2 1.3 The Quantitative Analysis Approach 3 Defining the Problem 3Developing a Model 3Acquiring Input Data 4Developing a Solution 5Testing the Solution 5Analyzing the Results and Sensitiv
Trang 2Boston Columbus Indianapolis New York San Francisco Upper Saddle River
Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto
Delhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo
Quantitative Analysis For Management
ELEVENTH EDITION
BARRY RENDER
Charles Harwood Professor of Management Science
Graduate School of Business, Rollins College
RALPH M STAIR, JR.
Professor of Information and Management Sciences,
Florida State University
MICHAEL E HANNA
Professor of Decision Sciences,
University of Houston—Clear Lake
Trang 3To Lila and Leslie – RMS
To Susan, Mickey, and Katie – MEH
Editorial Director: Sally Yagan
Editor in Chief: Eric Svendsen
Senior Acquisitions Editor: Chuck Synovec
Product Development Manager: Ashley Santora
Director of Marketing: Patrice Lumumba Jones
Senior Marketing Manager: Anne Fahlgren
Marketing Assistant: Melinda Jones
Senior Managing Editor: Judy Leale
Project Manager: Mary Kate Murray
Senior Operations Specialist: Arnold Vila
Operations Specialist: Cathleen Petersen
Senior Art Director: Janet Slowik
Art Director: Steve Frim
Text and Cover Designer: Wee Design Group
Manager, Rights and Permissions:
Credits and acknowledgments borrowed from other sources and reproduced, with permission, in this textbook appear
on appropriate page within text.
Microsoft ® and Windows ® are registered trademarks of the Microsoft Corporation in the U.S.A and other countries Screen shots and icons reprinted with permission from the Microsoft Corporation This book is not sponsored or endorsed by or affiliated with the Microsoft Corporation.
Copyright © 2012, 2009, 2006, 2003, 2000 Pearson Education, Inc., publishing as Prentice Hall, One Lake Street,
Upper Saddle River, New Jersey 07458 All rights reserved Manufactured in the United States of America This cation is protected by Copyright, and permission should be obtained from the publisher prior to any prohibited repro- duction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopy- ing, recording, or likewise To obtain permission(s) to use material from this work, please submit a written request to Pearson Education, Inc., Permissions Department, One Lake Street, Upper Saddle River, New Jersey 07458.
publi-Many of the designations by manufacturers and seller to distinguish their products are claimed as trademarks Where those designations appear in this book, and the publisher was aware of a trademark claim, the designations have been printed in initial caps or all caps.
CIP data for this title is available on file at the Library of Congress
ISBN-13: 978-0-13-214911-2 ISBN-10: 0-13-214911-7
10 9 8 7 6 5 4 3 2 1
Trang 4ABOUT THE AUTHORS
Barry Render Professor Emeritus, the Charles Harwood Distinguished Professor of management
sci-ence at the Roy E Crummer Graduate School of Business at Rollins College in Winter Park, Florida
He received his MS in Operations Research and his PhD in Quantitative Analysis at the University ofCincinnati He previously taught at George Washington University, the University of New Orleans,Boston University, and George Mason University, where he held the Mason Foundation Professorship
in Decision Sciences and was Chair of the Decision Science Department Dr Render has also worked
in the aerospace industry for General Electric, McDonnell Douglas, and NASA
Dr Render has coauthored 10 textbooks published by Prentice Hall, including Managerial Decision Modeling with Spreadsheets, Operations Management, Principles of Operations Management, Service Management, Introduction to Management Science, and Cases and Readings
in Management Science Dr Render’s more than 100 articles on a variety of management topics have appeared in Decision Sciences, Production and Operations Management, Interfaces, Information and Management, Journal of Management Information Systems, Socio-Economic Planning Sciences, IIE Solutions and Operations Management Review, among others.
Dr Render has been honored as an AACSB Fellow, and he was named a Senior FulbrightScholar in 1982 and again in 1993 He was twice vice president of the Decision Science Institute
Southeast Region and served as software review editor for Decision Line from 1989 to 1995 He has also served as editor of the New York Times Operations Management special issues from 1996 to
2001 From 1984 to 1993, Dr Render was president of Management Service Associates of Virginia,Inc., whose technology clients included the FBI; the U.S Navy; Fairfax County, Virginia and C&PTelephone
Dr Render has taught operations management courses in Rollins College’s MBA andExecutive MBA programs He has received that school’s Welsh Award as leading professor and wasselected by Roosevelt University as the 1996 recipient of the St Claire Drake Awardfor Outstanding Scholarship In 2005, Dr Render received the Rollins College MBA Student Awardfor Best Overall Course, and in 2009 was named Professor of the Year by full-time MBA students
Ralph Stair is Professor Emeritus at Florida State University He earned a BS in chemical
engineer-ing from Purdue University and an MBA from Tulane University Under the guidance of KenRamsing and Alan Eliason, he received a PhD in operations management from the University ofOregon He has taught at the University of Oregon, the University of Washington, the University ofNew Orleans, and Florida State University
He has twice taught in Florida State University’s Study Abroad Program in London Over theyears, his teaching has been concentrated in the areas of information systems, operations research,and operations management
Dr Stair is a member of several academic organizations, including the Decision SciencesInstitute and INFORMS, and he regularly participates at national meetings He has published
numerous articles and books, including Managerial Decision Modeling with Spreadsheets, Introduction to Management Science, Cases and Readings in Management Science, Production and Operations Management: A Self-Correction Approach, Fundamentals of Information Systems, Principles of Information Systems, Introduction to Information Systems, Computers in Today’s World, Principles of Data Processing, Learning to Live with Computers, Programming in BASIC, Essentials of BASIC Programming, Essentials of FORTRAN Programming, and Essentials of COBOL Programming Dr Stair divides his time between Florida and Colorado He enjoys skiing,
biking, kayaking, and other outdoor activities
Trang 5Michael E Hanna is Professor of Decision Sciences at the University of Houston–Clear Lake
(UHCL) He holds a BA in Economics, an MS in Mathematics, and a PhD in Operations Researchfrom Texas Tech University For more than 25 years, he has been teaching courses in statistics, man-agement science, forecasting, and other quantitative methods His dedication to teaching has beenrecognized with the Beta Alpha Psi teaching award in 1995 and the Outstanding Educator Award in
2006 from the Southwest Decision Sciences Institute (SWDSI)
Dr Hanna has authored textbooks in management science and quantitative methods, has lished numerous articles and professional papers, and has served on the Editorial Advisory Board of
pub-Computers and Operations Research In 1996, the UHCL Chapter of Beta Gamma Sigma presented
him with the Outstanding Scholar Award
Dr Hanna is very active in the Decision Sciences Institute, having served on the InnovativeEducation Committee, the Regional Advisory Committee, and the Nominating Committee He hasserved two terms on the board of directors of the Decision Sciences Institute (DSI) and as regionallyelected vice president of DSI For SWDSI, he has held several positions, including president, and hereceived the SWDSI Distinguished Service Award in 1997 For overall service to the profession and
to the university, he received the UHCL President’s Distinguished Service Award in 2001
Trang 6CHAPTER 1 Introduction to Quantitative Analysis 1
CHAPTER 2 Probability Concepts and Applications 21
CHAPTER 3 Decision Analysis 69
CHAPTER 4 Regression Models 115
CHAPTER 5 Forecasting 153
CHAPTER 6 Inventory Control Models 195
CHAPTER 7 Linear Programming Models: Graphical
and Computer Methods 249
CHAPTER 8 Linear Programming Applications 307
CHAPTER 9 Transportation and Assignment Models 341
CHAPTER 10 Integer Programming, Goal Programming,
and Nonlinear Programming 395
CHAPTER 11 Network Models 429
CHAPTER 12 Project Management 459
CHAPTER 13 Waiting Lines and Queuing Theory
Models 499
CHAPTER 14 Simulation Modeling 533
CHAPTER 15 Markov Analysis 573
CHAPTER 16 Statistical Quality Control 601
Trang 8PREFACE xv CHAPTER 1 Introduction to Quantitative
Analysis 1
1.1 Introduction 2
1.2 What Is Quantitative Analysis? 2
1.3 The Quantitative Analysis Approach 3
Defining the Problem 3Developing a Model 3Acquiring Input Data 4Developing a Solution 5Testing the Solution 5Analyzing the Results and Sensitivity Analysis 5Implementing the Results 5
The Quantitative Analysis Approach and Modeling in the Real World 7
1.4 How to Develop a Quantitative Analysis
Model 7
The Advantages of Mathematical Modeling 8Mathematical Models Categorized by Risk 8
1.5 The Role of Computers and Spreadsheet Models
in the Quantitative Analysis Approach 9 1.6 Possible Problems in the Quantitative Analysis
Approach 12
Defining the Problem 12Developing a Model 13Acquiring Input Data 13Developing a Solution 14Testing the Solution 14Analyzing the Results 14
1.7 Implementation—Not Just the Final Step 15
Lack of Commitment and Resistance to Change 15Lack of Commitment by Quantitative Analysts 15
Summary 16 Glossary 16 Key Equations 16 Self-Test 17 Discussion Questions and Problems
17 Case Study: Food and Beverages at Southwestern University Football Games 19 Bibliography 19
CHAPTER 2 Probability Concepts and Applications 21
2.4 Statistically Independent Events 27 2.5 Statistically Dependent Events 28 2.6 Revising Probabilities with Bayes’ Theorem 29
General Form of Bayes’ Theorem 31
2.7 Further Probability Revisions 32 2.8 Random Variables 33
2.10 The Binomial Distribution 38
Solving Problems with the Binomial Formula 39Solving Problems with Binomial Tables 40
2.11 The Normal Distribution 41
Area Under the Normal Curve 42Using the Standard Normal Table 42Haynes Construction Company Example 44The Empirical Rule 48
2.12 The F Distribution 48 2.13 The Exponential Distribution 50
Arnold’s Muffler Example 51
2.14 The Poisson Distribution 52
Summary 54 Glossary 54 Key Equations 55 Solved Problems 56 Self-Test 59 Discussion Questions and Problems 60 Case Study: WTVX 65 Bibliography 66
Appendix 2.1 Derivation of Bayes’ Theorem 66 Appendix 2.2 Basic Statistics Using Excel 66
CHAPTER 3 Decision Analysis 69
3.1 Introduction 70 3.2 The Six Steps in Decision Making 70 3.3 Types of Decision-Making Environments 71 3.4 Decision Making Under Uncertainty 72
Optimistic 72Pessimistic 73Criterion of Realism (Hurwicz Criterion) 73CONTENTS
vii
Trang 9Equally Likely (Laplace) 74Minimax Regret 74
3.5 Decision Making Under Risk 76
Expected Monetary Value 76Expected Value of Perfect Information 77Expected Opportunity Loss 78
Sensitivity Analysis 79Using Excel QM to Solve Decision TheoryProblems 80
Utility as a Decision-Making Criterion 93
Summary 95 Glossary 95 Key Equations 96 Solved Problems 97 Self-Test 102 Discussion Questions and Problems 103 Case Study:
Starting Right Corporation 110 Case Study:
Blake Electronics 111 Bibliography 113 Appendix 3.1 Decision Models with QM for Windows 113
Appendix 3.2 Decision Trees with QM for Windows 114
CHAPTER 4 Regression Models 115
4.1 Introduction 116
4.2 Scatter Diagrams 116
4.3 Simple Linear Regression 117
4.4 Measuring the Fit of the Regression Model 119
Coefficient of Determination 120Correlation Coefficient 121
4.5 Using Computer Software for Regression 122
4.6 Assumptions of the Regression Model 123
Estimating the Variance 125
4.7 Testing the Model for Significance 125
Triple A Construction Example 127The Analysis of Variance (ANOVA) Table 127Triple A Construction ANOVA Example 128
4.8 Multiple Regression Analysis 128
Evaluating the Multiple Regression Model 129Jenny Wilson Realty Example 130
4.9 Binary or Dummy Variables 131
4.10 Model Building 132
4.11 Nonlinear Regression 133
4.12 Cautions and Pitfalls in Regression
