book

Quantitative Analysis for Management, 13/e

by Barry Render, Ralph M. Stair, Michael E. Hanna, Trevor S. Hale

January 2017

Beginner to intermediate

280 pages

217h 11m

English

Pearson

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OverviewSpecial FeaturesSignificant Changes to the Thirteenth EditionOnline ModulesSoftwareCompanion WebsiteInstructor Resources
Learning Objectives
Defining the ProblemDeveloping a ModelAcquiring Input DataDeveloping a SolutionTesting the SolutionAnalyzing the Results and Sensitivity AnalysisImplementing the ResultsThe Quantitative Analysis Approach and Modeling in the Real World
The Advantages of Mathematical ModelingMathematical Models Categorized by Risk

Defining the ProblemConflicting ViewpointsImpact on Other DepartmentsBeginning AssumptionsSolution OutdatedDeveloping a ModelFitting the Textbook ModelsUnderstanding the ModelAcquiring Input DataUsing Accounting DataValidity of DataDeveloping a SolutionHard-to-Understand MathematicsOnly One Answer is LimitingTesting the SolutionAnalyzing the Results
Lack of Commitment and Resistance to ChangeLack of Commitment by Quantitative Analysts
Discussion QuestionsProblems
Learning Objectives
Two Basic Rules of ProbabilityTypes of ProbabilityMutually Exclusive and Collectively Exhaustive EventsUnions and Intersections of EventsProbability Rules for Unions, Intersections, and Conditional Probabilities
General Form of Bayes’ Theorem
Probability Distribution of a Discrete Random VariableExpected Value of a Discrete Probability DistributionVariance of a Discrete Probability DistributionProbability Distribution of a Continuous Random Variable
Solving Problems with the Binomial FormulaSolving Problems with Binomial Tables
Area Under the Normal CurveUsing the Standard Normal TableHaynes Construction Company ExampleThe Empirical Rule
Arnold’s Muffler Example
Solution Solution Solution Solution Solution Solution Solution Solution
Discussion Questions Problems
Learning Objectives
OptimisticPessimistic Criterion of Realism (Hurwicz Criterion) Equally Likely (Laplace) Minimax Regret
Expected Monetary Value Expected Value of Perfect Information Expected Opportunity Loss Sensitivity Analysis A Minimization Example
QM for Windows Excel QM
Efficiency of Sample Information Sensitivity Analysis
Calculating Revised Probabilities Potential Problem in Using Survey Results
Measuring Utility and Constructing a Utility Curve Utility as a Decision-Making Criterion
SolutionSolution Solution Solution
Discussion Questions Problems
Learning Objectives
Coefficient of DeterminationCorrelation Coefficient
Estimating the Variance
Triple A Construction ExampleThe Analysis of Variance (ANOVA) TableTriple A Construction ANOVA Example
Excel 2016Excel QMQM for Windows
Evaluating the Multiple Regression ModelJenny Wilson Realty Example
Stepwise RegressionMulticollinearity
SolutionSolution
Discussion QuestionsProblems
Learning Objectives
Qualitative ModelsCausal ModelsTime-Series Models
Moving AveragesWallace Garden Supply ExampleWeighted Moving AveragesExponential SmoothingGetting StartedPort of Baltimore ExampleUsing Software for Forecasting Time Series
Exponential Smoothing with TrendTrend Projections
Seasonal IndicesCalculating Seasonal Indices with No TrendCalculating Seasonal Indices with Trend
The Decomposition MethodSoftware for DecompositionUsing Regression with Trend and Seasonal Components
Adaptive Smoothing
SolutionSolution
Discussion QuestionsProblemsBibliography
Learning Objectives
Decoupling FunctionStoring ResourcesIrregular Supply and DemandQuantity DiscountsAvoiding Stockouts and Shortages
Inventory Costs in the EOQ SituationFinding the EOQSumco Pump Company ExampleUsing Excel QM for Basic EOQ Inventory ProblemsPurchase Cost of Inventory ItemsSensitivity Analysis with the EOQ Model
