(BQ) Part 1 book An introduction to management science - Quantitative approaches to decision making has contents: An introduction to linear programming; linear programming applications in marketing, finance, and operations management; advanced linear programming applications; distribution and network models; integer linear programming; nonlinear optimization models,...and other contents.
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Trang 7An Introduction to Management Science:
Quantitative Approaches to Decision
Making, Revised Thirteenth Edition
David R Anderson, Dennis J Sweeney,
Thomas A Williams, Jeffrey D Camm, &
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1 2 3 4 5 6 7 14 13 12 11 10
Trang 11Brief Contents
Preface xxv
About the Authors xxix Chapter 1 Introduction 1 Chapter 2 An Introduction to Linear Programming 28 Chapter 3 Linear Programming: Sensitivity Analysis and
Interpretation of Solution 92 Chapter 4 Linear Programming Applications in Marketing,
Finance, and Operations Management 153 Chapter 5 Advanced Linear Programming Applications 214 Chapter 6 Distribution and Network Models 255
Chapter 7 Integer Linear Programming 317 Chapter 8 Nonlinear Optimization Models 365 Chapter 9 Project Scheduling: PERT/CPM 412 Chapter 10 Inventory Models 453
Chapter 11 Waiting Line Models 502 Chapter 12 Simulation 542
Chapter 13 Decision Analysis 602 Chapter 14 Multicriteria Decisions 659 Chapter 15 Time Series Analysis and Forecasting 703 Chapter 16 Markov Processes 761
Chapter 17 Linear Programming: Simplex Method On Website Chapter 18 Simplex-Based Sensitivity Analysis and Duality
On Website Chapter 19 Solution Procedures for Transportation and
Assignment Problems On Website Chapter 20 Minimal Spanning Tree On Website Chapter 21 Dynamic Programming On Website
Appendixes 787 Appendix A Building Spreadsheet Models 788 Appendix B Areas for the Standard Normal Distribution 815 Appendix C Values of eⴚλ 817
Appendix D References and Bibliography 818 Appendix E Self-Test Solutions and Answers
to Even-Numbered Problems 820
Index 853
Trang 13Preface xxv About the Authors xxix
Chapter 1 Introduction 11.1 Problem Solving and Decision Making 3 1.2 Quantitative Analysis and Decision Making 4 1.3 Quantitative Analysis 6
Model Development 7Data Preparation 10Model Solution 11Report Generation 12
A Note Regarding Implementation 12
1.4 Models of Cost, Revenue, and Profit 14
Cost and Volume Models 14Revenue and Volume Models 15Profit and Volume Models 15Breakeven Analysis 16
1.5 Management Science Techniques 16
Methods Used Most Frequently 18
Summary 19 Glossary 19 Problems 20
Case Problem Scheduling a Golf League 23
Appendix 1.1 Using Excel for Breakeven Analysis 24
Chapter 2 An Introduction to Linear Programming 282.1 A Simple Maximization Problem 30
Problem Formulation 31Mathematical Statement of the Par, Inc., Problem 33
2.2 Graphical Solution Procedure 35
A Note on Graphing Lines 44Summary of the Graphical Solution Procedurefor Maximization Problems 46
Trang 142.5 A Simple Minimization Problem 52
Summary of the Graphical Solution Procedure for Minimization Problems 54
Surplus Variables 55Computer Solution of the M&D Chemicals Problem 56
Case Problem 1 Workload Balancing 82 Case Problem 2 Production Strategy 83 Case Problem 3 Hart Venture Capital 84
Appendix 2.1 Solving Linear Programs with LINGO 85 Appendix 2.2 Solving Linear Programs with Excel 87
Chapter 3 Linear Programming: Sensitivity Analysis
and Interpretation of Solution 923.1 Introduction to Sensitivity Analysis 94
3.2 Graphical Sensitivity Analysis 95
Objective Function Coefficients 95Right-Hand Sides 100
3.3 Sensitivity Analysis: Computer Solution 103
Interpretation of Computer Output 103Cautionary Note on the Interpretation of Dual Values 106The Modified Par, Inc., Problem 106
3.4 Limitations of Classical Sensitivity Analysis 110
Simultaneous Changes 111Changes in Constraint Coefficients 112Nonintuitive Dual Values 112
3.5 The Electronic Communications Problem 116
Problem Formulation 117Computer Solution and Interpretation 118
Summary 122 Glossary 123 Problems 123
Case Problem 1 Product Mix 145 Case Problem 2 Investment Strategy 146 Case Problem 3 Truck Leasing Strategy 147
Appendix 3.1 Sensitivity Analysis with Excel 148 Appendix 3.2 Sensitivity Analysis with LINGO 150
Trang 15Chapter 4 Linear Programming Applications in
Marketing, Finance, and Operations Management 153
Case Problem 1 Planning an Advertising Campaign 202
Case Problem 2 Phoenix Computer 203
Case Problem 3 Textile Mill Scheduling 204
Case Problem 4 Workforce Scheduling 205
Case Problem 5 Duke Energy Coal Allocation 207
Appendix 4.1 Excel Solution of Hewlitt Corporation Financial
Planning Problem 210
Chapter 5 Advanced Linear Programming
Applications 2145.1 Data Envelopment Analysis 215
Evaluating the Performance of Hospitals 216
Overview of the DEA Approach 216
DEA Linear Programming Model 217
Summary of the DEA Approach 222
5.2 Revenue Management 223
5.3 Portfolio Models and Asset Allocation 229
A Portfolio of Mutual Funds 229
Conservative Portfolio 230
Moderate Risk Portfolio 232
5.4 Game Theory 236
Competing for Market Share 236
Identifying a Pure Strategy Solution 238
Identifying a Mixed Strategy Solution 239
Summary 247
Glossary 247
Problems 248
Trang 16Chapter 6 Distribution and Network Models 2556.1 Transportation Problem 256
A General Linear Programming Model 279
6.5 Maximal Flow Problem 279 6.6 A Production and Inventory Application 283 Summary 286
Glossary 287 Problems 288