Analysis 136 Summary 136 Glossary 137 Key Equations 137 Solved Problems 138 Self-Test 140 Discussion Questions and Problems 140 Case Study:
North–South Airline 145 Bibliography 146 Appendix 4.1 Formulas for Regression Calculations 146
Appendix 4.2 Regression Models Using QM for
Windows 148 Appendix 4.3 Regression Analysis in Excel QM or
Excel 2007 150
CHAPTER 5 Forecasting 153
5.1 Introduction 154 5.2 Types of Forecasts 154
Time-Series Models 154Causal Models 154Qualitative Models 155
5.3 Scatter Diagrams and Time Series 156 5.4 Measures of Forecast Accuracy 158 5.5 Time-Series Forecasting Models 160
Components of a Time Series 160Moving Averages 161
Exponential Smoothing 164Using Excel QM for Trend-Adjusted ExponentialSmoothing 169
Trend Projections 169Seasonal Variations 171Seasonal Variations with Trend 173The Decomposition Method of Forecasting withTrend and Seasonal Components 175Using Regression with Trend and SeasonalComponents 177
5.6 Monitoring and Controlling Forecasts 179
Adaptive Smoothing 181
Summary 181 Glossary 182 Key Equations 182 Solved Problems 183 Self-Test 184 Discussion Questions and Problems 185 Case Study: Forecasting Attendance at SWU Football Games 189
Case Study: Forecasting Monthly Sales 190 Bibliography 191
Appendix 5.1 Forecasting with QM for Windows 191
CHAPTER 6 Inventory Control Models 195
6.1 Introduction 196 6.2 Importance of Inventory Control 196
Decoupling Function 197Storing Resources 197Irregular Supply and Demand 197Quantity Discounts 197
Avoiding Stockouts and Shortages 197
6.3 Inventory Decisions 197 6.4 Economic Order Quantity: Determining How
6.5 Reorder Point: Determining When to Order 205
Trang 106.7 Quantity Discount Models 210
Brass Department Store Example 212
6.8 Use of Safety Stock 213
6.9 Single-Period Inventory Models 220
Marginal Analysis with Discrete Distributions 221Café du Donut Example 222
Marginal Analysis with the Normal Distribution 222
6.12 Just-in-Time Inventory Control 230
6.13 Enterprise Resource Planning 232
Summary 232 Glossary 232 Key Equations 233 Solved Problems 234 Self-Test 237 Discussion Questions and Problems 238 Case Study:
Martin-Pullin Bicycle Corporation 245 Bibliography 246
Appendix 6.1 Inventory Control with QM for Windows 246
CHAPTER 7 Linear Programming Models: Graphical
and Computer Methods 249
7.1 Introduction 250
7.2 Requirements of a Linear Programming
Problem 250 7.3 Formulating LP Problems 251
Flair Furniture Company 252
7.4 Graphical Solution to an LP Problem 253
Graphical Representation of Constraints 253Isoprofit Line Solution Method 257Corner Point Solution Method 260Slack and Surplus 262
7.5 Solving Flair Furniture’s LP Problem Using
QM For Windows and Excel 263
Using QM for Windows 263Using Excel’s Solver Command to Solve
LP Problems 264
7.6 Solving Minimization Problems 270
Holiday Meal Turkey Ranch 270
7.7 Four Special Cases in LP 274
No Feasible Solution 274Unboundedness 275Redundancy 275Alternate Optimal Solutions 276
QM for Windows and Changes in Side Values 283
Right-Hand-Excel Solver and Changes in Right-Hand-SideValues 285
Summary 285 Glossary 285 Solved Problems 286 Self-Test 291 Discussion Questions and Problems 292 Case Study: Mexicana Wire Works 300 Bibliography 302 Appendix 7.1 Excel QM 302
CHAPTER 8 Linear Programming Applications 307
8.1 Introduction 308 8.2 Marketing Applications 308
Media Selection 308Marketing Research 309
8.3 Manufacturing Applications 312
Production Mix 312Production Scheduling 313
8.4 Employee Scheduling Applications 317
Labor Planning 317
8.5 Financial Applications 319
Portfolio Selection 319Truck Loading Problem 322
8.6 Ingredient Blending Applications 324
Diet Problems 324Ingredient Mix and Blending Problems 325
8.7 Transportation Applications 327
Shipping Problem 327
Summary 330 Self-Test 330 Problems 331 Case Study: Chase Manhattan Bank 339 Bibliography 339
CHAPTER 9 Transportation and Assignment
Models 341
9.1 Introduction 342 9.2 The Transportation Problem 342
Linear Program for the Transportation Example 342
A General LP Model for Transportation Problems 343
9.3 The Assignment Problem 344
Linear Program for Assignment Example 345
9.4 The Transshipment Problem 346
Linear Program for Transshipment Example 347
Trang 119.5 The Transportation Algorithm 348
Developing an Initial Solution: Northwest Corner Rule 350
Stepping-Stone Method: Finding a Least-CostSolution 352
9.6 Special Situations with the Transportation
Algorithm 358
Unbalanced Transportation Problems 358Degeneracy in Transportation Problems 359More Than One Optimal Solution 362Maximization Transportation Problems 362Unacceptable or Prohibited Routes 362Other Transportation Methods 362
9.7 Facility Location Analysis 363
Locating a New Factory for Hardgrave MachineCompany 363
9.8 The Assignment Algorithm 365
The Hungarian Method (Flood’s Technique) 366Making the Final Assignment 369
9.9 Special Situations with the Assignment
Andrew–Carter, Inc 391 Case Study: Old Oregon Wood Store 392 Bibliography 393 Appendix 9.1 Using QM for Windows 393
CHAPTER 10 Integer Programming, Goal Programming,
and Nonlinear Programming 395
10.3 Modeling with 0–1 (Binary) Variables 402
Capital Budgeting Example 402Limiting the Number of Alternatives Selected 404Dependent Selections 404
Fixed-Charge Problem Example 404Financial Investment Example 405
CHAPTER 11 Network Models 429
11.1 Introduction 430 11.2 Minimal-Spanning Tree Problem 430 11.3 Maximal-Flow Problem 433
Maximal-Flow Technique 433Linear Program for Maximal Flow 438
11.4 Shortest-Route Problem 439
Shortest-Route Technique 439Linear Program for Shortest-Route Problem 441
Summary 444 Glossary 444 Solved Problems 445 Self-Test 447 Discussion Questions and Problems 448 Case Study: Binder’s Beverage 455 Case Study: Southwestern University Traffic Problems 456 Bibliography 457
CHAPTER 12 Project Management 459
12.1 Introduction 460 12.2 PERT/CPM 460
General Foundry Example of PERT/CPM 461Drawing the PERT/CPM Network 462Activity Times 463
How to Find the Critical Path 464Probability of Project Completion 469What PERT Was Able to Provide 471Using Excel QM for the General Foundry Example 471
Sensitivity Analysis and Project Management 471
12.3 PERT/Cost 473
Planning and Scheduling Project Costs:
Budgeting Process 473Monitoring and Controlling Project Costs 477
Summary 484 Glossary 485 Key Equations 485 Solved Problems 486 Self-Test 487 Discussion Questions and Problems 488 Case Study: Southwestern University Stadium Construction 494 Case Study: Family Planning Research Center
of Nigeria 494 Bibliography 496 Appendix 12.1 Project Management with QM for Windows 497
Trang 12CONTENTS XI
CHAPTER 13 Waiting Lines and Queuing Theory
Models 499
13.1 Introduction 500
13.2 Waiting Line Costs 500
Three Rivers Shipping Company Example 501
13.3 Characteristics of a Queuing System 501
Arrival Characteristics 501Waiting Line Characteristics 502Service Facility Characteristics 503Identifying Models Using Kendall Notation 503
13.4 Single-Channel Queuing Model with Poisson
Arrivals and Exponential Service Times (M/M/1) 506
Assumptions of the Model 506Queuing Equations 506Arnold’s Muffler Shop Case 507Enhancing the Queuing Environment 511
13.5 Multichannel Queuing Model with Poisson
Arrivals and Exponential Service Times (M/M/M) 511
Equations for the Multichannel Queuing Model 512
Arnold’s Muffler Shop Revisited 512
13.6 Constant Service Time Model (M/D/1) 514
Equations for the Constant Service Time Model 515
Garcia-Golding Recycling, Inc 515
13.7 Finite Population Model (M/M/1 with Finite
the Use of Simulation 519 Summary 520 Glossary 520 Key Equations
521 Solved Problems 522 Self-Test 524 Discussion Questions and Problems 525 Case Study: New England Foundry 530 Case Study:
Winter Park Hotel 531 Bibliography 532 Appendix 13.1 Using QM for Windows 532
CHAPTER 14 Simulation Modeling 533
14.1 Introduction 534
14.2 Advantages and Disadvantages
of Simulation 535 14.3 Monte Carlo Simulation 536
Harry’s Auto Tire Example 536Using QM for Windows for Simulation 541Simulation with Excel Spreadsheets 541
14.4 Simulation and Inventory Analysis 545
Simkin’s Hardware Store 545Analyzing Simkin’s Inventory Costs 548
14.5 Simulation of a Queuing Problem 550
Port of New Orleans 550
Using Excel to Simulate the Port of New OrleansQueuing Problem 551
14.6 Simulation Model for a Maintenance
Policy 553
Three Hills Power Company 553Cost Analysis of the Simulation 557
14.7 Other Simulation Issues 557
Two Other Types of Simulation Models 557Verification and Validation 559
Role of Computers in Simulation 560
Summary 560 Glossary 560 Solved Problems 561 Self-Test 564 Discussion Questions and Problems 565 Case Study: Alabama Airlines 570 Case Study: Statewide Development Corporation 571 Bibliography 572
CHAPTER 15 Markov Analysis 573
15.1 Introduction 574 15.2 States and State Probabilities 574
The Vector of State Probabilities for ThreeGrocery Stores Example 575
15.3 Matrix of Transition Probabilities 576
Transition Probabilities for the Three GroceryStores 577
15.4 Predicting Future Market Shares 577 15.5 Markov Analysis of Machine Operations 578 15.6 Equilibrium Conditions 579
15.7 Absorbing States and the Fundamental
Matrix: Accounts Receivable Application 582 Summary 586 Glossary 587 Key Equations
587 Solved Problems 587 Self-Test 591 Discussion Questions and Problems 591 Case Study: Rentall Trucks 595 Bibliography 597 Appendix 15.1 Markov Analysis with QM for Windows 597 Appendix 15.2 Markov Analysis With Excel 599
CHAPTER 16 Statistical Quality Control 601
16.1 Introduction 602 16.2 Defining Quality and TQM 602 16.3 Statiscal Process Control 603
Variability in the Process 603
16.4 Control Charts for Variables 605
The Central Limit Theorem 605Setting -Chart Limits 606Setting Range Chart Limits 609
16.5 Control Charts for Attributes 610
p-Charts 610 c-Charts 613 Summary 614 Glossary 614 Key Equations
614 Solved Problems 615 Self-Test 616 Discussion Questions and Problems 617 Bibliography 619
Appendix 16.1 Using QM for Windows for SPC 619
x
Trang 13APPENDICES 621 APPENDIX A Areas Under the Standard
Normal Curve 622
APPENDIX B Binomial Probabilities 624
APPENDIX C Values of e for use in the Poisson
Distribution 629
APPENDIX D F Distribution Values 630
APPENDIX E Using POM-QM for Windows 632
APPENDIX F Using Excel QM and Excel Add-Ins 635
APPENDIX G Solutions to Selected Problems 636
APPENDIX H Solutions to Self-Tests 639
INDEX 641
ONLINE MODULES MODULE 1 Analytic Hierarchy Process M1-1
M1.1 Introduction M1-2
M1.2 Multifactor Evaluation Process M1-2
M1.3 Analytic Hierarchy Process M1-4
Judy Grim’s Computer Decision M1-4Using Pairwise Comparisons M1-5Evaluations for Hardware M1-7Determining the Consistency Ratio M1-7Evaluations for the Other Factors M1-9Determining Factor Weights M1-10Overall Ranking M1-10
Using the Computer to Solve Analytic HierarchyProcess Problems M1-10
M1.4 Comparison of Multifactor Evaluation and
Analytic Hierarchy Processes M1-11 Summary M1-12 Glossary M1-12 Key Equations M1-12 Solved Problems M1-12 Self- Test M1-14 Discussion Questions and Problems M1-14 Bibliography M1-16
Appendix M1.1 Using Excel for the Analytic Hierarchy Process
M2.4 Dynamic Programming Notation M2-8
M2.5 Knapsack Problem M2-9
Types of Knapsack Problems M2-9Roller’s Air Transport Service Problem M2-9
Summary M2-16 Glossary M2-16 Key Equations M2-16 Solved Problems M2-17 Self-Test M2-19 Discussion Questions and Problems M2-20 Case Study: United Trucking M2-22 Internet Case Study M2-22 Bibliography M2-23
ⴚL
MODULE 3 Decision Theory and the Normal
Distribution M3-1
M3.1 Introduction M3-2 M3.2 Break-Even Analysis and the Normal
M3.3 Expected Value of Perfect Information and the
Normal Distribution M3-6
Opportunity Loss Function M3-6Expected Opportunity Loss M3-6
Summary M3-8 Glossary M3-8 Key Equations M3-8 Solved Problems M3-9 Self-Test M3-10 Discussion Questions and Problems M3-10 Bibliography M3-12
Appendix M3.1 Derivation of the Break-Even
Point M3-12 Appendix M3.2 Unit Normal Loss Integral M3-13
MODULE 4 Game Theory M4-1
M4.1 Introduction M4-2 M4.2 Language of Games M4-2 M4.3 The Minimax Criterion M4-3 M4.4 Pure Strategy Games M4-4 M4.5 Mixed Strategy Games M4-5 M4.6 Dominance M4-7
Summary M4-7 Glossary M4-8 Solved Problems M4-8 Self-Test M4-10 Discussion Questions and Problems M4-10 Bibliography M4-12
Appendix M4.1 Game Theory
with QM for Windows M4-12
MODULE 5 Mathematical Tools: Determinants
