnati Gas & Electric have funded his research, which has been published in Management Science, Operations Research, Mathematical Programming, Decision Sciences, and other journals.

Professor Sweeney has coauthored 10 textbooks in the areas of statistics, management science, linear programming, and production and operations management.

Thomas A. Williams. Thomas A. Williams is Professor of Management Science in the College of Business at Rochester Institute of Technology. Born in Elmira, New York, he earned his B.S. degree at Clarkson University. He did his graduate work at Rensselaer Polytechnic Institute, where he received his M.S. and Ph.D. degrees.

Before joining the College of Business at RIT, Professor Williams served for seven years as a faculty member in the College of Business Administration at the University of Cincinnati, where he developed the undergraduate program in Information Systems and then served as its coordinator. At RIT he was the first chairman of the Decision Sciences Department. He teaches courses in management science and statistics, as well as graduate courses in regression and decision analysis.

Professor Williams is the coauthor of 11 textbooks in the areas of management science, statistics, production and operations management, and mathematics. He has been

xxvi About the Authors

a consultant for numerous Fortune 500 companies and has worked on projects ranging from the use of data analysis to the development of large-scale regression models.

Jeffrey D. Camm Jeffrey D. Camm is Professor of Quantitative Analysis and College of Business Research Fellow in the Carl H. Lindner College of Business at the University of Cincinnati. Born in Cincinnati, Ohio, he holds a B.S. from Xavier University and a Ph.D. from Clemson University. He has been at the University of Cincinnati since 1984, and has been a visiting scholar at Stanford University and a visiting professor of business adminis- tration at the Tuck School of Business at Dartmouth College.

Dr. Camm has published over 30 papers in the general area of optimization applied to problems in operations management. He has published his research in Science, Man- agement Science, Operations Research, Interfaces and other professional journals. At the University of Cincinnati, he was named the Dornoff Fellow of Teaching Excellence and he was the 2006 recipient of the INFORMS Prize for the Teaching of Operations Research Practice. A firm believer in practicing what he preaches, he has served as an operations re- search consultant to numerous companies and government agencies. From 2005 to 2010 he served as editor-in-chief of Interfaces, and is currently on the editorial board of INFORMS Transactions on Education.

James J. Cochran James J. Cochran is Professor of Applied Statistics and the Rogers- Spivey Faculty Fellow in the Department of Information Systems, Statistics, and Manage- ment Science at The University of Alabama. Born in Dayton, Ohio, he holds a B.S., an M.S., and an M.B.A. from Wright State University and a Ph.D. from the University of Cincinnati. He has been a visiting scholar at Stanford University, Universidad de Talca, the University of South Africa, and Pole Universitaire Leonard de Vinci.

Professor Cochran has published over 30 papers in the development and application of operations research and statistical methods. He has published his research in Manage- ment Science, The American Statistician, Communications in Statistics - Theory and Meth- ods, European Journal of Operational Research, Journal of Combinatorial Optimization, and other professional journals. He was the 2008 recipient of the INFORMS Prize for the Teaching of Operations Research Practice and the 2010 recipient of the Mu Sigma Rho Statistical Education Award. Professor Cochran was elected to the International Statistics Institute in 2005, named a Fellow of the American Statistical Association in 2011, and received the Founders Award from the American Statistical Association in 2014. A strong advocate for effective operations research and statistics education as a means of improving the quality of applications to real problems, Professor Cochran has organized and chaired teaching effectiveness workshops in Montevideo, Uruguay; Cape Town, South Africa; Cartagena, Colombia; Jaipur, India; Buenos Aires, Argentina; Nairobi, Kenya; Buea, Cam- eroon; and Osijek, Croatia. He has served as an operations research or statistical consultant to numerous companies and not-for-profit organizations. From 2007 to 2012 Professor Cochran served as editor-in-chief of INFORMS Transactions on Education, and he is on the editorial board of several journals including Interfaces, the Journal of the Chilean In- stitute of Operations Research, and ORiON.

Michael J. Fry Michael J. Fry is Professor and Lindner Research Fellow in the Department of Operations, Business Analytics, and Information Systems in the Carl H. Lindner College of Business at the University of Cincinnati. Born in Killeen, Texas, he earned a B.S. from Texas A&M University, and M.S.E. and Ph.D. degrees from the University of Michigan. He has been at the University of Cincinnati since 2002, and he has been a visiting professor at

About the Authors xxvii

the Samuel Curtis Johnson Graduate School of Management at Cornell University and the Sauder School of Business at the University of British Columbia.