Case Problem 1 Solutions Plus 305 Case Problem 2 Distribution System Design 306
Appendix 6.1 Excel Solution of Transportation, Assignment, and Transshipment Problems 308
Chapter 7 Integer Linear Programming 3177.1 Types of Integer Linear Programming Models 319 7.2 Graphical and Computer Solutions for an All-Integer
Linear Program 321
Graphical Solution of the LP Relaxation 322Rounding to Obtain an Integer Solution 322Graphical Solution of the All-Integer Problem 323Using the LP Relaxation to Establish Bounds 323Computer Solution 324
7.3 Applications Involving 0-1 Variables 325
Capital Budgeting 325Fixed Cost 326Distribution System Design 329Bank Location 334
Product Design and Market Share Optimization 337
7.4 Modeling Flexibility Provided by 0-1 Integer Variables 341
Multiple-Choice and Mutually Exclusive Constraints 341
k out of n Alternatives Constraint 342
Conditional and Corequisite Constraints 342
A Cautionary Note About Sensitivity Analysis 344
Trang 17Summary 344
Glossary 345
Problems 346
Case Problem 1 Textbook Publishing 357
Case Problem 2 Yeager National Bank 358
Case Problem 3 Production Scheduling with Changeover Costs 359
Appendix 7.1 Excel Solution of Integer Linear Programs 360
Appendix 7.2 LINGO Solution of Integer Linear Programs 361
Chapter 8 Nonlinear Optimization Models 365
8.1 A Production Application—Par, Inc., Revisited 367
An Unconstrained Problem 367
A Constrained Problem 368
Local and Global Optima 371
Dual Values 374
8.2 Constructing an Index Fund 374
8.3 Markowitz Portfolio Model 379
8.4 Blending: The Pooling Problem 382
8.5 Forecasting Adoption of a New Product 387
Case Problem 2 CAFE Compliance in the Auto Industry 405
Appendix 8.1 Solving Nonlinear Problems with LINGO 408
Appendix 8.2 Solving Nonlinear Problems with Excel Solver 409Chapter 9 Project Scheduling: PERT/CPM 412
9.1 Project Scheduling with Known Activity Times 413
The Concept of a Critical Path 414
Determining the Critical Path 416
Contributions of PERT/CPM 420
Summary of the PERT/CPM Critical Path Procedure 421
9.2 Project Scheduling with Uncertain Activity Times 422
The Daugherty Porta-Vac Project 423
Uncertain Activity Times 423
The Critical Path 425
Variability in Project Completion Time 428
9.3 Considering Time-Cost Trade-Offs 431
Crashing Activity Times 432
Linear Programming Model for Crashing 434
Trang 18Summary 436 Glossary 437 Problems 438
Case Problem R C Coleman 448
Appendix 9.1 Using Microsoft Office Project 450
Chapter 10 Inventory Models 45310.1 Economic Order Quantity (EOQ) Model 454
The How-Much-to-Order Decision 459The When-to-Order Decision 460Sensitivity Analysis for the EOQ Model 461Excel Solution of the EOQ Model 462Summary of the EOQ Model Assumptions 463
10.2 Economic Production Lot Size Model 464
Total Cost Model 465Economic Production Lot Size 467
10.3 Inventory Model with Planned Shortages 467 10.4 Quantity Discounts for the EOQ Model 472 10.5 Single-Period Inventory Model with Probabilistic Demand 474
Johnson Shoe Company 475Nationwide Car Rental 479
10.6 Order-Quantity, Reorder Point Model with Probabilistic
Demand 480
The How-Much-to-Order Decision 481The When-to-Order Decision 482
10.7 Periodic Review Model with Probabilistic Demand 484
More Complex Periodic Review Models 487
Summary 488 Glossary 489 Problems 491
Case Problem 1 Wagner Fabricating Company 498 Case Problem 2 River City Fire Department 499
Appendix 10.1 Development of the Optimal Order Quantity (Q*)
Formula for the EOQ Model 500
Appendix 10.2 Development of the Optimal Lot Size (Q*) Formula
for the Production Lot Size Model 501
Chapter 11 Waiting Line Models 50211.1 Structure of a Waiting Line System 504
Single-Channel Waiting Line 504Distribution of Arrivals 504Distribution of Service Times 506
Trang 19Queue Discipline 507
Steady-State Operation 507
11.2 Single-Channel Waiting Line Model with Poisson Arrivals
and Exponential Service Times 508
Operating Characteristics 508
Operating Characteristics for the Burger Dome Problem 509
Managers’ Use of Waiting Line Models 510
Improving the Waiting Line Operation 510
Excel Solution of Waiting Line Model 511
11.3 Multiple-Channel Waiting Line Model with Poisson Arrivals
and Exponential Service Times 512
Operating Characteristics 513
Operating Characteristics for the Burger Dome Problem 515
11.4 Some General Relationships for Waiting Line Models 517
11.5 Economic Analysis of Waiting Lines 519
11.6 Other Waiting Line Models 520
11.7 Single-Channel Waiting Line Model with Poisson Arrivals
and Arbitrary Service Times 521
Operating Characteristics for the M/G/1 Model 521
Constant Service Times 523
11.8 Multiple-Channel Model with Poisson Arrivals, Arbitrary Service
Times, and No Waiting Line 524
Operating Characteristics for the M/G/k Model with Blocked
Customers Cleared 524
11.9 Waiting Line Models with Finite Calling Populations 526
Operating Characteristics for the M/M/1 Model with a Finite
Calling Population 527
Summary 529
Glossary 531
Problems 531
Case Problem 1 Regional Airlines 539
Case Problem 2 Office Equipment, Inc 540
Butler Inventory Simulation 561
12.3 Waiting Line Simulation 563
Hammondsport Savings Bank ATM Waiting Line 563
Customer Arrival Times 564
Trang 20Customer Service Times 565Simulation Model 565Hammondsport Savings Bank ATM Simulation 569Simulation with Two ATMs 570
Simulation Results with Two ATMs 572
12.4 Other Simulation Issues 574
Computer Implementation 574Verification and Validation 575Advantages and Disadvantages of Using Simulation 575
Summary 576 Glossary 577 Problems 578