and Matrices M5-1
M5.1 Introduction M5-2 M5.2 Matrices and Matrix
M5.3 Determinants, Cofactors,
and Adjoints M5-7
Determinants M5-7Matrix of Cofactors and Adjoint M5-9
M5.4 Finding the Inverse of a Matrix M5-10
Trang 14CONTENTS XIII
Summary M5-12 Glossary M5-12 Key Equations M5-12 Self-Test M5-13 Discussion Questions and Problems M5-13 Bibliography M5-14
Appendix M5.1 Using Excel for Matrix Calculations M5-15
MODULE 6 Calculus-Based Optimization M6-1
M6.1 Introduction M6-2
M6.2 Slope of a Straight Line M6-2
M6.3 Slope of a Nonlinear Function M6-3
M6.4 Some Common Derivatives M6-5
MODULE 7 Linear Programming: The Simplex
M7.3 Simplex Solution Procedures M7-8
M7.4 The Second Simplex Tableau M7-9
Interpreting the Second Tableau M7-12
M7.5 Developing the Third Tableau M7-13
M7.6 Review of Procedures for Solving LP
Maximization Problems M7-16 M7.7 Surplus and Artificial Variables M7-16
Surplus Variables M7-17Artificial Variables M7-17Surplus and Artificial Variables in the ObjectiveFunction M7-18
M7.8 Solving Minimization Problems M7-18
The Muddy River Chemical Company Example M7-18
Graphical Analysis M7-19Converting the Constraints and ObjectiveFunction M7-20
Rules of the Simplex Method for MinimizationProblems M7-21
First Simplex Tableau for the Muddy RiverChemical Corporation Problem M7-21Developing a Second Tableau M7-23Developing a Third Tableau M7-24Fourth Tableau for the Muddy River ChemicalCorporation Problem M7-26
M7.9 Review of Procedures for Solving LP
Minimization Problems M7-27 M7.10 Special Cases M7-28
Infeasibility M7-28Unbounded Solutions M7-28Degeneracy M7-29
More Than One Optimal Solution M7-30
M7.11 Sensitivity Analysis with the Simplex
Tableau M7-30
High Note Sound Company Revisited M7-30Changes in the Objective Function
Coefficients M7-31Changes in Resources or RHS Values M7-33
M7.12 The Dual M7-35
Dual Formulation Procedures M7-37Solving the Dual of the High Note SoundCompany Problem M7-37
M7.13 Karmarkar’s Algorithm M7-39
Summary M7-39 Glossary M7-39 Key Equation M7-40 Solved Problems M7-40 Self-Test M7-44 Discussion Questions and Problems M7-45 Bibliography M7-53
Trang 16PREFACE
OVERVIEW
The eleventh edition of Quantitative Analysis for Management continues to provide both graduate
and undergraduate students with a solid foundation in quantitative methods and management ence Thanks to the comments and suggestions from numerous users and reviewers of this textbookover the last thirty years, we are able to make this best-selling textbook even better
sci-We continue to place emphasis on model building and computer applications to help studentsunderstand how the techniques presented in this book are actually used in business today In eachchapter, managerial problems are presented to provide motivation for learning the techniques thatcan be used to address these problems Next, the mathematical models, with all necessary assump-tions, are presented in a clear and concise fashion The techniques are applied to the sampleproblems with complete details provided We have found that this method of presentation is veryeffective, and students are very appreciative of this approach If the mathematical computations for
a technique are very detailed, the mathematical details are presented in such a way that the tor can easily omit these sections without interrupting the flow of the material The use of computersoftware allows the instructor to focus on the managerial problem and spend less time on the math-ematical details of the algorithms Computer output is provided for many examples
instruc-The only mathematical prerequisite for this textbook is algebra One chapter on probability andanother chapter on regression analysis provide introductory coverage of these topics We use stan-dard notation, terminology, and equations throughout the book Careful verbal explanation is pro-vided for the mathematical notation and equations used
NEW TO THIS EDITION
䊉 Excel 2010 is incorporated throughout the chapters
䊉 The Poisson and exponential distribution discussions were moved to Chapter 2 with the otherstatistical background material used in the textbook
䊉 The simplex algorithm content has been moved from the textbook to Module 7 on theCompanion Website
䊉 There are 11 new QA in Action boxes, 4 new Model in the Real World boxes, and more than
Trang 17SPECIAL FEATURES
Many features have been popular in previous editions of this textbook, and they have been updatedand expanded in this edition They include the following:
䊉 Modeling in the Real World boxes demonstrate the application of the quantitative analysis
approach to every technique discussed in the book New ones have been added
䊉 Procedure boxes summarize the more complex quantitative techniques, presenting them as a
series of easily understandable steps
䊉 Margin notes highlight the important topics in the text.
䊉 History boxes provide interesting asides related to the development of techniques and the
peo-ple who originated them
䊉 QA in Action boxes illustrate how real organizations have used quantitative analysis to solve
problems Eleven new QA in Action boxes have been added
䊉 Solved Problems, included at the end of each chapter, serve as models for students in solving
their own homework problems
䊉 Discussion Questions are presented at the end of each chapter to test the student’s
understand-ing of the concepts covered and definitions provided in the chapter
䊉 Problems included in every chapter are applications oriented and test the student’s ability to solve
exam-type problems They are graded by level of difficulty: introductory (one bullet), moderate(two bullets), and challenging (three bullets) More than 40 new problems have been added
䊉 Internet Homework Problems provide additional problems for students to work They are
available on the Companion Website
䊉 Self-Tests allow students to test their knowledge of important terms and concepts in
prepara-tion for quizzes and examinaprepara-tions
䊉 Case Studies, at the end of each chapter, provide additional challenging managerial applications.
䊉 Glossaries, at the end of each chapter, define important terms.
䊉 Key Equations, provided at the end of each chapter, list the equations presented in that chapter.
䊉 End-of-chapter bibliographies provide a current selection of more advanced books and articles.
䊉 The software POM-QM for Windows uses the full capabilities of Windows to solve
quantita-tive analysis problems
䊉 Excel QM and Excel 2010 are used to solve problems throughout the book.
䊉 Data files with Excel spreadsheets and POM-QM for Windows files containing all the ples in the textbook are available for students to download from the Companion Website.Instructors can download these plus additional files containing computer solutions to the rele-vant end-of-chapter problems from the Instructor Resource Center website
exam-䊉 Online modules provide additional coverage of topics in quantitative analysis.
䊉 The Companion Website, at www.pearsonhighered.com/render, provides the online modules,additional problems, cases, and other material for almost every chapter
SIGNIFICANT CHANGES TO THE ELEVENTH EDITION
In the eleventh edition, we have incorporated the use of Excel 2010 throughout the chapters.Whereas information about Excel 2007 is also included in appropriate appendices, screen capturesand formulas from Excel 2010 are used extensively Most of the examples have spreadsheet solu-tions provided The Excel QM add-in is used with Excel 2010 to provide students with the mostup-to-date methods available
An even greater emphasis on modeling is provided as the simplex algorithm has been movedfrom the textbook to a module on the Companion Website Linear programming models are pre-sented with the transportation, transshipment, and assignment problems These are presented from anetwork approach, providing a consistent and coherent discussion of these important types ofproblems Linear programming models are provided for some other network models as well While
a few of the special purpose algorithms are still available in the textbook, they may be easily ted without loss of continuity should the instructor choose that option
Trang 18omit-PREFACE xvii
In addition to the use of Excel 2010, the use of new screen captures, and the discussion of ware changes throughout the book, other modifications have been made to almost every chapter Webriefly summarize the major changes here
soft-Chapter 1 Introduction to Quantitative Analysis New QA in Action boxes and Managing in the
Real World applications have been added One new problem has been added
Chapter 2 Probability Concepts and Applications The presentation of discrete random variables
has been modified The empirical rule has been added, and the discussion of the normal distributionhas been modified The presentations of the Poisson and exponential distributions, which are impor-tant in the waiting line chapter, have been expanded Three new problems have been added
Chapter 3 Decision Analysis The presentation of the expected value criterion has been modified A
discussion is provided of using the decision criteria for both maximization and minimization lems An Excel 2010 spreadsheet for the calculations with Bayes theorem is provided A new QA inAction box and six new problems have been added
prob-Chapter 4 Regression Models Stepwise regression is mentioned when discussing model building.
Two new problems have been added Other end-of-chapter problems have been modified
Chapter 5 Forecasting The presentation of exponential smoothing with trend has been modified.
Three new end-of-chapter problems and one new case have been added
Chapter 6 Inventory Control Models The use of safety stock has been significantly modified, with
the presentation of three distinct situations that would require the use of safety stock Discussion ofinventory position has been added One new QA in Action, five new problems, and two new solvedproblems have been added
Chapter 7 Linear Programming Models: Graphical and Computer Methods Discussion has been
expanded on interpretation of computer output, the use of slack and surplus variables, and the entation of binding constraints The use of Solver in Excel 2010 is significantly changed from Excel
pres-2007, and the use of the new Solver is clearly presented Two new problems have been added, andothers have been modified
Chapter 8 Linear Programming Modeling Applications with Computer Analysis The production
mix example was modified To enhance the emphasis on model building, discussion of developingthe model was expanded for many examples One new QA in Action box and two new end-of-chapterproblems were added
Chapter 9 Transportation and Assignment Models Major changes were made in this chapter, as
less emphasis was placed on the algorithmic approach to solving these problems A network sentation, as well as the linear programming model for each type of problem, were presented Thetransshipment model is presented as an extension of the transportation problem The basic trans-portation and assignment algorithms are included, but they are at the end of the chapter and may beomitted without loss of flow Two QA in Action boxes, one Managing in the Real World situation,and 11 new end-of-chapter problems were added
repre-Chapter 10 Integer Programming, Goal Programming, and Nonlinear Programming More emphasis
was placed on modeling and less emphasis was placed on manual solution methods One newManaging in the Real World application, one new solved problem, and three new problems were added
Chapter 11 Network Models Linear programming formulations for the max-flow and shortest
route problems were added The algorithms for solving these network problems were retained, butthese can easily be omitted without loss of continuity Six new end-of-chapter problems were added
Chapter 12 Project Management Screen captures for the Excel QM software application were
added One new problem was added
Chapter 13 Waiting Lines and Queuing Models The discussion of the Poisson and exponential
dis-tribution were moved to Chapter 2 with the other statistical background material used in the book Two new QA in Action boxes and two new end-of-chapter problems were added
text-Chapter 14 Simulation Modeling The use of Excel 2010 is the major change to this chapter Chapter 15 Markov Analysis One Managing in the Real World application was added.