Professor Fry has published over 20 research publications in journals such as Opera- tions Research, M&SOM, Transportation Science, Naval Research Logistics, IIE Transac- tions and Interfaces. His research interests are in applying management science methods to the areas of supply chain analytics, sports analytics, and public-policy operations. He has worked with many different organizations for his research, including Dell, Inc., Copeland Corporation, Starbucks Coffee Company, the Cincinnati Fire Department, the State of Ohio Election Commission, the Cincinnati Bengals, and the Cincinnati Zoo. Professor Fry has won multiple teaching awards including the 2013 Michael L. Dean Excellence in Grad- uate Teaching Award and the 2006 Daniel J. Westerbeck Junior Faculty Teaching Award.

Jeffrey W. Ohlmann Jeffrey W. Ohlmann is Associate Professor of Management Sciences in the Tippie College of Business at the University of Iowa. Born in Valentine, Nebraska, he earned a B.S. from the University of Nebraska, and M.S. and Ph.D. degrees from the University of Michigan. He has been at the University of Iowa since 2003.

Professor Ohlmann’s research on the modeling and solution of decision-making prob- lems has produced over a dozen research papers in journals such as Mathematics of Opera- tions Research, INFORMS Journal on Computing, Transportation Science, and Interfaces. He has collaborated with companies such as Transfreight, LeanCor, Cargill, the Hamilton County Board of Elections, and the Cincinnati Bengals. Due to the relevance of his work to industry, he was bestowed the George B. Dantzig Dissertation Award and was recognized as a finalist for the Daniel H. Wagner Prize for Excellence in Operations Research Practice.

An Introduction to Management Science: Quantitative Approaches

to Decision Making14e

CHAPTER 1 Introduction

CONTENTS

1.1 PROBLEM SOLVING AND DECISION MAKING

1.2 QUANTITATIVE ANALYSIS AND DECISION MAKING

1.3 QUANTITATIVE ANALYSIS Model Development Data Preparation Model Solution Report Generation A Note Regarding Implementation

1.4 MODELS OF COST, REVENUE, AND PROFIT Cost and Volume Models Revenue and Volume Models Profit and Volume Models Breakeven Analysis

1.5 MANAGEMENT SCIENCE TECHNIQUES Methods Used Most Frequently

AppENdix 1.1 USING EXCEL FOR BREAKEVEN ANALYSIS

Chapter 1 Introduction2

Management science, an approach to decision making based on the scientific method, makes extensive use of quantitative analysis. A variety of names exists for the body of knowledge involving quantitative approaches to decision making; in addition to manage- ment science, two other widely known and accepted names are operations research and decision science. Today, many use the terms management science, operations research, and decision science interchangeably.

The scientific management revolution of the early 1900s, initiated by Frederic W. Taylor, provided the foundation for the use of quantitative methods in management. But modern management science research is generally considered to have originated during the World War II period, when teams were formed to deal with strategic and tactical problems faced by the military. These teams, which often consisted of people with diverse specialties (e.g., mathematicians, engineers, and behavioral scientists), were joined together to solve a common problem by utilizing the scientific method. After the war, many of these team members continued their research in the field of management science.

Two developments that occurred during the post–World War II period led to the growth and use of management science in nonmilitary applications. First, continued research resulted in numerous methodological developments. Probably the most significant development was the discovery by George Dantzig, in 1947, of the simplex method for solving linear program- ming problems. At the same time these methodological developments were taking place, digital computers prompted a virtual explosion in computing power. Computers enabled practitioners to use the methodological advances to solve a large variety of problems. The computer technol- ogy explosion continues; smart phones, tablets and other mobile-computing devices can now be used to solve problems larger than those solved on mainframe computers in the 1990s.

More recently, the explosive growth of data from sources such as smart phones and other personal-electronic devices provide access to much more data today than ever before. Additionally, the internet allows for easy sharing and storage of data, providing extensive access to a variety of users to the necessary inputs to management-science models.