Case Problem 1 Tri-State Corporation 585 Case Problem 2 Harbor Dunes Golf Course 587 Case Problem 3 County Beverage Drive-Thru 589
Appendix 12.1 Simulation with Excel 590 Appendix 12.2 Simulation Using Crystal Ball 597Chapter 13 Decision Analysis 602
13.1 Problem Formulation 604
Influence Diagrams 605Payoff Tables 605Decision Trees 606
13.2 Decision Making Without Probabilities 607
Optimistic Approach 607Conservative Approach 607Minimax Regret Approach 608
13.3 Decision Making with Probabilities 610
Expected Value of Perfect Information 613
13.4 Risk Analysis and Sensitivity Analysis 615
Risk Analysis 615Sensitivity Analysis 616
13.5 Decision Analysis with Sample Information 620
Influence Diagram 620Decision Tree 621Decision Strategy 623Risk Profile 627Expected Value of Sample Information 629Efficiency of Sample Information 630
13.6 Computing Branch Probabilities 630 Summary 634
Glossary 635 Problems 637
Case Problem 1 Property Purchase Strategy 651
Trang 21Case Problem 2 Lawsuit Defense Strategy 652
Appendix 13.1 Decision Analysis with Treeplan 653
Chapter 14 Multicriteria Decisions 659
14.1 Goal Programming: Formulation and Graphical Solution 660
Developing the Constraints and the Goal Equations 661
Developing an Objective Function with Preemptive Priorities 663Graphical Solution Procedure 664
Goal Programming Model 667
14.2 Goal Programming: Solving More Complex Problems 668
Suncoast Office Supplies Problem 668
Formulating the Goal Equations 669
Formulating the Objective Function 670
Computer Solution 671
14.3 Scoring Models 674
14.4 Analytic Hierarchy Process 679
Developing the Hierarchy 680
14.5 Establishing Priorities Using AHP 680
Pairwise Comparisons 681
Pairwise Comparison Matrix 682
Synthesization 684
Consistency 685
Other Pairwise Comparisons for the Car Selection Problem 687
14.6 Using AHP to Develop an Overall Priority Ranking 688
Summary 690
Glossary 690
Problems 691
Case Problem EZ Trailers, Inc 700
Appendix 14.1 Scoring Models with Excel 701
Chapter 15 Time Series Analysis and Forecasting 703
15.1 Time Series Patterns 705
Trang 2215.4 Trend Projection 726
Linear Trend 726Nonlinear Trend 730
15.5 Seasonality 733
Seasonality Without Trend 734Seasonality and Trend 737Models Based on Monthly Data 739
Summary 740 Glossary 741 Problems 741
Case Problem 1 Forecasting Food and Beverage Sales 751 Case Problem 2 Forecasting Lost Sales 751
Appendix 15.1 Forecasting with Excel Data Analysis Tools 753 Appendix 15.2 Forecasting with Excel Solver 754
Appendix 15.3 Forecasting with LINGO 759
Chapter 16 Markov Processes 76116.1 Market Share Analysis 763
16.2 Accounts Receivable Analysis 771
Fundamental Matrix and Associated Calculations 772Establishing the Allowance for Doubtful Accounts 774
Summary 776 Glossary 776 Problems 777
Case Problem Dealer’s Absorbing State Probabilities in Blackjack 781
Appendix 16.1 Matrix Notation and Operations 782 Appendix 16.2 Matrix Inversion with Excel 785
Chapter 17 Linear Programming: Simplex Method On Website
17.1 An Algebraic Overview of the Simplex Method 17-2
Algebraic Properties of the Simplex Method 17-3Determining a Basic Solution 17-3
Basic Feasible Solution 17-4
17.2 Tableau Form 17-5 17.3 Setting up the Initial Simplex Tableau 17-7 17.4 Improving the Solution 17-10
17.5 Calculating the Next Tableau 17-12
Interpreting the Results of an Iteration 17-15Moving Toward a Better Solution 17-15Interpreting the Optimal Solution 17-18Summary of the Simplex Method 17-19
Trang 2317.6 Tableau Form: The General Case 17-20
Greater-Than-or-Equal-to Constraints 17-20
Equality Constraints 17-24
Eliminating Negative Right-Hand-Side Values 17-25
Summary of the Steps to Create Tableau Form 17-26
17.7 Solving a Minimization Problem 17-27
18.1 Sensitivity Analysis with the Simplex Tableau 18-2
Objective Function Coefficients 18-2
Right-Hand-Side Values 18-6
Simultaneous Changes 18-13
18.2 Duality 18-14
Economic Interpretation of the Dual Variables 18-16
Using the Dual to Identify the Primal Solution 18-18
Finding the Dual of Any Primal Problem 18-18
Summary 18-20
Glossary 18-21
Problems 18-21
Chapter 19 Solution Procedures for Transportation
and Assignment Problems On Website
19.1 Transportation Simplex Method: A Special-Purpose Solution
Procedure 19-2
Phase I: Finding an Initial Feasible Solution 19-2
Phase II: Iterating to the Optimal Solution 19-7
Summary of the Transportation Simplex Method 19-17
Problem Variations 19-17
19.2 Assignment Problem: A Special-Purpose Solution Procedure 19-18
Finding the Minimum Number of Lines 19-21
Problem Variations 19-21
Glossary 19-25
Problems 19-26
Trang 24Chapter 20 Minimal Spanning Tree On Website
A Minimal Spanning Tree Algorithm 20-2
Glossary 20-5 Problems 20-5
Chapter 21 Dynamic Programming On Website
21.1 A Shortest-Route Problem 21-2 21.2 Dynamic Programming Notation 21-6 21.3 The Knapsack Problem 21-10
21.4 A Production and Inventory Control Problem 21-16 Summary 21-20
Glossary 21-21 Problems 21-22 Case Problem Process Design 21-26Appendixes 787
Appendix A Building Spreadsheet Models 788 Appendix B Areas for the Standard Normal Distribution 815 Appendix C Values of eⴚλ 817
Appendix D References and Bibliography 818 Appendix E Self-Test Solutions and Answers
to Even-Numbered Problems 820 Index 853
Trang 27We are very excited to publish the revised thirteenth edition of a text that has been a leader