Chapter 16 Statistical Quality Control One new QA in Action box was added The chapter on the
simplex algorithm was converted to a module that is now available on the Companion Website withthe other modules Instructors who choose to cover this can tell students to download the completediscussion
Trang 192007 are provided in an appendix The use of Excel is more prevalent in this edition of the book than
in previous editions
Excel QM Using the Excel QM add-in that is available on the Companion Website makes the use
of Excel even easier Students with limited Excel experience can use this and learn from the las that are automatically provided by Excel QM This is used in many of the chapters
formu-POM-QM for Windows This software, developed by Professor Howard Weiss, is available tostudents at the Companion Website This is very user friendly and has proven to be a very popularsoftware tool for users of this textbook Modules are available for every major problem type pre-sented in the textbook
COMPANION WEBSITE
The Companion Website, located at www.pearsonhighered.com/render, contains a variety of rials to help students master the material in this course These include:
mate-Modules There are seven modules containing additional material that the instructor may choose
to include in the course Students can download these from the Companion Website
Self-Study Quizzes Some multiple choice, true-false, fill-in-the-blank, and discussion questionsare available for each chapter to help students test themselves over the material covered in that chapter
Files for Examples in Excel, Excel QM, and POM-QM for Windows Students can downloadthe files that were used for examples throughout the book This helps them become familiar with thesoftware, and it helps them understand the input and formulas necessary for working the examples
Internet Homework Problems In addition to the end-of-chapter problems in the textbook,there are additional problems that instructors may assign These are available for download at theCompanion Website
Internet Case Studies Additional case studies are available for most chapters
POM-QM for Windows Developed by Howard Weiss, this very user-friendly software can beused to solve most of the homework problems in the text
Trang 20PREFACE xix
Excel QM This Excel add-in will automatically create worksheets for solving problems This isvery helpful for instructors who choose to use Excel in their classes but who may have studentswith limited Excel experience Students can learn by examining the formulas that have been cre-ated, and by seeing the inputs that are automatically generated for using the Solver add-in for lin-ear programming
INSTRUCTOR RESOURCES
䊉 Instructor Resource Center: The Instructor Resource Center contains the electronic files for
the test bank, PowerPoint slides, the Solutions Manual, and data files for both Excel andPOM-QM for Windows for all relevant examples and end-of-chapter problems (www.pear-sonhighered.com/render)
䊉 Register, Redeem, Login: At www.pearsonhighered.com/irc, instructors can access a variety
of print, media, and presentation resources that are available with this text in downloadable,digital format For most texts, resources are also available for course management platformssuch as Blackboard, WebCT, and Course Compass
䊉 Need help? Our dedicated technical support team is ready to assist instructors with questions
about the media supplements that accompany this text Visit http://247.prenhall.com/ foranswers to frequently asked questions and toll-free user support phone numbers The supple-ments are available to adopting instructors Detailed descriptions are provided on theInstructor Resource Center
Instructor’s Solutions ManualThe Instructor’s Solutions Manual, updated by the authors, isavailable to adopters in print form and as a download from the Instructor Resource Center Solutions
to all Internet Homework Problems and Internet Case Studies are also included in the manual
Test Item File The updated test item file is available to adopters as a downloaded from theInstructor Resource Center
TestGen The computerized TestGen package allows instructors to customize, save, and generateclassroom tests The test program permits instructors to edit, add, or delete questions from the testbank; edit existing graphics and create new graphics; analyze test results; and organize a database oftest and student results This software allows for extensive flexibility and ease of use It providesmany options for organizing and displaying tests, along with search and sort features The softwareand the test banks can be downloaded at www.pearsonhighered.com/render
ACKNOWLEDGMENTS
We gratefully thank the users of previous editions and the reviewers who provided valuable tions and ideas for this edition Your feedback is valuable in our efforts for continuous improvement
sugges-The continued success of Quantitative Analysis for Management is a direct result of instructor and
student feedback, which is truly appreciated
The authors are indebted to many people who have made important contributions to this ect Special thanks go to Professors F Bruce Simmons III, Khala Chand Seal, Victor E Sower,Michael Ballot, Curtis P McLaughlin, and Zbigniew H Przanyski for their contributions to theexcellent cases included in this edition Special thanks also goes out to Trevor Hale for his extensivehelp with the Modeling in the Real World vignettes and the QA in Action applications, and for hisserving as a sounding board for many of the ideas that resulted in significant improvements for thisedition
Trang 21proj-We thank Howard proj-Weiss for providing Excel QM and POM-QM for Windows, two of the mostoutstanding packages in the field of quantitative methods We would also like to thank the reviewerswho have helped to make this one of the most widely used textbooks in the field of quantitativeanalysis:
Stephen Achtenhagen, San Jose University
M Jill Austin, Middle Tennessee State University
Raju Balakrishnan, Clemson University
Hooshang Beheshti, Radford University
Bruce K Blaylock, Radford University
Rodney L Carlson, Tennessee Technological University
Edward Chu, California State University, Dominguez Hills
John Cozzolino, Pace University–Pleasantville
Shad Dowlatshahi, University of Wisconsin, Platteville
Ike Ehie, Southeast Missouri State University
Sean Eom, Southeast Missouri State University
Ephrem Eyob, Virginia State University
Mira Ezvan, Lindenwood University
Wade Ferguson, Western Kentucky University
Robert Fiore, Springfield College
Frank G Forst, Loyola University of Chicago
Ed Gillenwater, University of Mississippi
Stephen H Goodman, University of Central Florida
Irwin Greenberg, George Mason University
Trevor S Hale, University of Houston–Downtown
Nicholas G Hall, Ohio State University
Robert R Hill, University of Houston–Clear Lake
Gordon Jacox, Weber State University
Bharat Jain, Towson State University
Vassilios Karavas, University of Massachusetts–Amherst
Darlene R Lanier, Louisiana State University
Kenneth D Lawrence, New Jersey Institute of Technology
Jooh Lee, Rowan College
Richard D Legault, University of Massachusetts–Dartmouth
Douglas Lonnstrom, Siena College
Daniel McNamara, University of St Thomas
Robert C Meyers, University of Louisiana
Peter Miller, University of Windsor
Ralph Miller, California State Polytechnic University
Shahriar Mostashari, Campbell University David Murphy, Boston College
Robert Myers, University of Louisville Barin Nag, Towson State University
Nizam S Najd, Oklahoma State University
Harvey Nye, Central State University Alan D Olinsky, Bryant College Savas Ozatalay, Widener University Young Park, California University of Pennsylvania
Cy Peebles, Eastern Kentucky University
Yusheng Peng, Brooklyn College
Dane K Peterson,
Southwest Missouri State University
Sanjeev Phukan, Bemidji State University
Ranga Ramasesh, Texas Christian University William Rife, West Virginia University Bonnie Robeson, Johns Hopkins University Grover Rodich, Portland State University
L Wayne Shell, Nicholls State University Richard Slovacek, North Central College John Swearingen, Bryant College
F S Tanaka, Slippery Rock State University Jack Taylor, Portland State University Madeline Thimmes, Utah State University
M Keith Thomas, Olivet College Andrew Tiger, Southeastern Oklahoma State University Chris Vertullo, Marist College
James Vigen, California State University, Bakersfield William Webster, The University of Texas at San Antonio Larry Weinstein, Eastern Kentucky University
Fred E Williams, University of Michigan-Flint Mela Wyeth, Charleston Southern University
We are very grateful to all the people at Prentice Hall who worked so hard to make this book asuccess These include Chuck Synovec, our editor; Judy Leale, senior managing editor; Mary KateMurray, project manager; and Jason Calcano, editorial assistant We are also grateful to Jen Carley,our project manager at PreMediaGlobal Book Services We are very appreciative of the work ofAnnie Puciloski in error checking the textbook and Solutions Manual Thank you all!
Barry Renderbrender@rollins.eduRalph Stair
Michael Hanna281-283-3201 (phone)281-226-7304 (fax)hanna@uhcl.edu
Trang 221 Describe the quantitative analysis approach.
2 Understand the application of quantitative analysis
in a real situation
3 Describe the use of modeling in quantitative
analysis
1.1 Introduction
1.2 What Is Quantitative Analysis?
1.3 The Quantitative Analysis Approach
1.4 How to Develop a Quantitative Analysis
Model
1.5 The Role of Computers and Spreadsheet Models
in the Quantitative Analysis Approach
1.6 Possible Problems in the Quantitative AnalysisApproach
1.7 Implementation—Not Just the Final Step
4 Use computers and spreadsheet models to performquantitative analysis
5 Discuss possible problems in using quantitativeanalysis
6 Perform a break-even analysis
CHAPTER
Summary • Glossary • Key Equations • Self-Test • Discussion Questions and Problems • Case Study: Food and
Beverages at Southwestern University Football Games • Bibliography
Trang 231.1 Introduction
People have been using mathematical tools to help solve problems for thousands of years; ever, the formal study and application of quantitative techniques to practical decision making islargely a product of the twentieth century The techniques we study in this book have beenapplied successfully to an increasingly wide variety of complex problems in business, govern-ment, health care, education, and many other areas Many such successful uses are discussedthroughout this book
how-It isn’t enough, though, just to know the mathematics of how a particular quantitativetechnique works; you must also be familiar with the limitations, assumptions, and specificapplicability of the technique The successful use of quantitative techniques usually results
in a solution that is timely, accurate, flexible, economical, reliable, and easy to understandand use
In this and other chapters, there are QA (Quantitative Analysis) in Action boxes that provide success stories on the applications of management science They show how organi-zations have used quantitative techniques to make better decisions, operate more efficiently,and generate more profits Taco Bell has reported saving over $150 million with better forecast-ing of demand and better scheduling of employees NBC television increased advertisingrevenue by over $200 million between 1996 and 2000 by using a model to help develop salesplans for advertisers Continental Airlines saves over $40 million per year by using mathe-matical models to quickly recover from disruptions caused by weather delays and otherfactors These are but a few of the many companies discussed in QA in Action boxes throughoutthis book
To see other examples of how companies use quantitative analysis or operations researchmethods to operate better and more efficiently, go to the website www.scienceofbetter.org Thesuccess stories presented there are categorized by industry, functional area, and benefit Thesesuccess stories illustrate how operations research is truly the “science of better.”