Annual Carrying Cost for Production Run ModelAnnual Setup Cost or Annual Ordering CostDetermining the Optimal Production QuantityBrown Manufacturing ExampleUsing Excel QM for Production Run Models
Brass Department Store ExampleUsing Excel QM for Quantity Discount Problems
Marginal Analysis with Discrete DistributionsCafé du Donut ExampleMarginal Analysis with the Normal DistributionNewspaper Example
Material Structure TreeGross and Net Material Requirements PlansTwo or More End Products
SolutionSolutionSolutionSolutionSolution
Discussion QuestionsProblemsBibliographyAppendix 6.1: Inventory Control with QM for Windows
Learning Objectives
Flair Furniture Company
Graphical Representation of ConstraintsIsoprofit Line Solution Method
Using QM for WindowsUsing Excel’s Solver Command to Solve LP ProblemsPreparing the Spreadsheet For SolverUsing SolverUsing Excel QM
Holiday Meal Turkey RanchUsing The Corner Point Method On A Minimization ProblemIsocost Line Approach
No Feasible SolutionUnboundednessRedundancyAlternate Optimal Solutions
High Note Sound CompanyChanges in the Objective Function CoefficientQM for Windows and Changes in Objective Function CoefficientsExcel Solver and Changes in Objective Function CoefficientsChanges in the Technological CoefficientsChanges in the Resources or Right-Hand-Side ValuesQM for Windows and Changes in Right-Hand-Side ValuesExcel Solver and Changes in Right-Hand-Side Values
SolutionSolutionSolutionSolution
Discussion QuestionsProblemsDiscussion QuestionsBibliography
Learning Objectives
Media SelectionMarketing Research
Production MixProduction Scheduling
Labor Planning
Portfolio SelectionTruck Loading Problem
Diet ProblemsIngredient Mix and Blending Problems
Learning Objectives
Linear Program for the Transportation ExampleSolving Transportation Problems Using Computer SoftwareA General LP Model for Transportation ProblemsFacility Location Analysis
Linear Program for Assignment Example
Linear Program for Transshipment Example
Solution
Discussion QuestionsProblems*BibliographyAppendix 9.1: Using QM for Windows
Learning Objectives
Harrison Electric Company Example of Integer ProgrammingUsing Software to Solve the Harrison Integer Programming ProblemMixed-Integer Programming Problem ExampleUsing QM For Windows And Excel to Solve Bagwell’s Integer Programming Model
Capital Budgeting ExampleLimiting the Number of Alternatives SelectedDependent SelectionsFixed-Charge Problem ExampleFinancial Investment Example
Extension to Equally Important Multiple GoalsRanking Goals with Priority LevelsGoal Programming with Weighted GoalsUsing QM For Windows To Solve Harrison’s Problem
Nonlinear Objective Function and Linear ConstraintsBoth Nonlinear Objective Function and Nonlinear ConstraintsLinear Objective Function with Nonlinear Constraints
SolutionSolutionSolution
Discussion QuestionsProblemsBibliography
Learning Objectives
General Foundry Example of PERT/CPMDrawing the PERT/CPM NetworkActivity TimesHow to Find the Critical PathEarliest TimesLatest TimesConcept Of Slack In Critical Path ComputationsProbability of Project CompletionWhat PERT Was Able to ProvideUsing Excel QM for the General Foundry ExampleSensitivity Analysis and Project Management
Planning and Scheduling Project Costs: Budgeting ProcessBudgeting For General FoundryMonitoring and Controlling Project Costs
General Foundry ExampleProject Crashing with Linear ProgrammingObjective FunctionCrash Time ConstraintsProject Completion ConstraintConstraints Describing The Network
SubprojectsMilestonesResource LevelingSoftware
SolutionSolution
Discussion QuestionsProblemsDiscussion Question
Learning Objectives
Three Rivers Shipping Company Example
