GLOBAL EDITION Quantitative Analysis for Management THIRTEENTH EDITION Barry Render • Ralph M Stair, Jr • Michael E Hanna • Trevor S Hale Q Pearson THIRTEENTH EDITION GLOBAL EDITION QUANTITATIVE ANALYSIS for MANAGEMENT BARRYRENDER Chatles HarwoodProfessorEmeritus of ManagementScjence Crummer GtaduateSchool of Business, Rollins College RALPH M STAIR,JR ProfessorEmeritus of Informationand ManagementSciences, Florida State University MICHAEL E HANNA Professorof Decision Sciences, University of Houston—ClearLake TREVOR S HALE Associate Professorof ManagementSciences University of Houston—Downtown Pearson About the Authors his S an Rescan h and l'ti IY jn at Collcgr and of and •n ot Nev Oilcans lie tile t:nncruty in and Chao ot Ihc Sctcncc Ik•pavuocnt- Render al•.• jn Induslh Gcncral I•.lectnc.McDonnell Douglas, and NASA l)r_ Render has coauthored 10 textbooks published by Pearson in.•ludtng Modeling Spreadsheets of Afanugcmcnt.Servtce Managenn•nt,Introduction to Management S' and und Readings in AfanagejnentScience More than 100 articles by Dr, Render on of ageinent topics haxe appeared in Decision Sciences Pnnluctlon and Operations Interfaces I"fonnation and Managenwnt, Journal of Management I"/ormunon S»Items Econotnic Planning Sciences, IIE Solutions, and Operations Munugetnent Rev Dr Render has been honored as an AACSB Fellow and was named tmcc Scmoc Fulbright Scholar He was Vice President of the Decision Science Institute Southeast and ser, ed as software review editor for Decision Line for six years and as Editor of \Q- )'ork TunesOperations Management special issues for five years From 1984 to 1993 Dr was President of ManagementService Associates of Virginia, Inc qhose technolog• cbcnts included the FBI, the U.S Navy, Fairfax County.Virginia, and C&P Telephone He currently Consulting Editor to Financial TitnesPress Dr Render has taught operations management courses at Rollins College for MBA and Executive MBA programs He has received that school's Welsh Award as leading profev,oc was selected by Roosevelt University as the 1996 recipient of the St Claire Drake A*Üd Outstanding Scholarship In 2005, Dr Render received the Rollins College MBA Student A•aard for Best Overall Course, and in 2009 was named Professor of the Year by full-time MBA students Ralph Stair is ProfessorEmeritus at Florida State Uni•.ersity,He earned a B S in chenucal engtneering from Purdue University and an M.B.A from Tulane Under the gutdance ot Ken Ramsingand Alan Eliason,he receiveda Ph.D in operationsmanagetnenttiom the Uniserstts ot Oregon He has taught at the University of Oregon, the Unnersity of the Unnerstty otã New Orleans and Florida State IJni\Gòity He has taughttwice in Florida State StudyAbroad tn London (her the years his teaching has been concentrated in the of jntonnauon stems ojx•tattons research and operations lljanagenn•nt Dr Stair is a member oi several acadejnic organizations including the Institute and INIT)RM.S,and he regulavlyparticipates in national Ile numerous articles and books including Managerial Modeling Spreadsheet' Intnnluction to ManagctnentScience, and Readings in Soot v and Managetncnt: A Self-Cornauon Pringåples of Inf0nnation to ( ABOUT AUTHORS Computers world Pnnorlc• of Imumng to IORIR?IN of of n.ASlC and OJ C ORC Pn•gmmmjng his Stan He enjoys slung kayaking and ottu•t in BASIC, Michael E Hanna 'IR-lO "c Rcv•arsh a 01 an M S •n A tx•cn tc.