1.2 What Is Quantitative Analysis?
Quantitative analysis is the scientific approach to managerial decision making Whim,
emo-tions, and guesswork are not part of the quantitative analysis approach The approach starts withdata Like raw material for a factory, these data are manipulated or processed into informationthat is valuable to people making decisions This processing and manipulating of raw data intomeaningful information is the heart of quantitative analysis Computers have been instrumental
in the increasing use of quantitative analysis
In solving a problem, managers must consider both qualitative and quantitative factors Forexample, we might consider several different investment alternatives, including certificates ofdeposit at a bank, investments in the stock market, and an investment in real estate We can usequantitative analysis to determine how much our investment will be worth in the future whendeposited at a bank at a given interest rate for a certain number of years Quantitative analysiscan also be used in computing financial ratios from the balance sheets for several companieswhose stock we are considering Some real estate companies have developed computer pro-grams that use quantitative analysis to analyze cash flows and rates of return for investmentproperty
In addition to quantitative analysis, qualitative factors should also be considered The
weather, state and federal legislation, new technological breakthroughs, the outcome of an tion, and so on may all be factors that are difficult to quantify
elec-Because of the importance of qualitative factors, the role of quantitative analysis in thedecision-making process can vary When there is a lack of qualitative factors and when the problem, model, and input data remain the same, the results of quantitative analysis
can automate the decision-making process For example, some companies use quantitative inventory models to determine automatically when to order additional new materials In most cases, however, quantitative analysis will be an aid to the decision-making process
The results of quantitative analysis will be combined with other (qualitative) information inmaking decisions
Quantitative analysis uses
a scientific approach to decision
making.
Both qualitative and quantitative
factors must be considered.
Trang 241.3 THE QUANTITATIVE ANALYSIS APPROACH 3
Quantitative analysis has been in existence since the beginning
of recorded history, but it was Frederick W Taylor who in the early
1900s pioneered the principles of the scientific approach to
man-agement During World War II, many new scientific and
quantita-tive techniques were developed to assist the military These new
developments were so successful that after World War II many
companies started using similar techniques in managerial decision
making and planning Today, many organizations employ a staff
of operations research or management science personnel or consultants to apply the principles of scientific management to problems and opportunities In this book, we use the terms
management science, operations research, and quantitative
analysis interchangeably.
The origin of many of the techniques discussed in this book can be traced to individuals and organizations that have applied the principles of scientific management first developed by Taylor;
they are discussed in History boxes scattered throughout the book.
HISTORY The Origin of Quantitative Analysis
1.3 The Quantitative Analysis Approach
The quantitative analysis approach consists of defining a problem, developing a model, ing input data, developing a solution, testing the solution, analyzing the results, and implement-ing the results (see Figure 1.1) One step does not have to be finished completely before the next
acquir-is started; in most cases one or more of these steps will be modified to some extent before the nal results are implemented This would cause all of the subsequent steps to be changed In somecases, testing the solution might reveal that the model or the input data are not correct Thiswould mean that all steps that follow defining the problem would need to be modified
fi-Defining the Problem
The first step in the quantitative approach is to develop a clear, concise statement of the
problem This statement will give direction and meaning to the following steps.
In many cases, defining the problem is the most important and the most difficult step It isessential to go beyond the symptoms of the problem and identify the true causes One problemmay be related to other problems; solving one problem without regard to other related problemscan make the entire situation worse Thus, it is important to analyze how the solution to oneproblem affects other problems or the situation in general
It is likely that an organization will have several problems However, a quantitative analysisgroup usually cannot deal with all of an organization’s problems at one time Thus, it is usuallynecessary to concentrate on only a few problems For most companies, this means selectingthose problems whose solutions will result in the greatest increase in profits or reduction in costs
to the company The importance of selecting the right problems to solve cannot be sized Experience has shown that bad problem definition is a major reason for failure of man-agement science or operations research groups to serve their organizations well
overempha-When the problem is difficult to quantify, it may be necessary to develop specific, measurable objectives A problem might be inadequate health care delivery in a hospital The
objectives might be to increase the number of beds, reduce the average number of days a patientspends in the hospital, increase the physician-to-patient ratio, and so on When objectives areused, however, the real problem should be kept in mind It is important to avoid obtaining spe-cific and measurable objectives that may not solve the real problem
Developing a Model
Once we select the problem to be analyzed, the next step is to develop a model Simply stated, a
model is a representation (usually mathematical) of a situation
Even though you might not have been aware of it, you have been using models most of yourlife You may have developed models about people’s behavior Your model might be that friend-ship is based on reciprocity, an exchange of favors If you need a favor such as a small loan, yourmodel would suggest that you ask a good friend
Of course, there are many other types of models Architects sometimes make a physical model of a building that they will construct Engineers develop scale models of chemical plants,
Defining the problem can be the
most important step.
Concentrate on only a few
problems.
The types of models include
physical, scale, schematic, and
mathematical models.
Trang 25Operations Research and Oil Spills
Operations researchers and decision scientists have been
investi-gating oil spill response and alleviation strategies since long before
the BP oil spill disaster of 2010 in the Gulf of Mexico A four-phase
classification system has emerged for disaster response research:
mit-igation, preparedness, response, and recovery Mitigation means
re-ducing the probability that a disaster will occur and implementing
robust, forward-thinking strategies to reduce the effects of a disaster
that does occur Preparedness is any and all organization efforts that
happen a priori to a disaster Response is the location, allocation, and
overall coordination of resources and procedures during the disaster
that are aimed at preserving life and property Recovery is the set of
actions taken to minimize the long-term impacts of a particular
dis-aster after the immediate situation has stabilized.
Many quantitative tools have helped in areas of risk analysis, insurance, logistical preparation and supply management, evacu- ation planning, and development of communication systems Re- cent research has shown that while many strides and discoveries have been made, much research is still needed Certainly each of the four disaster response areas could benefit from additional re- search, but recovery seems to be of particular concern and per- haps the most promising for future research.
Source: Based on N Altay and W Green “OR/MS Research in Disaster
Oper-ations Management,” European Journal of Operational Research 175, 1 (2006):
475–493.
called pilot plants A schematic model is a picture, drawing, or chart of reality Automobiles,
lawn mowers, gears, fans, typewriters, and numerous other devices have schematic models(drawings and pictures) that reveal how these devices work What sets quantitative analysis apart
from other techniques is that the models that are used are mathematical A mathematical model
is a set of mathematical relationships In most cases, these relationships are expressed in tions and inequalities, as they are in a spreadsheet model that computes sums, averages, or stan-dard deviations
equa-Although there is considerable flexibility in the development of models, most of the models
presented in this book contain one or more variables and parameters A variable, as the name
implies, is a measurable quantity that may vary or is subject to change Variables can be
controllable or uncontrollable A controllable variable is also called a decision variable An
example would be how many inventory items to order A parameter is a measurable quantity
that is inherent in the problem The cost of placing an order for more inventory items is anexample of a parameter In most cases, variables are unknown quantities, while parametersare known quantities All models should be developed carefully They should be solvable, real-
istic, and easy to understand and modify, and the required input data should be obtainable.
The model developer has to be careful to include the appropriate amount of detail to be solvableyet realistic
Acquiring Input Data
Once we have developed a model, we must obtain the data that are used in the model (input data) Obtaining accurate data for the model is essential; even if the model is a perfect represen- tation of reality, improper data will result in misleading results This situation is called garbage
in, garbage out For a larger problem, collecting accurate data can be one of the most difficult
steps in performing quantitative analysis
There are a number of sources that can be used in collecting data In some cases, companyreports and documents can be used to obtain the necessary data Another source is interviewswith employees or other persons related to the firm These individuals can sometimes provideexcellent information, and their experience and judgment can be invaluable A production su-pervisor, for example, might be able to tell you with a great degree of accuracy the amount oftime it takes to produce a particular product Sampling and direct measurement provide othersources of data for the model You may need to know how many pounds of raw material are used
in producing a new photochemical product This information can be obtained by going to theplant and actually measuring with scales the amount of raw material that is being used In othercases, statistical sampling procedures can be used to obtain data
Garbage in, garbage out means
that improper data will result
in misleading results.
IN ACTION
Trang 261.3 THE QUANTITATIVE ANALYSIS APPROACH 5
Developing a Solution
Developing a solution involves manipulating the model to arrive at the best (optimal) solution tothe problem In some cases, this requires that an equation be solved for the best decision In
other cases, you can use a trial and error method, trying various approaches and picking the one
that results in the best decision For some problems, you may wish to try all possible values for
the variables in the model to arrive at the best decision This is called complete enumeration.
This book also shows you how to solve very difficult and complex problems by repeating a fewsimple steps until you find the best solution A series of steps or procedures that are repeated is
called an algorithm, named after Algorismus, an Arabic mathematician of the ninth century.
The accuracy of a solution depends on the accuracy of the input data and the model If the put data are accurate to only two significant digits, then the results can be accurate to only two sig-nificant digits For example, the results of dividing 2.6 by 1.4 should be 1.9, not 1.857142857
in-Testing the Solution
Before a solution can be analyzed and implemented, it needs to be tested completely Becausethe solution depends on the input data and the model, both require testing
Testing the input data and the model includes determining the accuracy and completeness
of the data used by the model Inaccurate data will lead to an inaccurate solution There are eral ways to test input data One method of testing the data is to collect additional data from adifferent source If the original data were collected using interviews, perhaps some additionaldata can be collected by direct measurement or sampling These additional data can then becompared with the original data, and statistical tests can be employed to determine whether thereare differences between the original data and the additional data If there are significant differ-ences, more effort is required to obtain accurate input data If the data are accurate but the results are inconsistent with the problem, the model may not be appropriate The model can bechecked to make sure that it is logical and represents the real situation
sev-Although most of the quantitative techniques discussed in this book have been ized, you will probably be required to solve a number of problems by hand To help detect bothlogical and computational mistakes, you should check the results to make sure that they are con-sistent with the structure of the problem For example, (1.96)(301.7) is close to (2)(300), which
computer-is equal to 600 If your computations are significantly different from 600, you know you havemade a mistake
Analyzing the Results and Sensitivity Analysis
Analyzing the results starts with determining the implications of the solution In most cases, asolution to a problem will result in some kind of action or change in the way an organization isoperating The implications of these actions or changes must be determined and analyzed beforethe results are implemented
Because a model is only an approximation of reality, the sensitivity of the solution tochanges in the model and input data is a very important part of analyzing the results This type
of analysis is called sensitivity analysis or postoptimality analysis It determines how much the
solution will change if there were changes in the model or the input data When the solution issensitive to changes in the input data and the model specification, additional testing should beperformed to make sure that the model and input data are accurate and valid If the model or dataare wrong, the solution could be wrong, resulting in financial losses or reduced profits
The importance of sensitivity analysis cannot be overemphasized Because input data maynot always be accurate or model assumptions may not be completely appropriate, sensitivityanalysis can become an important part of the quantitative analysis approach Most of the chap-ters in the book cover the use of sensitivity analysis as part of the decision-making and problem-solving process
Implementing the Results
The final step is to implement the results This is the process of incorporating the solution into
the company This can be much more difficult than you would imagine Even if the solution
is optimal and will result in millions of dollars in additional profits, if managers resist thenew solution, all of the efforts of the analysis are of no value Experience has shown that a large
The input data and model
determine the accuracy of the
solution.
Testing the data and model is
done before the results are
analyzed.
Sensitivity analysis determines
how the solutions will change
with a different model or input
data.
Trang 27Defining the Problem
CSX Transportation, Inc., has 35,000 employees and annual revenue of $11 billion It provides rail freight services to 23 states east of the Mississippi River, as well as parts of Canada CSX receives orders for rail deliv- ery service and must send empty railcars to customer locations Moving these empty railcars results in hun- dreds of thousands of empty-car miles every day If allocations of railcars to customers is not done properly, problems arise from excess costs, wear and tear on the system, and congestion on the tracks and at rail yards.
Developing a Model
In order to provide a more efficient scheduling system, CSX spent 2 years and $5 million developing its Dynamic Car-Planning (DCP) system This model will minimize costs, including car travel distance, car han- dling costs at the rail yards, car travel time, and costs for being early or late It does this while at the same time filling all orders, making sure the right type of car is assigned to the job, and getting the car to the destination in the allowable time.
Acquiring Input Data
In developing the model, the company used historical data for testing In running the model, the DCP uses three external sources to obtain information on the customer car orders, the available cars of the type needed, and the transit-time standards In addition to these, two internal input sources provide informa- tion on customer priorities and preferences and on cost parameters.