in the field for over 20 years The purpose of this revised thirteenth edition, as with ous editions, is to provide undergraduate and graduate students with a sound conceptualunderstanding of the role that management science plays in the decision-making process.The text describes many of the applications where management science is used success-fully Former users of this text have told us that the applications we describe have led them
previ-to find new ways previ-to use management science in their organizations
An Introduction to Management Science is applications oriented and continues to use
the problem-scenario approach that is a hallmark of every edition of the text Using theproblem-scenario approach, we describe a problem in conjunction with the managementscience model being introduced The model is then solved to generate a solution and rec-ommendation to management We have found that this approach helps to motivate the stu-dent by not only demonstrating how the procedure works, but also how it contributes to thedecision-making process
From the very first edition we have been committed to the challenge of writing a book that would help make the mathematical and technical concepts of management sci-ence understandable and useful to students of business and economics Judging from theresponses from our teaching colleagues and thousands of students, we have successfullymet the challenge Indeed, it is the helpful comments and suggestions of many loyal usersthat have been a major reason why the text is so successful
text-Throughout the text we have utilized generally accepted notation for the topic beingcovered so those students who pursue study beyond the level of this text should be comfort-able reading more advanced material To assist in further study, a references and bibliogra-phy section is included at the back of the book
CHANGES IN THE REVISED THIRTEENTH EDITION
about it and want to tell you about some of the changes we have made and why
2010 This involves some changes in the user interface of Excel and major changes in the terface and functionality of Excel Solver The Solver in Excel 2010 is more reliable than inprevious editions and offers new alternatives such as a multistart option for difficult nonlin-ear problems
in-New Member of the ASWM Team
Prior to getting into the content changes, we want to announce that we are adding a newmember to the ASWM author team His name is Jeffrey Camm Jeff received his Ph.D.from Clemson University He has been at the University of Cincinnati since 1984, and hasbeen a visiting scholar at Stanford University and a visiting professor of business adminis-tration at the Tuck School of Business at Dartmouth College Jeff has published over 30 pa-pers in the general area of optimization applied to problems in operations management Atthe University of Cincinnati, he was named the Dornoff Fellow of Teaching Excellence and
Trang 28he was the 2006 recipient of the INFORMS Prize for the Teaching of Operations Research
of INFORMS Transactions on Education We welcome Jeff to the new ASWCM team and
expect the new ideas from Jeff will make the text even better in the years to come
In preparing this thirteenth edition, we have been careful to maintain the overall formatand approach of the previous edition However, based on our classroom experiences andsuggestions from users of previous editions, a number of changes have been made to en-hance the text
Made the Book Less Reliant on Specific Software
The first eight chapters on optimization no longer use output from The Management tist software All figures illustrating computer output are generic and are totally indepen-dent of software selection This provides flexibility for the instructor In addition, weprovide appendices that describe how to use Excel Solver and LINGO For every modelillustrated in the text we have both Excel and LINGO files available at the website Priorusers of The Management Scientist wishing to upgrade to similar software should considerusing LINGO This will be an easy transition and LINGO is far more flexible than TheManagement Scientist The documented LINGO models (not available in MS 12e), avail-able at the website, will aide in the transition Excel Solver and LINGO have an advantageover The Management Scientist in that they do not require the user to move all variables tothe left-hand side of the constraint This eliminates the need to algebraically manipulate themodel and allows the student to enter the model in the computer in its more natural form.For users wishing to use The Management Scientist, it will continue to be available on thewebsite for the text
Scien-New Appendix A: Building Spreadsheet Models
This appendix will prove useful to professors and students wishing to solve optimizationmodels with Excel Solver The appendix also contains a section on the principles of goodspreadsheet modeling and a section on auditing tips Exercises are also provided
Chapter 15 Thoroughly Revised
Chapter 15, Times Series Analysis and Forecasting, has been thoroughly revised The vised chapter is more focused on time series data and methods A new section on forecastaccuracy has been added and there is more emphasis on curve fitting A new section onnonlinear trend has been added In order to better integrate this chapter with the text, weshow how finding the best parameter values in forecasting models is an application ofoptimization, and illustrate with Excel Solver and LINGO
re-New Project Management Software
In Chapter 9, Project Scheduling: PERT/CPM, we added an appendix on Microsoft OfficeProject This popular software is a valuable aid for project management and is software thatthe student may well encounter on the job This software is available on the CD that ispackaged with every new copy of the text