*hjng than manageovnt Il's •ng has I of and a Ph l) tn to Outstanding Inng atol tn lianna has authon•el pobt•s.hcv" numen•us and •n and quantitat•se•rncth.ds and has 01 ( and In 1996 Ull( •l Of llcta (iamnu Sigma tum " ith the OutstandingScholarA" ard Hanna is the Decision Sciences Institutc il).Sl) •.cr•cd on Education Comnuttee the Regional Advisory Conunnttee,and lie has on the boardof directors01 D.SIfor terms and elected president of D.SluFor SWD.SI.he has held several positions Including prc•odcnt and he recencd the Distinguished Service Award in 1997 For overall prolessjon and to the unnersity he receised the UI-ICI-President's Dist•ngujshcd Scr•.xc in 2001 Trevor S Hale is AssociateProfessorof ManagementScience at the Unisersity of Housu•Dovsntovsn(UHD) He receiveda B.S in IndustrialEngineering from Penn State an M.SD Engineenng Management from Northeastern University, and a Ph.D in Resealvhfrom Texas Unisersity.He was previouslyon the faculty of both Ohio U'tuvcrseryAthens and Colorado State University—Pueblo Dr, Hale honoredthree times as an Office of Naval Research Senior Facultv Fello•a H: spent the summers of 2009, 201 1, and 2013 performing energy security/cyber security Ior the U.S Navy at Base VenturaCounty in Port Hueneme, Californiw Dr Hale has publisheddozens of articles in the areas of operationsresearch and quantit•use analysusin journals suchas the InternationalJournal of Production Rescan"', the Journal Operational Research, Annuls of Operations Reseatell, the Journal the Research Society, and the International Journal of Physical Distribution anal Management, among others He teaches quantitative analysis courses at the oi He is a senior member of both the Decision Sciences Instituteand INFORMS Brief Contents CHAPTER Introduction to Quantitative Analysis 19 CHAPTER Probability Concepts and Applications 39 CHAPTER Decision Analysts 81 CHAPTER4 Regression Models 129 CHAPTER Forecasting 165 CHAPTER Inventory Control Models 203 CHAPTER Linear Programming Models: Graphical and Computer Methods 255 CHAPTER Linear ProgrammingApplications 307 CHAPTER Transportation,Assignment, and NetworkModels 337 CHAPTER 10 Integer Programming, Goal Programming, and Nonlinear Programming375 CHAPTER 11 Project Management 405 CHAPTER 12 Waiting Lines and Queuing Theory Models 445 CHAPTER 13 Simulation Modeling 479 CHAPTER 14 MarkovAnalysis 519 CHAPTER 15 Statistical Quality Control 547 ONLINE MODULES Analytic Hierarchy Process Ml-I Dynamic Programming M2-1 Decision Theory and the Normal Distribution M3-l Game Theory M4-1 Mathematical Tools: Determinants and Matrices M5-l Calculus-Based Optimization M6-l Linear Programming:The Simplex Method M7-l Transportation, Assignment, and Network Algorithms MS-I Contents PREFACE 13 CHAPTER1 1.1 1.2 Probability Concepts and CHAPIfR Applications 39 Introduction to Quantitative Analysis 19 Is Quantitatiu• Anabsis? 20 Business Analuics 20 The Quantitatfi@ Anaßsis Approach 21 Fundajnental Concepts 40 40 Rules of Probability4') Acqu.nngInputData 2' a Solution 23 Testingthe Solution28 Egh.au•.tnt Slutually F.scluqvcand the lh•oblern 2.2 the Results and Sensitivity Events41 Unionsand Intersectionsof li•.cnts 43 ProbabilityRulesfor Unions.Inter• ccuon•, andConditionalProbabilities43 Revising Probabilities with Bayes' Theorem 45 General Form of Bayes' Theorem 46 Implementing the Results 24 Quantitative Analysis Approach and Modeling in the Real 24 1.4 2.3 2.4 2.5 How to Deselop a Quantitative Analysis Model 24 The Advantagesof MalhematicalModeling 27 Variable 50 ExpectedValueof a DiscreteProbability Distribution50 Mathematical Models Categorized Risk 27 1.5 The Role of Computers and Spreadsheet Models in the Quantitative Analysis Approach 27 Possible Problems in the Quantitative Analysis Approach 30 Definingthe Problem30 Variance of'a Discrete Probability Distribution 51 Probability Distributionof a Continuous Random Variable 52 2.6 2.7 Implementation—Not Just the Final Step 33 Lock of Commitment and Resislance to Change 34 Lack of Commilnjentby Quantilalise Analysts 34 Keyj:.qua'ions Summary _u Glossary Self-Tesl 35 DiscussionQuestionsand The Normal Distribution SO Area Under the Normal Cune SS Using the StandardNonnal Table SS