Developing a Solution
This model takes about 1 minute to load but only 10 seconds to solve Because supply and demand are stantly changing, the model is run about every 15 minutes This allows final decisions to be delayed until ab- solutely necessary.
con-Testing the Solution
The model was validated and verified using existing data The solutions found using the DCP were found
to be very good compared to assignments made without DCP.
Analyzing the Results
Since the implementation of DCP in 1997, more than $51 million has been saved annually Due to the proved efficiency, it is estimated that CSX avoided spending another $1.4 billion to purchase an additional 18,000 railcars that would have been needed without DCP Other benefits include reduced congestion in the rail yards and reduced congestion on the tracks, which are major concerns This greater efficiency means that more freight can ship by rail rather than by truck, resulting in significant public benefits These benefits include reduced pollution and greenhouse gases, improved highway safety, and reduced road maintenance costs.
im-Implementing the Results
Both senior-level management who championed DCP as well as key car-distribution experts who ported the new approach were instrumental in gaining acceptance of the new system and overcoming problems during the implementation The job description of the car distributors was changed from car al- locators to cost technicians They are responsible for seeing that accurate cost information is entered into DCP, and they also manage any exceptions that must be made They were given extensive training on how DCP works so they could understand and better accept the new system Due to the success of DCP, other railroads have implemented similar systems and achieved similar benefits CSX continues to enhance DCP to make DCP even more customer friendly and to improve car-order forecasts.
sup-Source: Based on M F Gorman, et al “CSX Railway Uses OR to Cash in on Optimized Equipment Distribution,” Interfaces
Trang 281.4 HOW TO DEVELOP A QUANTITATIVE ANALYSIS MODEL 7
The Quantitative Analysis Approach and Modeling in the Real World
The quantitative analysis approach is used extensively in the real world These steps, first seen
in Figure 1.1 and described in this section, are the building blocks of any successful use of
quan-titative analysis As seen in our first Modeling in the Real World box, the steps of the
quantita-tive analysis approach can be used to help a large company such as CSX plan for criticalscheduling needs now and for decades into the future Throughout this book, you will see howthe steps of the quantitative analysis approach are used to help countries and companies of allsizes save millions of dollars, plan for the future, increase revenues, and provide higher-quality
products and services The Modeling in the Real World boxes in every chapter will demonstrate
to you the power and importance of quantitative analysis in solving real problems for real ganizations Using the steps of quantitative analysis, however, does not guarantee success Thesesteps must be applied carefully
or-1.4 How to Develop a Quantitative Analysis Model
Developing a model is an important part of the quantitative analysis approach Let’s see how wecan use the following mathematical model, which represents profit:
In many cases, we can express revenues as price per unit multiplied times the number of unitssold Expenses can often be determined by summing fixed costs and variable cost Variable cost
is often expressed as variable cost per unit multiplied times the number of units Thus, we canalso express profit in the following mathematical model:
The number of springs sold is X, and our profit model becomes
If sales are 0, Bill will realize a $1,000 loss If sales are 1,000 units, he will realize a profit of
See if you can determine the profitfor other values of units sold
X = number of units sold
n = variable cost per unit
f = fixed cost
s = selling price per unit
Profit = sX - f - nX Profit = sX - 3f + nX4
- 3Fixed cost + (Variable cost per unit)(Number of units sold)4 Profit = (Selling price per unit)(Number of units sold)
Profit = Revenue - (Fixed cost + Variable cost)
Profit = Revenue - Expenses
Expenses include fixed and
variable costs.
Trang 29In addition to the profit models shown here, decision makers are often interested in the
break-even point (BEP) The BEP is the number of units sold that will result in $0 profits We
set profits equal to $0 and solve for X, the number of units at the break-even point:
This can be written as
Solving for X, we have
This quantity (X) that results in a profit of zero is the BEP, and we now have this model for the BEP:
(1-2)
For the Pritchett’s Precious Time Pieces example, the BEP can be computed as follows:
The Advantages of Mathematical Modeling
There are a number of advantages of using mathematical models:
1 Models can accurately represent reality If properly formulated, a model can be extremelyaccurate A valid model is one that is accurate and correctly represents the problem or sys-tem under investigation The profit model in the example is accurate and valid for manybusiness problems
2 Models can help a decision maker formulate problems In the profit model, for example,
a decision maker can determine the important factors or contributors to revenues andexpenses, such as sales, returns, selling expenses, production costs, transportation costs,and so on
3 Models can give us insight and information For example, using the profit model from thepreceding section, we can see what impact changes in revenues and expenses will have onprofits As discussed in the previous section, studying the impact of changes in a model,such as a profit model, is called sensitivity analysis
4 Models can save time and money in decision making and problem solving It usually takesless time, effort, and expense to analyze a model We can use a profit model to analyze theimpact of a new marketing campaign on profits, revenues, and expenses In most cases, using models is faster and less expensive than actually trying a new marketing campaign in
a real business setting and observing the results
5 A model may be the only way to solve some large or complex problems in a timelyfashion A large company, for example, may produce literally thousands of sizes of nuts,bolts, and fasteners The company may want to make the highest profits possible given itsmanufacturing constraints A mathematical model may be the only way to determine thehighest profits the company can achieve under these circumstances
6 A model can be used to communicate problems and solutions to others A decision analystcan share his or her work with other decision analysts Solutions to a mathematical modelcan be given to managers and executives to help them make final decisions
Mathematical Models Categorized by Risk
Some mathematical models, like the profit and break-even models previously discussed, do notinvolve risk or chance We assume that we know all values used in the model with complete
certainty These are called deterministic models A company, for example, might want to
BEP = $1,000>($10 - $5) = 200 units, or springs, at the break-even point
BEP = f
s - n
(Selling price per unit) - (Variable cost per unit)
The BEP results in $0 profits.
Deterministic means with
complete certainty.
Trang 301.5 THE ROLE OF COMPUTERS AND SPREADSHEET MODELS IN THE QUANTITATIVE ANALYSIS APPROACH 9
Main menu Toolbar Instruction
Other models involve risk or chance For example, the market for a new product might be
“good” with a chance of 60% (a probability of 0.6) or “not good” with a chance of 40% (a ability of 0.4) Models that involve chance or risk, often measured as a probability value, are
prob-called probabilistic models In this book, we will investigate both deterministic and
probabilis-tic models
1.5 The Role of Computers and Spreadsheet Models in the Quantitative Analysis Approach
Developing a solution, testing the solution, and analyzing the results are important steps in thequantitative analysis approach Because we will be using mathematical models, these steps re-quire mathematical calculations Fortunately, we can use the computer to make these steps eas-ier Two programs that allow you to solve many of the problems found in this book are provided
at the Companion Website for this book:
1 POM-QM for Windows is an easy-to-use decision support system that was developed for
use with production/operations management (POM) and quantitative methods or tive management (QM) courses POM for Windows and QM for Windows were originallyseparate software packages for each type of course These are now combined into one pro-gram called POM-QM for Windows As seen in Program 1.1, it is possible to display allthe modules, only the POM modules, or only the QM modules The images shown in thistextbook will typically display only the QM modules Hence, in this book, reference willusually be made to QM for Windows Appendix E at the end of the book and many of theend-of-chapter appendices provide more information about QM for Windows
quantita-2 Excel QM, which can also be used to solve many of the problems discussed in this book,
works automatically within Excel spreadsheets Excel QM makes using a spreadsheet eveneasier by providing custom menus and solution procedures that guide you through everystep In Excel 2007, the main menu is found in the Add-Ins tab, as shown in Program 1.2.Appendix F provides further details of how to install this add-in program to Excel 2010and Excel 2007 To solve the break-even problem discussed in Section 1.4, we illustrateExcel QM features in Programs 1.3A and 1.3B
Trang 31Select the Add-Ins tab.
Click Excel QM and the drop-down menu opens with the list of models available in Excel QM.
Select the Add-Ins tab.
Click Excel QM, and the drop-down menu opens with the list of models available in Excel QM.
1 Solver Solver is an optimization technique that can maximize or minimize a quantity
given a set of limitations or constraints We will be using Solver throughout the text to
Trang 321.5 THE ROLE OF COMPUTERS AND SPREADSHEET MODELS IN THE QUANTITATIVE ANALYSIS APPROACH 11
Put any value in B13, and Excel will compute the profit in B23.
The break-even point is given
in units and also in dollars.
To see the formula used for the calculations, hold down the Ctrl key and press the ` (grave accent) key Doing this a second time returns to the display of the results.
2 Goal Seek This feature of Excel allows you to specify a goal or target (Set Cell) and what
variable (Changing Cell) that you want Excel to change in order to achieve a desired goal.Bill Pritchett, for example, would like to determine how many springs must be sold tomake a profit of $175 Program 1.4 shows how Goal Seek can be used to make thenecessary calculations
Select the Data tab and then select What-If Analysis.
Then select Goal Seek.
Put the cell that has the profit (B23) into the Set Cell window.
Put in the desired profit and specify the location for the volume cell (B13) Click OK, and Excel will change the value in
cell B13 Other cells are changed according
to the formulas in those cells
Trang 33Major League Operations Research
at the Department of Agriculture
In 1997, the Pittsburgh Pirates signed Ross Ohlendorf because
of his 95-mph sinking fastball Little did they know that Ross
pos-sessed operations research skills also worthy of national merit.
Ross Ohlendorf had graduated from Princeton University with a
3.8 GPA in operations research and financial engineering.
Indeed, after the 2009 baseball season, when Ross applied for
an 8-week unpaid internship with the U.S Department of
Agricul-ture, he didn’t need to mention his full-time employer because the
Secretary of the Department of Agriculture at the time, Tom Vilsack, was born and raised in Pittsburgh and was an avid Pittsburgh Pirates fan Ross spent 2 months of the ensuing off-season utiliz- ing his educational background in operations research, helping the Department of Agriculture track disease migration in livestock, a subject Ross has a vested interest in as his family runs a cattle ranch in Texas Moreover, when ABC News asked Ross about his off-season unpaid internship experience, he replied, “This one’s been, I’d say, the most exciting off-season I’ve had.”
All viewpoints should be
considered before formally
defining the problem.