Arrival CharacteristicsSize Of The Calling PopulationPattern Of Arrivals At The SystemBehavior Of The ArrivalsWaiting Line CharacteristicsService Facility CharacteristicsBasic Queuing System ConfigurationsService Time DistributionIdentifying Models Using Kendall Notation
Assumptions of the ModelQueuing EquationsArnold’s Muffler Shop CaseUsing Excel QM On The Arnold’s Muffler Shop QueueIntroducing Costs Into The ModelEnhancing the Queuing Environment
Equations for the Multichannel Queuing ModelArnold’s Muffler Shop RevisitedUsing Excel QM For Analysis Of Arnold’s Multichannel Queuing Model
Equations for the Constant Service Time ModelGarcia-Golding Recycling, Inc.Using Excel QM For Garcia-Golding’s Constant Service Time Model
Equations for the Finite Population ModelDepartment of Commerce ExampleSolving The Department Of Commerce Finite Population Model With Excel QM
SolutionSolutionSolutionSolution
Discussion QuestionsProblems
Learning Objectives
Harry’s Auto Tire ExampleStep 1: Establishing Probability Distributions.Step 2: Building a Cumulative Probability Distribution for Each Variable.Step 3: Setting Random Number Intervals.Step 4: Generating Random Numbers.Step 5: Simulating the Experiment.Using QM for Windows for SimulationSimulation with Excel Spreadsheets
Simkin’s Hardware StoreAnalyzing Simkin’s Inventory Costs
Port of New OrleansUsing Excel to Simulate the Port of New Orleans Queuing Problem
Three Hills Power CompanyColumn 1: Breakdown NumberColumn 2: Random Number for BreakdownsColumn 3: Time Between BreakdownsColumn 4: Time of BreakdownColumn 5: Time Repairperson Is Free to Begin RepairColumn 6: Random Number for Repair TimeColumn 7: Repair Time RequiredColumn 8: Time Repair EndsColumn 9: Number of Hours the Machine Is DownCost Analysis of the SimulationBuilding An Excel Simulation Model For Three Hills Power Company
Two Other Types of Simulation ModelsOperational GamingSystems SimulationVerification and ValidationRole of Computers in Simulation
SolutionSolution
Discussion QuestionsProblems
Learning Objectives
The Vector of State Probabilities for Grocery Store Example
Transition Probabilities for Grocery Store Example
SolutionSolution
Discussion QuestionsProblems
Learning Objectives
Variability in the ProcessBuilding Control ChartsNatural VariationsAssignable Variations
The Central Limit TheoremSetting X -Chart LimitsBox-Filling ExampleUsing Excel QM For Box-Filling ExampleSuper Cola ExampleUsing Excel QM For Super Cola ExampleSetting Range Chart LimitsRange Example
p-ChartsARCO p-Chart ExampleUsing Excel QM For p-Chartsc-ChartsRed Top Cab Company c-Chart ExampleUsing Excel QM For c-Charts
SolutionSolutionSolution
Discussion QuestionsProblems
Learning Objectives
Barclay Brothers Company’s New Product DecisionProbability Distribution of DemandUsing Expected Monetary Value to Make a Decision
Opportunity Loss FunctionExpected Opportunity Loss
SolutionSolution
Discussion QuestionsProblems
Learning Objectives
SolutionSolution
Discussion QuestionsProblemsBibliography

Content preview from Quantitative Analysis for Management, 13/e

10.4 Nonlinear Programming

Linear, integer, and goal programming all assume that a problem’s objective function and constraints are linear. That means that they contain no nonlinear terms such as $X_{1} 3, 1 / X_{2}, log X_{3}$ , or $5 X_{1} X_{2}$ . Yet in many mathematical programming problems, the objective function and/or one or more of the constraints are nonlinear.

Unlike with linear programming methods, computational procedures for solving many nonlinear programming (NLP) problems do not always yield an optimal solution. In many NLP problems, a particular solution may be better than any other point nearby, but it may not be the overall best point. This is called a local optimum, and the overall best solution is called the global optimum. Thus, for a particular ...

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ISBN: 9780134543161