Chapter 3 Significantly Revised
We significantly revised Chapter 3, Linear Programming: Sensitivity Analysis and pretation of Solution The material is now presented in a more up-to-date fashion andemphasizes the ease of using software to analyze optimization models
Trang 29Inter-New Management Science in Action, Cases, and Problems
Management Science in Action is the name of the short summaries that describe how thematerial covered in a chapter has been used in practice In this edition you will find numer-ous Management Science in Action vignettes, cases, and homework problems
Other Content Changes
A variety of other changes, too numerous to mention individually, have been madethroughout the text in responses to suggestions of users and our students
COMPUTER SOFTWARE INTEGRATION
We have been careful to write the text so that it is not dependent on any particular softwarepackage But, we have included materials that facilitate using our text with several ofthe more popular software packages The following software and files are available on thewebsite for the text:
text,
Microsoft Project is provided on the CD that is packaged with every new copy of the text
FEATURES AND PEDAGOGY
We have continued many of the features that appeared in previous editions Some of theimportant ones are noted here
Annotations
Annotations that highlight key points and provide additional insights for the student are acontinuing feature of this edition These annotations, which appear in the margins, aredesigned to provide emphasis and enhance understanding of the terms and concepts beingpresented in the text
Notes and Comments
At the end of many sections, we provide Notes and Comments designed to give the studentadditional insights about the statistical methodology and its application Notes and Com-ments include warnings about or limitations of the methodology, recommendations forapplication, brief descriptions of additional technical considerations, and other matters
Self-Test Exercises
Certain exercises are identified as self-test exercises Completely worked-out solutions forthose exercises are provided in an appendix at the end of the text Students can attempt theself-test exercises and immediately check the solution to evaluate their understanding ofthe concepts presented in the chapter
Trang 30ACKNOWLEDGMENTS
We owe a debt to many of our academic colleagues and friends for their helpful commentsand suggestions during the development of this and previous editions Our associates fromorganizations who supplied several of the Management Science in Action vignettes make amajor contribution to the text These individuals are cited in a credit line associated witheach vignette
We are also indebted to our senior acquisitions editor, Charles McCormick, Jr.; ourmarketing communications manager, Libby Shipp; our developmental editor, MaggieKubale; our content project manager, Jacquelyn K Featherly; our media editor, ChrisValentine; and others at Cengage Business and Economics for their counsel and supportduring the preparation of this text We also wish to thank Lynn Lustberg, Project Manager
at MPS Content Services for her help in manuscript preparation
David R Anderson Dennis J Sweeney Thomas A Williams Jeffrey D Camm Kipp Martin
Trang 31About the Authors
David R Anderson. David R Anderson is Professor Emeritus of Quantitative Analysis
in the College of Business Administration at the University of Cincinnati Born in GrandForks, North Dakota, he earned his B.S., M.S., and Ph.D degrees from Purdue University.Professor Anderson has served as Head of the Department of Quantitative Analysis andOperations Management and as Associate Dean of the College of Business Administration
In addition, he was the coordinator of the College’s first Executive Program
At the University of Cincinnati, Professor Anderson has taught introductory statisticsfor business students as well as graduate-level courses in regression analysis, multivariateanalysis, and management science He has also taught statistical courses at the Department
of Labor in Washington, D.C He has been honored with nominations and awards for cellence in teaching and excellence in service to student organizations
ex-Professor Anderson has coauthored ten textbooks in the areas of statistics, ment science, linear programming, and production and operations management He is anactive consultant in the field of sampling and statistical methods
manage-Dennis J Sweeney. Dennis J Sweeney is Professor Emeritus of Quantitative Analysisand Founder of the Center for Productivity Improvement at the University of Cincinnati.Born in Des Moines, Iowa, he earned a B.S.B.A degree from Drake University and hisM.B.A and D.B.A degrees from Indiana University, where he was an NDEA Fellow Dur-ing 1978–79, Professor Sweeney worked in the management science group at Procter &Gamble; during 1981–82, he was a visiting professor at Duke University ProfessorSweeney served as Head of the Department of Quantitative Analysis and as AssociateDean of the College of Business Administration at the University of Cincinnati
Professor Sweeney has published more than thirty articles and monographs in the area
of management science and statistics The National Science Foundation, IBM, Procter &Gamble, Federated Department Stores, Kroger, and Cincinnati Gas & Electric have funded
Mathematical Programming, Decision Sciences, and other journals.