1.6 Possible Problems in the Quantitative Analysis Approach
We have presented the quantitative analysis approach as a logical, systematic means of tacklingdecision-making problems Even when these steps are followed carefully, there are many diffi-culties that can hurt the chances of implementing solutions to real-world problems We now take
a look at what can happen during each of the steps
Defining the Problem
One view of decision makers is that they sit at a desk all day long, waiting until a problem arises,and then stand up and attack the problem until it is solved Once it is solved, they sit down, re-lax, and wait for the next big problem In the worlds of business, government, and education,problems are, unfortunately, not easily identified There are four potential roadblocks that quan-titative analysts face in defining a problem We use an application, inventory analysis, through-out this section as an example
CONFLICTING VIEWPOINTS The first difficulty is that quantitative analysts must often considerconflicting viewpoints in defining the problem For example, there are at least two views thatmanagers take when dealing with inventory problems Financial managers usually feel thatinventory is too high, as inventory represents cash not available for other investments Salesmanagers, on the other hand, often feel that inventory is too low, as high levels of inventory may
be needed to fill an unexpected order If analysts assume either one of these statements as theproblem definition, they have essentially accepted one manager’s perception and can expectresistance from the other manager when the “solution” emerges So it’s important to considerboth points of view before stating the problem Good mathematical models should include allpertinent information As we shall see in Chapter 6, both of these factors are included in inven-tory models
IMPACT ON OTHER DEPARTMENTS The next difficulty is that problems do not exist in isolationand are not owned by just one department of a firm Inventory is closely tied with cash flowsand various production problems A change in ordering policy can seriously hurt cash flows andupset production schedules to the point that savings on inventory are more than offset by in-creased costs for finance and production The problem statement should thus be as broad as pos-sible and include input from all departments that have a stake in the solution When a solution isfound, the benefits to all areas of the organization should be identified and communicated to thepeople involved
BEGINNING ASSUMPTIONS The third difficulty is that people have a tendency to state blems in terms of solutions The statement that inventory is too low implies a solution that in-ventory levels should be raised The quantitative analyst who starts off with this assumption will
pro-IN ACTION
Trang 341.6 POSSIBLE PROBLEMS IN THE QUANTITATIVE ANALYSIS APPROACH 13
probably indeed find that inventory should be raised From an implementation standpoint, a
“good” solution to the right problem is much better than an “optimal” solution to the wrong
problem If a problem has been defined in terms of a desired solution, the quantitative analystshould ask questions about why this solution is desired By probing further, the true problemwill surface and can be defined properly
SOLUTION OUTDATED Even with the best of problem statements, however, there is a fourth ger The problem can change as the model is being developed In our rapidly changing businessenvironment, it is not unusual for problems to appear or disappear virtually overnight The ana-lyst who presents a solution to a problem that no longer exists can’t expect credit for providingtimely help However, one of the benefits of mathematical models is that once the original modelhas been developed, it can be used over and over again whenever similar problems arise Thisallows a solution to be found very easily in a timely manner
dan-Developing a Model
FITTING THE TEXTBOOK MODELS One problem in developing quantitative models is that a ager’s perception of a problem won’t always match the textbook approach Most inventorymodels involve minimizing the total of holding and ordering costs Some managers view thesecosts as unimportant; instead, they see the problem in terms of cash flow, turnover, and levels
man-of customer satisfaction Results man-of a model based on holding and ordering costs are probablynot acceptable to such managers This is why the analyst must completely understand the modeland not simply use the computer as a “black box” where data are input and results are givenwith no understanding of the process The analyst who understands the process can explain
to the manager how the model does consider these other factors when estimating the differenttypes of inventory costs If other factors are important as well, the analyst can consider theseand use sensitivity analysis and good judgment to modify the computer solution before it isimplemented
UNDERSTANDING THE MODEL A second major concern involves the trade-off between the plexity of the model and ease of understanding Managers simply will not use the results of amodel they do not understand Complex problems, though, require complex models One trade-off is to simplify assumptions in order to make the model easier to understand The model losessome of its reality but gains some acceptance by management
com-One simplifying assumption in inventory modeling is that demand is known and stant This means that probability distributions are not needed and it allows us to build simple,easy-to-understand models Demand, however, is rarely known and constant, so the model webuild lacks some reality Introducing probability distributions provides more realism but mayput comprehension beyond all but the most mathematically sophisticated managers Oneapproach is for the quantitative analyst to start with the simple model and make sure that it iscompletely understood Later, more complex models can be introduced slowly as managers gainmore confidence in using the new approach Explaining the impact of the more sophisticatedmodels (e.g., carrying extra inventory called safety stock) without going into complete mathe-matical details is sometimes helpful Managers can understand and identify with this concept,even if the specific mathematics used to find the appropriate quantity of safety stock is nottotally understood
con-Acquiring Input Data
Gathering the data to be used in the quantitative approach to problem solving is often not a ple task One-fifth of all firms in a recent study had difficulty with data access
sim-USING ACCOUNTING DATA One problem is that most data generated in a firm come from basicaccounting reports The accounting department collects its inventory data, for example, in terms
of cash flows and turnover But quantitative analysts tackling an inventory problem need to lect data on holding costs and ordering costs If they ask for such data, they may be shocked tofind that the data were simply never collected for those specified costs
col-An optimal solution to the wrong
problem leaves the real problem
unsolved.
Obtaining accurate input data
can be very difficult.
Trang 35Professor Gene Woolsey tells a story of a young quantitative analyst sent down to ing to get “the inventory holding cost per item per day for part 23456/AZ.” The accountant askedthe young man if he wanted the first-in, first-out figure, the last-in, first-out figure, the lower ofcost or market figure, or the “how-we-do-it” figure The young man replied that the inventorymodel required only one number The accountant at the next desk said, “Hell, Joe, give the kid anumber.” The kid was given a number and departed.
account-VALIDITY OF DATA A lack of “good, clean data” means that whatever data are available must often
be distilled and manipulated (we call it “fudging”) before being used in a model Unfortunately,the validity of the results of a model is no better than the validity of the data that go into the model.You cannot blame a manager for resisting a model’s “scientific” results when he or she knows thatquestionable data were used as input This highlights the importance of the analyst understandingother business functions so that good data can be found and evaluated by the analyst It also em-phasizes the importance of sensitivity analysis, which is used to determine the impact of minorchanges in input data Some solutions are very robust and would not change at all for certainchanges in the input data
Developing a Solution
HARD-TO-UNDERSTAND MATHEMATICS The first concern in developing solutions is that though the mathematical models we use may be complex and powerful, they may not be com-pletely understood Fancy solutions to problems may have faulty logic or data The aura ofmathematics often causes managers to remain silent when they should be critical The well-known operations researcher C W Churchman cautions that “because mathematics has been sorevered a discipline in recent years, it tends to lull the unsuspecting into believing that he whothinks elaborately thinks well.”1
al-ONLY ONE ANSWER IS LIMITING The second problem is that quantitative models usually give
just one answer to a problem Most managers would like to have a range of options and not be
put in a take-it-or-leave-it position A more appropriate strategy is for an analyst to present arange of options, indicating the effect that each solution has on the objective function This givesmanagers a choice as well as information on how much it will cost to deviate from the optimalsolution It also allows problems to be viewed from a broader perspective, since nonquantitativefactors can be considered
Testing the Solution
The results of quantitative analysis often take the form of predictions of how things will work inthe future if certain changes are made now To get a preview of how well solutions will reallywork, managers are often asked how good the solution looks to them The problem is that com-plex models tend to give solutions that are not intuitively obvious Such solutions tend to be re-jected by managers The quantitative analyst now has the chance to work through the model andthe assumptions with the manager in an effort to convince the manager of the validity of the re-sults In the process of convincing the manager, the analyst will have to review every assump-tion that went into the model If there are errors, they may be revealed during this review Inaddition, the manager will be casting a critical eye on everything that went into the model, and
if he or she can be convinced that the model is valid, there is a good chance that the solution sults are also valid
re-Analyzing the Results
Once a solution has been tested, the results must be analyzed in terms of how they will affect thetotal organization You should be aware that even small changes in organizations are often diffi-cult to bring about If the results indicate large changes in organization policy, the quantitativeanalyst can expect resistance In analyzing the results, the analyst should ascertain who mustchange and by how much, if the people who must change will be better or worse off, and whohas the power to direct the change
Hard-to-understand mathematics
and one answer can be a problem
in developing a solution.
Assumptions should be reviewed.
1C W Churchman “Relativity Models in the Social Sciences,” Interfaces 4, 1 (November 1973).
Trang 361.7 IMPLEMENTATION—NOT JUST THE FINAL STEP 15
IN ACTION PLATO Helps 2004 Olympic Games in Athens
The 2004 Olympic Games were held in Athens, Greece, over a
period of 16 days More than 2,000 athletes competed in 300
events in 28 sports The events were held in 36 different venues
(stadia, competition centers, etc.), and 3.6 million tickets were
sold to people who would view these events In addition, 2,500
members of international committees and 22,000 journalists and
broadcasters attended these games Home viewers spent more
than 34 billion hours watching these sporting events The 2004
Olympic Games was the biggest sporting event in the history of
the world up to that point.
In addition to the sporting venues, other noncompetitive
ven-ues, such as the airport and Olympic village, had to be
consid-ered A successful Olympics requires tremendous planning for the
transportation system that will handle the millions of spectators.
Three years of work and planning were needed for the 16 days of
the Olympics.
The Athens Olympic Games Organizing Committee (ATHOC)
had to plan, design, and coordinate systems that would be
deliv-ered by outside contractors ATHOC personnel would later be
re-sponsible for managing the efforts of volunteers and paid staff
during the operations of the games To make the Athens
Olympics run efficiently and effectively, the Process Logistics
Advanced Technical Optimization (PLATO) project was begun Innovative techniques from management science, systems engi- neering, and information technology were used to change the planning, design, and operations of venues.
The objectives of PLATO were to (1) facilitate effective tional transformation, (2) help plan and manage resources in a cost- effective manner, and (3) document lessons learned so future Olympic committees could benefit The PLATO project developed business-process models for the various venues, developed simula- tion models that enable the generation of what-if scenarios, devel- oped software to aid in the creation and management of these models, and developed process steps for training ATHOC personnel
organiza-in usorganiza-ing these models Generic solutions were developed so that this knowledge and approach could be made available to other users PLATO was credited with reducing the cost of the 2004 Olympics by over $69 million Perhaps even more important is the fact that the Athens games were universally deemed an unquali- fied success The resulting increase in tourism is expected to re- sult in economic benefit to Greece for many years in the future.
Source: Based on D A Beis, et al “PLATO Helps Athens Win Gold: Olympic
Games Knowledge Modeling for Organizational Change and Resource
Man-agement,” Interfaces 36, 1 (January–February 2006): 26–42.
1.7 Implementation—Not Just the Final Step
We have just presented some of the many problems that can affect the ultimate acceptance ofthe quantitative analysis approach and use of its models It should be clear now that implemen-tation isn’t just another step that takes place after the modeling process is over Each one of thesesteps greatly affects the chances of implementing the results of a quantitative study
Lack of Commitment and Resistance to Change
Even though many business decisions can be made intuitively, based on hunches and experience,there are more and more situations in which quantitative models can assist Some managers,however, fear that the use of a formal analysis process will reduce their decision-making power.Others fear that it may expose some previous intuitive decisions as inadequate Still others justfeel uncomfortable about having to reverse their thinking patterns with formal decision making.These managers often argue against the use of quantitative methods
Many action-oriented managers do not like the lengthy formal decision-making process andprefer to get things done quickly They prefer “quick and dirty” techniques that can yield imme-diate results Once managers see some quick results that have a substantial payoff, the stage isset for convincing them that quantitative analysis is a beneficial tool
We have known for some time that management support and user involvement are critical
to the successful implementation of quantitative analysis projects A Swedish study found thatonly 40% of projects suggested by quantitative analysts were ever implemented But 70% of thequantitative projects initiated by users, and fully 98% of projects suggested by top managers,
were implemented.
Lack of Commitment by Quantitative Analysts
Just as managers’ attitudes are to blame for some implementation problems, analysts’ attitudesare to blame for others When the quantitative analyst is not an integral part of the departmentfacing the problem, he or she sometimes tends to treat the modeling activity as an end in itself
Management support and user
involvement are important.
Trang 37That is, the analyst accepts the problem as stated by the manager and builds a model to solveonly that problem When the results are computed, he or she hands them back to the managerand considers the job done The analyst who does not care whether these results help make thefinal decision is not concerned with implementation.