I-laynesConstructionContp•unyEsaunple Analynng the Results 33 1.7 The Binomial Distribution SS Solving Problems with the Binomial Formula 54 Solving Problemswith Binomial Tables 55 Developrng a Model j Acqujnng InputData 32 Solution32 the Soluuon 32 Testing Further Probability Revisions 47 Random Variables 48 Probability Distributions 50 ProbabilityDistributionof DiscreteRandom 2.8 2.9 2.10 Tile litnpivicalRule The F Distribution The Exponential Distribution 04 Nluillej 05 The Poisson Distribution Sunil'jary Sol',ed Questionsand CaseStudy:l:oodand Ptoblctns Beveragesat SouthuestclliUniversityFootball 38 Appendix 2.1: Derivation of Hayes' OS courtnrs CHAPTER3 3.1 3.2 3.3 Decision Analysis 81 The Six Steps in Decision Making Sl Types of Decision-Making Environments 83 Decision Making Under Uncertainty S/ Optimistic 84 Pessimtstic84 Criterionof Realism Cntcnony SS Equally Likely (Laplace) SS Minimax Regret SS 3.4 4.1 tisaluanng the Multiple Jenny Wilson Realty Esamplc 146 4.8 4.9 4.10 Nonlinear Regression 149 4.11 Cautionsand Pitfallsin Regression Analysis Summary Expected Monetary Valuc S? Value Ot IntonnanonSS Expected Opportunity S" 3.5 Problems 3.8 SttÄly Appendix 4.1: off Table 5.1 How Probability Values Are Estimated by Bayesian Analysis 101 CalculatingReused Probabilities101 167 5.2 5.3 5.4 only 172 Moving Averages 172 Utility Theory WeightedMovingAscrages 172 ExponentialSmoothing174 UsingSoftwarei0r ForecastingTtrne Curve 104 Regression Models 129 Scatter Diagrams 130 Simple Linear Regression 131 Measuring the Fit of the Regression Model 132 5.5 5.6 5.7 Assumptions of the Regression Model 135 The Analysis of Variance (ANOVA)Table 140 Triple A Construction ANOVA Example 4.6 Using Computer Software for Regression 140 Excel 2016 140 Excel QM 141 0M for Windows TrendProjections ISI Adjusting for Seasonal Variations IS-' SeasonalIndices I CalculatingSeasonalIndiceswith NoTrend 183 CalculatingSeasonalIndiceswith Trend 184 ForecastingModels—Trend.Seasonal, and Random Variations ISS The DecompositionMethod ISS Softwarefor DecompositionISS Using Regression ith Tn•neland Seasonal Cotnponents ISS Estimaung the Vanunce 137 Testing the Model for Significance 137 TripleA ConstructionExajnple1 Series 176 Forecasting Models—Trendand Random Variations 178 Exponential Smoothing with Trend 17S Coefficient of Determination 134 Correlation Coefficient 134 4.5 Components of a Time-Series 167 Measures of Forecast Accuracy 169 Forecasting Models—RandomVariations Potential Problem in Using Suney Results 103 Utility as a Decision-Making Critenon 106 Summary 109 Glossary 109 KeyEquations 110 SolvedPmblems 110 Self-Test115 Discussion Quesuonsand Problems 116 CaseStudy:Staning Right Corporation 125 Case Study:Toledo Leather Company 125 Case Study: Blake Electromes 126 Bibliography 128 4.4 Types of Forecasting Models 165 Qualitative Causal Models 166 Measurmg Utility and Constructing a Utility CHAPTER 4.1 4.2 4.3 for Regression Calculations Forecasting 165 CHAPTER Decision Trees 9.S Eiftcvency of Salnplc Infonnaiton 100 SensitiSAty Analysts 100 3.7 Key I SO Solved Problcnv• 91 QM tor indows 98 3.6 Binary or Dummy Variable 147 Model Building Regression Multi€oll•ocanty 149 Decision Making Under Risk Analss•s A Using Soft" arc for Multiple Regression Analysis 144 5.8 Monitoring and Controlling Forecasts I (A) Adaptive Stnoothing 192 Sununary192 192 K' Equations Solved 19.6 Questions and Studs Itorecasnng Attendan« at U Gaines '(Å) Study sates 201 CONTENTS CHAPTER 6.1 Inventory Control Models 203 Importancc of Imcntory Control 204 7.2 'Grn•turcCompany Graphical Solution to an LP Problem Decouplingl'unctn•n 204 Stonng Resourevs Im•gular Supply and Demand Quant") Discounts and 6.2 6.3 Formulating LP Problems 25' or Solution Mcth•Äl Graphieal Suwlu Insentory Decisions Nair I'urniturc's 1.1'Problem Usin