Professor Sweeney has coauthored ten textbooks in the areas of statistics, managementscience, linear programming, and production and operations management
Thomas A Williams. Thomas A Williams is Professor Emeritus of ManagementScience in the College of Business at Rochester Institute of Technology Born in Elmira,New York, he earned his B.S degree at Clarkson University He did his graduate work atRensselaer Polytechnic Institute, where he received his M.S and Ph.D degrees
Before joining the College of Business at RIT, Professor Williams served for sevenyears as a faculty member in the College of Business Administration at the University ofCincinnati, where he developed the undergraduate program in information systems andthen served as its coordinator At RIT he was the first chairman of the Decision SciencesDepartment He teaches courses in management science and statistics, as well as graduatecourses in regression and decision analysis
Trang 32Professor Williams is the coauthor of eleven textbooks in the areas of management ence, statistics, production and operations management, and mathematics He has been a
the use of data analysis to the development of large-scale regression models
Jeffrey D Camm. Jeffrey D Camm is Professor of Quantitative Analysis and Head ofthe Department of Quantitative Analysis and Operations Management at the University ofCincinnati Dr Camm earned a Ph.D in management science from Clemson Universityand a B.S in mathematics from Xavier University He has been at the University of Cincin-nati since 1984, has been a visiting scholar at Stanford University, and a visiting professor
of business administration at the Tuck School of Business at Dartmouth College Dr.Camm has published over 30 papers in the general area of optimization applied to problems
in operations management and his research has been funded by the Air Force Office of entific Research, the Office of Naval Research, and the U.S Department of Energy He wasnamed the Dornoff Fellow of Teaching Excellence by the University of Cincinnati College
Sci-of Business and he was the 2006 recipient Sci-of the INFORMS Prize for the Teaching Sci-of
Kipp Martin. Kipp Martin is Professor of Operations Research and Computing nology at the Booth School of Business, University of Chicago Born in St Bernard, Ohio,
Tech-he earned a B.A in matTech-hematics, an MBA, and a Ph.D in management science from tTech-heUniversity of Cincinnati While at the University of Chicago, Professor Martin has taughtcourses in management science, operations management, business mathematics, and infor-mation systems
Research interests include incorporating Web technologies such as XML, XSLT,XQuery, and Web Services into the mathematical modeling process; the theory of how toconstruct good mixed integer linear programming models; symbolic optimization; polyhe-dral combinatorics; methods for large scale optimization; bundle pricing models; comput-
of Computing, Management Science, Mathematical Programming, Operations Research, The Journal of Accounting Research, and other professional journals He is also the author
of The Essential Guide to Internet Business Technology (with Gail Honda) and Large Scale Linear and Integer Optimization.
Trang 33A Note Regarding Implementation
1.4 MODELS OF COST, REVENUE,AND PROFIT
Cost and Volume ModelsRevenue and Volume ModelsProfit and Volume ModelsBreakeven Analysis
TECHNIQUESMethods Used Most Frequently
Trang 34Management science, an approach to decision making based on the scientific method,makes extensive use of quantitative analysis A variety of names exists for the body ofknowledge involving quantitative approaches to decision making; in addition to manage-ment science, two other widely known and accepted names are operations research and
and decision science interchangeably.
The scientific management revolution of the early 1900s, initiated by Frederic W.Taylor, provided the foundation for the use of quantitative methods in management Butmodern management science research is generally considered to have originated during theWorld War II period, when teams were formed to deal with strategic and tactical problemsfaced by the military These teams, which often consisted of people with diverse specialties(e.g., mathematicians, engineers, and behavioral scientists), were joined together to solve
a common problem by utilizing the scientific method After the war, many of these teammembers continued their research in the field of management science
Two developments that occurred during the post–World War II period led to the growthand use of management science in nonmilitary applications First, continued researchresulted in numerous methodological developments Probably the most significant devel-opment was the discovery by George Dantzig, in 1947, of the simplex method for solvinglinear programming problems At the same time these methodological developments weretaking place, digital computers prompted a virtual explosion in computing power Computersenabled practitioners to use the methodological advances to solve a large variety of problems.The computer technology explosion continues, and personal computers can now be used tosolve problems larger than those solved on mainframe computers in the 1990s
As stated in the Preface, the purpose of the text is to provide students with a sound ceptual understanding of the role that management science plays in the decision-makingprocess We also said that the text is applications oriented To reinforce the applicationsnature of the text and provide a better understanding of the variety of applications in whichmanagement science has been used successfully, Management Science in Action articlesare presented throughout the text Each Management Science in Action article summarizes
con-an application of mcon-anagement science in practice The first Mcon-anagement Science in Action
in this chapter, Revenue Management at American Airlines, describes one of the mostsignificant applications of management science in the airline industry
MANAGEMENT SCIENCE IN ACTIONREVENUE MANAGEMENT AT AMERICAN AIRLINES*
One of the great success stories in management
sci-ence involves the work done by the operations
re-search (OR) group at American Airlines In 1982,
Thomas M Cook joined a group of 12 operations
research analysts at American Airlines Under
Cook’s guidance, the OR group quickly grew to a
staff of 75 professionals who developed models
and conducted studies to support senior
manage-ment decision making Today the OR group is
called Sabre and employs 10,000 professionals
worldwide
One of the most significant applications oped by the OR group came about because of the
devel-deregulation of the airline industry in the late
1970s As a result of deregulation, a number oflow-cost airlines were able to move into the market
by selling seats at a fraction of the price charged
by established carriers such as American Airlines.Facing the question of how to compete, the ORgroup suggested offering different fare classes(discount and full fare) and in the process created
a new area of management science referred to asyield or revenue management
The OR group used forecasting and tion techniques to determine how many seats tosell at a discount and how many seats to hold forfull fare Although the initial implementation wasrelatively crude, the group continued to improve
optimiza-According to Irv Lustig of
IBM ILOG, Inc., solution
methods developed today
are 10,000 times faster than
the ones used 15 years ago.