Successful implementation requires that the analyst not tell the users what to do, but work with them and take their feelings into account An article in Operations Research describes an
inventory control system that calculated reorder points and order quantities But instead ofinsisting that computer-calculated quantities be ordered, a manual override feature was installed.This allowed users to disregard the calculated figures and substitute their own The override wasused quite often when the system was first installed Gradually, however, as users came to real-ize that the calculated figures were right more often than not, they allowed the system’s figures
to stand Eventually, the override feature was used only in special circumstances This is a goodexample of how good relationships can aid in model implementation
Summary
Quantitative analysis is a scientific approach to decision
mak-ing The quantitative analysis approach includes defining the
problem, developing a model, acquiring input data, developing
a solution, testing the solution, analyzing the results, and
im-plementing the results In using the quantitative approach,
however, there can be potential problems, including conflicting
viewpoints, the impact of quantitative analysis models on other
departments, beginning assumptions, outdated solutions, fittingtextbook models, understanding the model, acquiring goodinput data, hard-to-understand mathematics, obtaining onlyone answer, testing the solution, and analyzing the results Inusing the quantitative analysis approach, implementation is notthe final step There can be a lack of commitment to theapproach and resistance to change
Glossary
Algorithm A set of logical and mathematical operations
per-formed in a specific sequence
Break-Even Point The quantity of sales that results in zero
profit
Deterministic Model A model in which all values used in
the model are known with complete certainty
Input Data Data that are used in a model in arriving at the
final solution
Mathematical Model A model that uses mathematical
equa-tions and statements to represent the relaequa-tionships within
the model
Model A representation of reality or of a real-life situation
Parameter A measurable input quantity that is inherent in
a problem
Probabilistic Model A model in which all values used in themodel are not known with certainty but rather involve somechance or risk, often measured as a probability value
Problem A statement, which should come from a manager,that indicates a problem to be solved or an objective or agoal to be reached
Quantitative Analysis or Management Science A scientificapproach that uses quantitative techniques as a tool in deci-sion making
Sensitivity Analysis A process that involves determininghow sensitive a solution is to changes in the formulation of
a problem
Stochastic Model Another name for a probabilistic model
Variable A measurable quantity that is subject to change
Key Equations
(1-1)
where
An equation to determine profit as a function of the
sell-ing price per unit, fixed costs, variable costs, and
num-ber of units sold
Xn = variable cost per unit= number of units sold
f = fixed cost
s = selling price per unit
Profit = sX - f - nX
(1-2)
An equation to determine the break-even point (BEP) in
units as a function of the selling price per unit (s), fixed costs ( f ), and variable costs ( ).n
s - n
Trang 38DISCUSSION QUESTIONS AND PROBLEMS 17
Self-Test
䊉 Before taking the self-test, refer to the learning objectives at the beginning of the chapter,
the notes in the margins, and the glossary at the end of the chapter
䊉 Use the key at the back of the book to correct your answers
䊉 Restudy pages that correspond to any questions that you answered incorrectly or material
you feel uncertain about
1 In analyzing a problem, you should normally study
a the qualitative aspects
b the quantitative aspects
c both a and b
d neither a nor b
2 Quantitative analysis is
a a logical approach to decision making
b a rational approach to decision making
c a scientific approach to decision making
d all of the above
3 Frederick Winslow Taylor
a was a military researcher during World War II
b pioneered the principles of scientific management
c developed the use of the algorithm for QA
d all of the above
4 An input (such as variable cost per unit or fixed cost) for
5 The point at which the total revenue equals total cost
(meaning zero profit) is called the
7 Sensitivity analysis is most often associated with which
step of the quantitative analysis approach?
a defining the problem
b acquiring input data
c implementing the results
d analyzing the results
8 A deterministic model is one in which
a there is some uncertainty about the parameters used inthe model
b there is a measurable outcome
c all parameters used in the model are known with complete certainty
d there is no available computer software
9 The term algorithm
a is named after Algorismus
b is named after a ninth-century Arabic mathematician
c describes a series of steps or procedures to be repeated
d all of the above
10 An analysis to determine how much a solution wouldchange if there were changes in the model or the inputdata is called
a sensitivity or postoptimality analysis
b schematic or iconic analysis
1-1 What is the difference between quantitative and
qualitative analysis? Give several examples
1-2 Define quantitative analysis What are some of the
organizations that support the use of the scientific
approach?
1-3 What is the quantitative analysis process? Give
sev-eral examples of this process
1-4 Briefly trace the history of quantitative analysis.What happened to the development of quantitativeanalysis during World War II?
1-5 Give some examples of various types of models.What is a mathematical model? Develop two exam-ples of mathematical models
1-6 List some sources of input data
1-7 What is implementation, and why is it important?
Trang 391-8 Describe the use of sensitivity analysis and
postopti-mality analysis in analyzing the results
1-9 Managers are quick to claim that quantitative
ana-lysts talk to them in a jargon that does not sound like
English List four terms that might not be
under-stood by a manager Then explain in nontechnical
terms what each term means
1-10 Why do you think many quantitative analysts don’t
like to participate in the implementation process?
What could be done to change this attitude?
1-11 Should people who will be using the results of a new
quantitative model become involved in the technical
aspects of the problem-solving procedure?
1-12 C W Churchman once said that “mathematics
tends to lull the unsuspecting into believing that he
who thinks elaborately thinks well.” Do you think
that the best QA models are the ones that are most
elaborate and complex mathematically? Why?
1-13 What is the break-even point? What parameters are
necessary to find it?
Problems
1-14 Gina Fox has started her own company, Foxy Shirts,
which manufactures imprinted shirts for special
oc-casions Since she has just begun this operation, she
rents the equipment from a local printing shop when
necessary The cost of using the equipment is $350
The materials used in one shirt cost $8, and Gina can
sell these for $15 each
(a) If Gina sells 20 shirts, what will her total
rev-enue be? What will her total variable cost be?
(b) How many shirts must Gina sell to break even?
What is the total revenue for this?
1-15 Ray Bond sells handcrafted yard decorations at
county fairs The variable cost to make these is $20
each, and he sells them for $50 The cost to rent a
booth at the fair is $150 How many of these must
Ray sell to break even?
1-16 Ray Bond, from Problem 1-15, is trying to find a new
supplier that will reduce his variable cost of
produc-tion to $15 per unit If he was able to succeed in
re-ducing this cost, what would the break-even point be?
1-17 Katherine D’Ann is planning to finance her college
education by selling programs at the football games
for State University There is a fixed cost of $400 for
printing these programs, and the variable cost is $3
There is also a $1,000 fee that is paid to the
univer-sity for the right to sell these programs If Katherine
was able to sell programs for $5 each, how many
would she have to sell in order to break even?
1-18 Katherine D’Ann, from Problem 1-17, has become
concerned that sales may fall, as the team is on a
terrible losing streak, and attendance has fallen off
In fact, Katherine believes that she will sell only 500programs for the next game If it was possible toraise the selling price of the program and still sell
500, what would the price have to be for Katherine
to break even by selling 500?
1-19 Farris Billiard Supply sells all types of billiardequipment, and is considering manufacturing theirown brand of pool cues Mysti Farris, the productionmanager, is currently investigating the production of
a standard house pool cue that should be very lar Upon analyzing the costs, Mysti determines thatthe materials and labor cost for each cue is $25, andthe fixed cost that must be covered is $2,400 perweek With a selling price of $40 each, how manypool cues must be sold to break even? What wouldthe total revenue be at this break-even point?1-20 Mysti Farris (see Problem 1-19) is considering rais-ing the selling price of each cue to $50 instead of
popu-$40 If this is done while the costs remain the same,what would the new break-even point be? Whatwould the total revenue be at this break-even point?1-21 Mysti Farris (see Problem 1-19) believes that there
is a high probability that 120 pool cues can be sold
if the selling price is appropriately set What sellingprice would cause the break-even point to be 120?1-22 Golden Age Retirement Planners specializes in pro-viding financial advice for people planning for acomfortable retirement The company offers semi-nars on the important topic of retirement planning.For a typical seminar, the room rental at a hotel is
$1,000, and the cost of advertising and other dentals is about $10,000 per seminar The cost of thematerials and special gifts for each attendee is $60per person attending the seminar The companycharges $250 per person to attend the seminar as thisseems to be competitive with other companies in thesame business How many people must attend eachseminar for Golden Age to break even?
inci-1-23 A couple of entrepreneurial business students atState University decided to put their education intopractice by developing a tutoring company for busi-ness students While private tutoring was offered, itwas determined that group tutoring before tests inthe large statistics classes would be most beneficial.The students rented a room close to campus for $300for 3 hours They developed handouts based on pasttests, and these handouts (including color graphs)cost $5 each The tutor was paid $25 per hour, for atotal of $75 for each tutoring session
(a) If students are charged $20 to attend the session,how many students must enroll for the company
to break even?
(b) A somewhat smaller room is available for $200for 3 hours The company is considering thispossibility How would this affect the break-evenpoint?
Note: means the problem may be solved with QM for Windows; means
the problem may be solved with Excel QM; and means the problem may be
solved with QM for Windows and/or Excel QM.
Trang 40six booths for 5 hours at $7 an hour These fixed costs will
be proportionately allocated to each of the products based onthe percentages provided in the table For example, the revenuefrom soft drinks would be expected to cover 25% of the totalfixed costs
Maddux wants to be sure that he has a number of things forPresident Starr: (1) the total fixed cost that must be covered ateach of the games; (2) the portion of the fixed cost allocated toeach of the items; (3) what his unit sales would be at break-evenfor each item—that is, what sales of soft drinks, coffee, hotdogs, and hamburgers are necessary to cover the portion of thefixed cost allocated to each of these items; (4) what the dollarsales for each of these would be at these break-even points; and(5) realistic sales estimates per attendee for attendance of60,000 and 35,000 (In other words, he wants to know howmany dollars each attendee is spending on food at his projectedbreak-even sales at present and if attendance grows to 60,000.)
He felt this last piece of information would be helpful to stand how realistic the assumptions of his model are, and thisinformation could be compared with similar figures from previ-ous seasons
under-Discussion Question
1 Prepare a brief report with the items noted so it is readyfor Dr Starr at the next meeting
Adapted from J Heizer and B Render Operations Management, 6th ed.
Upper Saddle River, NJ: Prentice Hall, 2000, pp 274–275.
BIBLIOGRAPHY 19
ITEM
SELLINGPRICE/UNIT
VARIABLE COST/UNIT
PERCENTREVENUE
Food and Beverages at Southwestern University Football Games
Southwestern University (SWU), a large state college in
Stephenville, Texas, 30 miles southwest of the Dallas/Fort
Worth metroplex, enrolls close to 20,000 students The school
is the dominant force in the small city, with more students
dur-ing fall and sprdur-ing than permanent residents
A longtime football powerhouse, SWU is a member of the
Big Eleven conference and is usually in the top 20 in college
football rankings To bolster its chances of reaching the elusive
and long-desired number-one ranking, in 2010 SWU hired the
legendary Bo Pitterno as its head coach Although the
number-one ranking remained out of reach, attendance at the five
Satur-day home games each year increased Prior to Pitterno’s arrival,
attendance generally averaged 25,000–29,000 Season ticket
sales bumped up by 10,000 just with the announcement of the
new coach’s arrival Stephenville and SWU were ready to move
to the big time!
With the growth in attendance came more fame, the need
for a bigger stadium, and more complaints about seating,
park-ing, long lines, and concession stand prices Southwestern
Uni-versity’s president, Dr Marty Starr, was concerned not only
about the cost of expanding the existing stadium versus
build-ing a new stadium but also about the ancillary activities He
wanted to be sure that these various support activities generated
revenue adequate to pay for themselves Consequently, he
wanted the parking lots, game programs, and food service to all
be handled as profit centers At a recent meeting discussing the
new stadium, Starr told the stadium manager, Hank Maddux,
to develop a break-even chart and related data for each of the
centers He instructed Maddux to have the food service area
break-even report ready for the next meeting After discussion
with other facility managers and his subordinates, Maddux
de-veloped the following table showing the suggested selling
prices, and his estimate of variable costs, and the percent
rev-enue by item It also provides an estimate of the percentage of
the total revenues that would be expected for each of the items
based on historical sales data
Maddux’s fixed costs are interesting He estimated that the
prorated portion of the stadium cost would be as follows:
salaries for food services at $100,000 ($20,000 for each of the
five home games); 2,400 square feet of stadium space at $2 per
square foot per game; and six people per booth in each of the
Bibliography
Ackoff, R L Scientific Method: Optimizing Applied Research Decisions New
York: John Wiley & Sons, Inc., 1962.
Beam, Carrie “ASP, the Art and Science of Practice: How I Started an OR/MS
Consulting Practice with a Laptop, a Phone, and a PhD,” Interfaces 34
(July–August 2004): 265–271.
Board, John, Charles Sutcliffe, and William T Ziemba “Applying Operations
Research Techniques to Financial Markets,” Interfaces 33 (March–April
Dutta, Goutam “Lessons for Success in OR/MS Practice Gained from
Experiences in Indian and U.S Steel Plants,” Interfaces 30, 5
(September–October 2000): 23–30.