As stated in the Preface, the purpose of the text is to provide students with a sound con- ceptual understanding of the role that management science plays in the decision-making process. We also said that the text is applications oriented. To reinforce the applications nature of the text and provide a better understanding of the variety of applications in which management science has been used successfully, Management Science in Action articles are presented throughout the text. Each Management Science in Action article summarizes an application of management science in practice. The first Management Science in Action in this chapter, Revenue Management at AT&T Park, describes one of the most important applications of management science in the sports and entertainment industry.

MANAGEMENT SCIENCE IN ACTION

REVENUE MANAGEMENT AT AT&T PARK*

Imagine the difficult position Russ Stanley, Vice President of Ticket Services for the San Francisco Giants, found himself facing late in the 2010 base- ball season. Prior to the season, his organization had adopted a dynamic approach to pricing its tick- ets similar to the model successfully pioneered by Thomas M. Cook and his operations research group at American Airlines. Stanley desparately wanted the Giants to clinch a playoff birth, but he didn’t want the team to do so too quickly.

When dynamically pricing a good or service, an organization regularly reviews supply and de- mand of the product and uses operations research to determine if the price should be changed to reflect these conditions. As the scheduled takeoff date for a flight nears, the cost of a ticket increases if seats for the flight are relatively scarce. On the other hand, the airline discounts tickets for an approach- ing flight with relatively few ticketed passengers. Through the use of optimization to dynamically set

331.1 Problem Solving and Decision Making

1.1 prOblEm SOlviNg ANd dECiSiON mAkiNg

problem solving can be defined as the process of identifying a difference between the actual and the desired state of affairs and then taking action to resolve the difference. For problems important enough to justify the time and effort of careful analysis, the problem- solving process involves the following seven steps:

1. Identify and define the problem. 2. Determine the set of alternative solutions. 3. Determine the criterion or criteria that will be used to evaluate the alternatives. 4. Evaluate the alternatives. 5. Choose an alternative. 6. Implement the selected alternative. 7. Evaluate the results to determine whether a satisfactory solution has been obtained.

decision making is the term generally associated with the first five steps of the problem-solving process. Thus, the first step of decision making is to identify and define the problem. Decision making ends with the choosing of an alternative, which is the act of making the decision.

Let us consider the following example of the decision-making process. For the moment assume that you are currently unemployed and that you would like a position that will lead to a satisfying career. Suppose that your job search has resulted in offers from compa- nies in Rochester, New York; Dallas, Texas; Greensboro, North Carolina; and Pittsburgh, Pennsylvania. Thus, the alternatives for your decision problem can be stated as follows:

1. Accept the position in Rochester. 2. Accept the position in Dallas.

ticket prices, American Airlines generates nearly $1 billion annually in incremental revenue.

The management team of the San Francisco Giants recognized similarities between their pri- mary product (tickets to home games) and the pri- mary product sold by airlines (tickets for flights) and adopted a similar revenue management system. If a particular Giants’ game is appealing to fans, tickets sell quickly and demand far exceeds sup- ply as the date of the game approaches; under these conditions fans will be willing to pay more and the Giants charge a premium for the ticket. Similarly, tickets for less attractive games are discounted to reflect relatively low demand by fans. This is why Stanley found himself in a quandary at the end of the 2010 baseball season. The Giants were in the middle of a tight pennant race with the San Diego Padres that effectively increased demand for tickets to Giants’ games, and the team was actually sched- uled to play the Padres in San Francisco for the last three games of the season. While Stanley certainly wanted his club to win its division and reach the Major League Baseball playoffs, he also recognized that his team’s revenues would be greatly enhanced if it didn’t qualify for the playoffs until the last day

of the season. “I guess financially it is better to go all the way down to the last game,” Stanley said in a late season interview. “Our hearts are in our stom- achs; we’re pacing watching these games.”

Does revenue management and operations re- search work? Today, virtually every airline uses some sort of revenue-management system, and the cruise, hotel, and car rental industries also now apply revenue-management methods. As for the Giants, Stanley said dynamic pricing provided a 7% to 8% increase in revenue per seat for Giants’ home games during the 2010 season. Coincidentally, the Giants did win the National League West division on the last day of the season and ultimately won the World Series. Several professional sports franchises are now looking to the Giants’ example and considering implementation of similar dynamic ticket-pricing systems.