Trang 351.1 PROBLEM SOLVING AND DECISION MAKING
Problem solving can be defined as the process of identifying a difference between the
actual and the desired state of affairs and then taking action to resolve the difference.For problems important enough to justify the time and effort of careful analysis, the problem-solving process involves the following seven steps:
Decision making is the term generally associated with the first five steps of the
problem-solving process Thus, the first step of decision making is to identify and define the lem Decision making ends with the choosing of an alternative, which is the act of makingthe decision
prob-Let us consider the following example of the decision-making process For the momentassume that you are currently unemployed and that you would like a position that will lead
to a satisfying career Suppose that your job search has resulted in offers from companies
in Rochester, New York; Dallas, Texas; Greensboro, North Carolina; and Pittsburgh,Pennsylvania Thus, the alternatives for your decision problem can be stated as follows:
The next step of the problem-solving process involves determining the criteria that will
be used to evaluate the four alternatives Obviously, the starting salary is a factor of someimportance If salary were the only criterion of importance to you, the alternative selected
as “best” would be the one with the highest starting salary Problems in which the objective
decision problems.
Suppose that you also conclude that the potential for advancement and the location ofthe job are two other criteria of major importance Thus, the three criteria in your decisionproblem are starting salary, potential for advancement, and location Problems that involve
The next step of the decision-making process is to evaluate each of the alternativeswith respect to each criterion For example, evaluating each alternative relative to the
the forecasting and optimization models that
drive the system and to obtain better data Tom
Cook counts at least four basic generations of
rev-enue management during his tenure Each
pro-duced in excess of $100 million in incremental
profitability over its predecessor This revenue
management system at American Airlines
gener-ates nearly $1 billion annually in incremental
revenue
Today, virtually every airline uses some sort ofrevenue management system The cruise, hotel,and car rental industries also now apply revenuemanagement methods, a further tribute to the pio-neering efforts of the OR group at AmericanAirlines and its leader, Thomas M Cook
*Based on Peter Horner, “The Sabre Story,” OR/MS Today (June 2000).
Trang 36starting salary criterion is done simply by recording the starting salary for each job native Evaluating each alternative with respect to the potential for advancement and thelocation of the job is more difficult to do, however, because these evaluations are basedprimarily on subjective factors that are often difficult to quantify Suppose for now thatyou decide to measure potential for advancement and job location by rating each of thesecriteria as poor, fair, average, good, or excellent The data that you compile are shown inTable 1.1.
alter-You are now ready to make a choice from the available alternatives What makes thischoice phase so difficult is that the criteria are probably not all equally important, and noone alternative is “best” with regard to all criteria Although we will present a method fordealing with situations like this one later in the text, for now let us suppose that after a care-ful evaluation of the data in Table 1.1, you decide to select alternative 3; alternative 3 is thus
At this point in time, the decision-making process is complete In summary, we see thatthis process involves five steps:
Note that missing from this list are the last two steps in the problem-solving process: plementing the selected alternative and evaluating the results to determine whether a satis-factory solution has been obtained This omission is not meant to diminish the importance
making as compared to the term problem solving Figure 1.1 summarizes the relationship
between these two concepts
1.2 QUANTITATIVE ANALYSIS AND DECISION MAKING
Consider the flowchart presented in Figure 1.2 Note that it combines the first three steps ofthe decision-making process under the heading of “Structuring the Problem” and the lattertwo steps under the heading “Analyzing the Problem.” Let us now consider in greater de-tail how to carry out the set of activities that make up the decision-making process.Figure 1.3 shows that the analysis phase of the decision-making process may taketwo basic forms: qualitative and quantitative Qualitative analysis is based primarily onthe manager’s judgment and experience; it includes the manager’s intuitive “feel” for theproblem and is more an art than a science If the manager has had experience with similar
TABLE 1.1 DATA FOR THE JOB EVALUATION DECISION-MAKING PROBLEM
Trang 37problems or if the problem is relatively simple, heavy emphasis may be placed upon aqualitative analysis However, if the manager has had little experience with similar prob-lems, or if the problem is sufficiently complex, then a quantitative analysis of the problemcan be an especially important consideration in the manager’s final decision.
When using the quantitative approach, an analyst will concentrate on the quantitativefacts or data associated with the problem and develop mathematical expressions that
Define the Problem
Identify the Alternatives
Determine the Criteria
Evaluate the Alternatives
Choose an Alternative
Implement the Decision
Evaluate the Results
Decision
Decision Making
Problem Solving
FIGURE 1.1 THE RELATIONSHIP BETWEEN PROBLEM SOLVING
AND DECISION MAKING
Structuring the Problem Analyzing the Problem
Choose an Alternative
Evaluate the Alternatives
Determine the Criteria
Identify the Alternatives
Define
the Problem
FIGURE 1.2 AN ALTERNATE CLASSIFICATION OF THE DECISION-MAKING PROCESS
Trang 38describe the objectives, constraints, and other relationships that exist in the problem Then,
by using one or more quantitative methods, the analyst will make a recommendation based
on the quantitative aspects of the problem
Although skills in the qualitative approach are inherent in the manager and usuallyincrease with experience, the skills of the quantitative approach can be learned only bystudying the assumptions and methods of management science A manager can increasedecision-making effectiveness by learning more about quantitative methodology and bybetter understanding its contribution to the decision-making process A manager who isknowledgeable in quantitative decision-making procedures is in a much better position tocompare and evaluate the qualitative and quantitative sources of recommendations andultimately to combine the two sources in order to make the best possible decision.The box in Figure 1.3 entitled “Quantitative Analysis” encompasses most of the sub-ject matter of this text We will consider a managerial problem, introduce the appropriatequantitative methodology, and then develop the recommended decision
In closing this section, let us briefly state some of the reasons why a quantitativeapproach might be used in the decision-making process:
the aid of quantitative analysis
the manager desires a thorough analysis before attempting to make a decision
draw
quantitative procedures to make routine decision recommendations
1.3 QUANTITATIVE ANALYSIS
From Figure 1.3, we see that quantitative analysis begins once the problem has been tured It usually takes imagination, teamwork, and considerable effort to transform a rathergeneral problem description into a well-defined problem that can be approached via quan-titative analysis The more the analyst is involved in the process of structuring the problem,
struc-Quantitative methods are
especially helpful with
large, complex problems.