QM for Windows Excel 2016 and Economic Order Quantits: I k'tcnuining How Much to Order Solic Isurs'has•c Anan 6.4 6.5 Rc•orajctPoint: I ictermining hen to Older LOQ ithout the Instantaneous Receipt Assumption 214 Annual ing Annual Setup Cost 7.8 Sols ing Minijnitation Problems 273 7.0 Four Special Cases in LP 279 No Solution279 Uliboundcdncss 279 Redundancy280 AlternateOptimalSolutions Run Annual Ordering 7.7 6.7 6.8 High Note Sound Company 283 Changesin the ObjectiveFunction Coefficient 284 Quantity Discount Models 21S QM tor Windows and Changes an FunctionCoefficients 284 Excel Solver and Changes in Coeilicients 285 Changes in the Technological Brass Depalljnc•ntStore Example 220 Use of safety stock 221 Single-Period Insentory Models 227 Anal»is Discrete Changesin the Resourcesor Right.Hand-Side Values 287 QM tor Windowsand Changes in Right-HardSide Values 288 Distributions 228 Cafe du DonutExample 228 MarganalAnaly unh the Normal Distnbunon Excel Solver and Changes cn Right• Hand-Sb&• Values 288 Summary 290 Glossar» Neu spapc•rExample 2.Ä() 6.9 6.10 ABC Analvsis 232 Dependent Demand: The Case for Material Requirements Planning 232 Probletns 291 Questionsand Problems Sleucana Wire MaterialStructureTree 233 Gross and Net Material RequirementsPlans Tuo or Mc•reEnd Products 236 6.11 Just-in-Time Inventory Control 237 6.12 Enterprise Resource Planning 238 Summary 239 Glossary 239 Key IAua1jons240 SoJscdProblenjs 241 Questionsand Self, 243 Bibliography CHAPTER8 8.1 Studs 804 Linear ProgrammingApplications 307 Marketing Applications SO? Selection 8.2 Manufacturing Applications 311 Windows 2.53 8.3 limployee Scheduling Applications Linear Programming Models: Graphical and Computer Methods 255 8.4 Financial Applications SIS 8.5 Ingredient Illending 244 Study Marlin-I'ulljn 2S8 Bicycle Corporation 2.42 Appendix I: Sensitivity Analysis 282 lietccnumny• Optimal Production QuantiO Brouoi Manutaciunng Example IO Inventory Control with QM for Scheduling l,aboc Planning CHAPTER 7.1 Requirements of a I.inear Programrning Problem 256 conrtNts Diet Problems InglCdjc•nt and Blending Problems A34 Other Linear Programming Applications 326 8.6 10.4 9.1 RanutngGoal' Goal Pvogramnung Nonlinear Programming aruJ Nonlinear Constratnt' 110thNonlinear Constraints 891 lonear ObjectiveEurwoonWith Constra'nt» Summary 328 Self-Test Problems 329 Casc Study Cablc Moore Bibliography CHAPTER 9 Transportation, Assignment, and Network Models 337 The Transportation Problem ,/./S and Prohk•ms I-mear Program for the Case Manetjng Rc•.earch •'02 lixamplc _OS Sol' Ing Compute' CHAPIER Il Project Management405 11.1 9.2 I ineaj 9.3 Erample oi PERL•CPM The Assignment Problem Asqgnmcnl The liansshipment Problem /4S Path 410 Transshipment 9.4 What Using Maximal-How Problem 348' Exaliiplc 9.5 9.0 Shortest-Route Problem 350 Minimal-Spanning Tree Problem 352 Summary Glossary A.S6Solsed Problems Self-Test Discussion Questionsand Problems359 Case Study: Andtew—Carter, Inc 370 Case Study: Nonheastern Airlines 371 Case Study: SouthwesternUniversityTramc Problems 372 Appendix 9.1: CHAPTER 10 Sensiti'.ity 11.2 Bibliography373 Using QM for Windows 373 11.3 Integer Programming, Goal Programming, and Nonlinear 11.4 Programmjng Problem 378 Mixed-Integer Programming Problem lumitmg the Numberof Alternatives Selected 383 Dependent Selections 38.3 Fixed-Charge Problem Example 384 FmanctalIn'.cstrnentExample 10.3 Goal Programming 386 Example of Goal Programming: IIN1ison Electric Company Revisited 387 Extension to Equally ltnponant Multiple Goals 388 428 Software428 Summary428 Glossar, 42S Ke• Equations429 SoÅedProblems4SO Self-Test432 and Problelli' 43.3 CaseStud' Southuesteru 440 UniversityStadium Programming 376 Using Softqareto Sol'.ethe HarrisonInteger 10.2 MomtonngandControlling costs 421 Project Crashing 423 