*Based on Peter Horner, “The Sabre Story,” OR/MS Today (June 2000); Ken Belson, “Baseball Tickets Too Much? Check Back Tomorrow,” NewYork Times.com (May 18, 2009); and Rob Gloster, “Giants Quadruple Price of Cheap Seats as Playoffs Drive Demand,” Bloomberg Business-week (September 30, 2010).

Chapter 1 Introduction4

3. Accept the position in Greensboro. 4. Accept the position in Pittsburgh.

The next step of the problem-solving process involves determining the criteria that will be used to evaluate the four alternatives. Obviously, the starting salary is a factor of some impor- tance. If salary were the only criterion of importance to you, the alternative selected as “best” would be the one with the highest starting salary. Problems in which the objective is to find the best solution with respect to one criterion are referred to as single-criterion decision problems.

Suppose that you also conclude that the potential for advancement and the location of the job are two other criteria of major importance. Thus, the three criteria in your decision problem are starting salary, potential for advancement, and location. Problems that involve more than one criterion are referred to as multicriteria decision problems.

The next step of the decision-making process is to evaluate each of the alternatives with respect to each criterion. For example, evaluating each alternative relative to the start- ing salary criterion is done simply by recording the starting salary for each job alternative. Evaluating each alternative with respect to the potential for advancement and the location of the job is more difficult to do, however, because these evaluations are based primarily on subjective factors that are often difficult to quantify. Suppose for now that you decide to measure potential for advancement and job location by rating each of these criteria as poor, fair, average, good, or excellent. The data that you compile are shown in Table 1.1.

You are now ready to make a choice from the available alternatives. What makes this choice phase so difficult is that the criteria are probably not all equally important, and no one alternative is “best” with regard to all criteria. Although we will present a method for dealing with situations like this one later in the text, for now let us suppose that after a careful evaluation of the data in Table 1.1, you decide to select alternative 3; alternative 3 is thus referred to as the decision.

At this point in time, the decision-making process is complete. In summary, we see that this process involves five steps:

1. Define the problem. 2. Identify the alternatives. 3. Determine the criteria. 4. Evaluate the alternatives. 5. Choose an alternative.

Note that missing from this list are the last two steps in the problem-solving process: imple- menting the selected alternative and evaluating the results to determine whether a satisfac- tory solution has been obtained. This omission is not meant to diminish the importance of each of these activities, but to emphasize the more limited scope of the term decision making as compared to the term problem solving. Figure 1.1 summarizes the relationship between these two concepts.

Starting potential for Job Alternative Salary Advancement location 1. Rochester $48,500 Average Average 2. Dallas $46,000 Excellent Good 3. Greensboro $46,000 Good Excellent 4. Pittsburgh $47,000 Average Good

TABLE 1.1 DATA FOR THE JOB EVALUATION DECISION-MAKING PROBLEM

551.2 Quantitative Analysis and Decision Making

1.2 QuANTiTATivE ANAlySiS ANd dECiSiON mAkiNg

Consider the flowchart presented in Figure 1.2. Note that it combines the first three steps of the decision-making process under the heading of “Structuring the Problem” and the latter two steps under the heading “Analyzing the Problem.” Let us now consider in greater detail how to carry out the set of activities that make up the decision-making process.

De�ne the

Problem

Identify the

Alternatives

Determine the

Criteria

Evaluate the

Alternatives

Choose an

Alternative

Implement the

Decision

Evaluate the

Results

Problem Solving

Decision Making

Decision

FIGURE 1.1 THE RELATIONSHIP BETWEEN PROBLEM SOLVING AND DECISION MAKING

Structuring the Problem Analyzing the Problem

Choose an

Alternative

Evaluate the

Alternatives

Determine the

Criteria

Identify the

Alternatives

De�ne the

Problem

FIGURE 1.2 AN ALTERNATE CLASSIFICATION OF THE DECISION-MAKING PROCESS

Chapter 1 Introduction6

Figure 1.3 shows that the analysis phase of the decision-making process may take two basic forms: qualitative and quantitative. Qualitative analysis is based primarily on the manager’s judgment and experience; it includes the manager’s intuitive “feel” for the problem and is more an art than a science. If the manager has had experience with similar problems or if the problem is relatively simple, heavy emphasis may be placed upon a qualitative analysis. However, if the manager has had little experience with similar prob- lems, or if the problem is sufficiently complex, then a quantitative analysis of the problem can be an especially important consideration in the manager’s final decision.