For example, in the
coordination of the
thousands of tasks
associated with landing
Apollo 11 safely on the
moon, quantitative
techniques helped to ensure
that more than 300,000
pieces of work performed
Structuring the Problem
Analyzing the Problem
Make the Decision
Summary and Evaluation
Define
the
Problem
Identify the Alternatives
Determine the Criteria
Qualitative Analysis
Quantitative Analysis
FIGURE 1.3 THE ROLE OF QUALITATIVE AND QUANTITATIVE ANALYSIS
Trang 39the more likely the ensuing quantitative analysis will make an important contribution to thedecision-making process.
To successfully apply quantitative analysis to decision making, the management tist must work closely with the manager or user of the results When both the managementscientist and the manager agree that the problem has been adequately structured, work canbegin on developing a model to represent the problem mathematically Solution procedurescan then be employed to find the best solution for the model This best solution for themodel then becomes a recommendation to the decision maker The process of developingand solving models is the essence of the quantitative analysis process
scien-Model Development
Models are representations of real objects or situations and can be presented in various
forms For example, a scale model of an airplane is a representation of a real airplane.Similarly, a child’s toy truck is a model of a real truck The model airplane and toy truckare examples of models that are physical replicas of real objects In modeling terminology,
A second classification includes models that are physical in form but do not have thesame physical appearance as the object being modeled Such models are referred to as
analog models The speedometer of an automobile is an analog model; the position of the
needle on the dial represents the speed of the automobile A thermometer is another analogmodel representing temperature
A third classification of models—the type we will primarily be studying—includesrepresentations of a problem by a system of symbols and mathematical relationships or
any quantitative approach to decision making For example, the total profit from the sale of
a product can be determined by multiplying the profit per unit by the quantity sold If we let
x represent the number of units sold and P the total profit, then, with a profit of $10 per unit,
to make inferences about how much profit will be earned if a specified quantity of a ular product is sold According to the mathematical model of equation (1.1), we would ex-
In general, experimenting with models requires less time and is less expensive than perimenting with the real object or situation A model airplane is certainly quicker and lessexpensive to build and study than the full-size airplane Similarly, the mathematical model
ex-in equation (1.1) allows a quick identification of profit expectations without actually
risk associated with experimenting with the real situation In particular, bad designs or baddecisions that cause the model airplane to crash or a mathematical model to project a
$10,000 loss can be avoided in the real situation
The value of model-based conclusions and decisions is dependent on how well themodel represents the real situation The more closely the model airplane represents the real
Trang 40airplane, the more accurate the conclusions and predictions will be Similarly, the moreclosely the mathematical model represents the company’s true profit-volume relationship,the more accurate the profit projections will be.
Because this text deals with quantitative analysis based on mathematical models, let uslook more closely at the mathematical modeling process When initially considering amanagerial problem, we usually find that the problem definition phase leads to a specificobjective, such as maximization of profit or minimization of cost, and possibly a set of re-
model and quantitative approach will depend heavily on how accurately the objective andconstraints can be expressed in terms of mathematical equations or relationships
A mathematical expression that describes the problem’s objective is referred to as the
objective function For example, the profit equation P ⫽ 10x would be an objective
func-tion for a firm attempting to maximize profit A producfunc-tion capacity constraint would benecessary if, for instance, 5 hours are required to produce each unit and only 40 hours of
week The production time constraint is given by
Herbert A Simon, a Nobel
Prize winner in economics
and an expert in decision
making, said that a
mathematical model does
not have to be exact; it just
has to be close enough to
provide better results than
can be obtained by common
sense.
(1.2)5x … 40
production time required must be less than or equal to the 40 hours available
The decision problem or question is the following: How many units of the productshould be scheduled each week to maximize profit? A complete mathematical model forthis simple production problem is
The x ⱖ 0 constraint requires the production quantity x to be greater than or equal to
zero, which simply recognizes the fact that it is not possible to manufacture a negativenumber of units The optimal solution to this model can be easily calculated and is given by
x ⫽ 8, with an associated profit of $80 This model is an example of a linear programmingmodel In subsequent chapters we will discuss more complicated mathematical models andlearn how to solve them in situations where the answers are not nearly so obvious
In the preceding mathematical model, the profit per unit ($10), the production time perunit (5 hours), and the production capacity (40 hours) are environmental factors that are notunder the control of the manager or decision maker Such environmental factors, which can
inputs to the model Inputs that are controlled or determined by the decision maker are
x is the controllable input to the model Controllable inputs are the decision alternatives
Once all controllable and uncontrollable inputs are specified, the objective functionand constraints can be evaluated and the output of the model determined In this sense,the output of the model is simply the projection of what would happen if those particular
5x … 40
x Ú 0 f constraints
Maximizesubject to (s.t.)
P = 10x objective function