GeneralFoundryIÄample 424 ProjectCrashingWithLinearPro•ramnung Other Topics in Project Management 42S Subprojects 428 Milestones 428 Resource Integer Programming 376 HarnsonElectncCompanyExampleof Integer Example 378 Modeling with 0—1(Binary) Variables 381 Capital BudgetingExample 382 Proycct Management417 PERT/Cost 418 Planmng and Scheduling Pro.cct Costs BudgetingPrexes»41S Programming375 10.1 WasAble QM tot thc Plannuns•Rocarch Center Bibliography 442 Appendix 11.1: Project Management SSithQM for Case Study Nigeria 44 Windows 442 CHAPTER 12 Waiting Lines and Queuing Theory Models 445 12.1 Waiting Line Costs 446 Three 12.2 Characteristics of a Queuing System Amval Watong I,ins• VIS 10 CONTENTS •JAS Ser-occ Facility Idcntjfyvng Models Usang Kendall Role of Computers •n Strnuiatvoo Solved Glossary Sumnuo 449 SCI' • Single-Channel Queuing Model PoissonArrivals and ExponentialScrsice Ttmes(M/M/l) 452 Qucutng Amold's Enhanonsthe Multichannel Queuing Pois»yn AITisals and 12.4 and A"ltnc• 91•1 Case Study State-auk SIS Cate Study MarkovAnalysis 519 Set' ice 14.1 State Qocutng 14.2 Constant Ser•iec lime Model 14.3 Constant Ser-occ T•rnc Garcia-GoldingReocljng Inc; 461 Finite Population Model (MIMI) with 14.4 14.5 14.6 Finite Source) 401 Some General Operating Characteristic Relationships 40.8 More Complex Queuing Models and the Use of Simulation 464 Glossary465 Summary Problems 467 4t'.S Sell-Test 469 DiscussionQuestionsand Problems 470 Case Study• New England Park 47' CaseStudy 477 Hotel Appendix 12.1: Using QM for Windows 478 CHAPTER 13 13.1 13.2 13.3 13.5 Windows 543 Appendix 14.2: Markov Analysis with Excel 544 CHAPTER 15 15.1 15.2 15,4 ControlCharts for Attributes SSS KO Solsevi Appendix 15.1: Using QM for Windowsfor sec sto APPENDICES 561 APPENDIX A Areas Under the Standard Normal curve 568 APPENDIX B Binomial Probabilities 570 j'ower Cotupany 99 ControlCharts for Variables SSO Sununar» of New Oilcans Other SimulationIssues 30,' StatisticalProcessControl 549 CentralLimit •meorem S.SI Setting i-Chart Li•uits Setting Range Chart Simulation and Inventory Analysis 489 Co.' Analysisof Statistical Quality Control 547 Defining Quality and TQM 547 Variabilityin the Process S49 Harry's AutoTire Evample 482 for W.ndo•asfor Simulation 486 Using Simulation %ith lÄcel Spreadsheets 487 Simulation Model for a Maintenance Policy 497 study: Bibliography 543 Appendix 14.1: Markov Analysis with QM for 15.3 Port 01 New Oilcans 494 Simulate the Using Problem Qucutny• AbsorbingStates and the Fundamental Matrix:AccountsReceivable Problems537 Simulation Modeling 479 Adsantages and Disadvantages of Simulation 4M/ MonteCarlo Simulation 481 Simulation of a Queuing Problem Predicting Future Market Shares 323 Markov Analysisof Machine Operations 524 Equilibrium Conditions 525 Self-Test536 DiscussionQuesuons Sirnkjn•s llald•aare Store Analyzing Stmkin'•, Insentot) Co€ts 498 13.4 for Grv•cr» Application 528 Summary532 Glossary 532 Ke, Equations532 SolvedProblems-S33 [Auatjonsiol the Finne Population Model typanmenl of CommerceExample 462 12.8 Matrixof 'liansition Probabilities 522 Transition Example 522 ASS 12.7 States and State Probabilities 320 Store tat 12.s SO? SOS Case Study Values ot tot Use in the Poisson 575 ...THIRTEENTH EDITION GLOBAL EDITION QUANTITATIVE ANALYSIS for MANAGEMENT BARRYRENDER Chatles HarwoodProfessorEmeritus of ManagementScjence Crummer GtaduateSchool of Business,... software review editor for Decision Line for six years and as Editor of Q- )'ork TunesOperations Management special issues for five years From 1984 to 1993 Dr was President of ManagementService Associates... anal Management, among others He teaches quantitative analysis courses at the oi He is a senior member of both the Decision Sciences Instituteand INFORMS Brief Contents CHAPTER Introduction to Quantitative