When using the quantitative approach, an analyst will concentrate on the quantita- tive facts or data associated with the problem and develop mathematical expressions that describe the objectives, constraints, and other relationships that exist in the problem. Then, by using one or more quantitative methods, the analyst will make a recommendation based on the quantitative aspects of the problem.

Although skills in the qualitative approach are inherent in the manager and usually increase with experience, the skills of the quantitative approach can be learned only by studying the assumptions and methods of management science. A manager can increase decision-making effectiveness by learning more about quantitative methodology and by better understanding its contribution to the decision-making process. A manager who is knowledgeable in quantitative decision-making procedures is in a much better position to compare and evaluate the qualitative and quantitative sources of recommendations and ultimately to combine the two sources in order to make the best possible decision.

The box in Figure 1.3 entitled “Quantitative Analysis” encompasses most of the sub- ject matter of this text. We will consider a managerial problem, introduce the appropriate quantitative methodology, and then develop the recommended decision.

In closing this section, let us briefly state some of the reasons why a quantitative approach might be used in the decision-making process:

1. The problem is complex, and the manager cannot develop a good solution without the aid of quantitative analysis.

2. The problem is especially important (e.g., a great deal of money is involved), and the manager desires a thorough analysis before attempting to make a decision.

Homework is Completed By:

Writer	Writer Name	Amount	Client Comments & Rating
ONLINE	Instant Homework Helper 4.8 4305 Orders Completed	$36	She helped me in last minute in a very reasonable price. She is a lifesaver, I got A+ grade in my homework, I will surely hire her again for my next assignments, Thumbs Up! 5.00
Answer.docx Turnitin Report.pdf Contact Writer For Solution Contact Writer For Solution

Order & Get This Solution Within 3 Hours in $25/Page

Custom Original Solution And Get A+ Grades

100% Plagiarism Free
Proper APA/MLA/Harvard Referencing
Delivery in 3 Hours After Placing Order
Free Turnitin Report
Unlimited Revisions
Privacy Guaranteed

Order Now

Order & Get This Solution Within 6 Hours in $20/Page

Custom Original Solution And Get A+ Grades

100% Plagiarism Free
Proper APA/MLA/Harvard Referencing
Delivery in 6 Hours After Placing Order
Free Turnitin Report
Unlimited Revisions
Privacy Guaranteed

Order Now

Order & Get This Solution Within 12 Hours in $15/Page

Custom Original Solution And Get A+ Grades

100% Plagiarism Free
Proper APA/MLA/Harvard Referencing
Delivery in 12 Hours After Placing Order
Free Turnitin Report
Unlimited Revisions
Privacy Guaranteed

Order Now

6 writers have sent their proposals to do this homework:

Writer	Writer Name	Offer	Chat
ONLINE	Coursework Help Online I reckon that I can perfectly carry this project for you! I am a research writer and have been writing academic papers, business reports, plans, literature review, reports and others for the past 1 decade. 4.8 1491 Orders Completed	$36	Chat With Writer
ONLINE	Homework Tutor I have read your project details and I can provide you QUALITY WORK within your given timeline and budget. 4.9 1575 Orders Completed	$37	Chat With Writer
ONLINE	Accounting Homework Help I have read your project description carefully and you will get plagiarism free writing according to your requirements. Thank You 4.9 1428 Orders Completed	$46	Chat With Writer
ONLINE	Premium Solutions I have worked on wide variety of research papers including; Analytical research paper, Argumentative research paper, Interpretative research, experimental research etc. 4.9 840 Orders Completed	$37	Chat With Writer
ONLINE	Math Specialist I can assist you in plagiarism free writing as I have already done several related projects of writing. I have a master qualification with 5 years’ experience in; Essay Writing, Case Study Writing, Report Writing. 4.9 1407 Orders Completed	$30	Chat With Writer
ONLINE	Professional Accountant I have read your project description carefully and you will get plagiarism free writing according to your requirements. Thank You 4.9 1470 Orders Completed	$36	Chat With Writer