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Operations research : an introduction

Author: Hamdy A Taha
Publisher: Upper Saddle River, N.J. : Pearson/Prentice Hall, ©2011
Edition/Format:   Print book : English : 9. ed., Int. edView all editions and formats
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Document Type: Book
All Authors / Contributors: Hamdy A Taha
ISBN: 9780131391994 0131391992
OCLC Number: 900473152
Notes: Table of Contents Chapter 1: What Is Operations Research? 1.1 Operations Research Models 1.2 Solving the OR Model 1.3 Queuing and Simulation Models 1.4 Art of Modeling 1.5 More Than Just Mathematics ... 1.6 Phases of an OR Study 1.7 About This Book References Chapter 2: Modeling with Linear Programming 2.1 Two-Variable LP Model 2.1.1 Properties of the LP Model 2.2 Graphical LP Solution 2.2.1 Solution of a Maximization Model 2.2.2 Solution of a Minimization Model 2.3 Computer Solution with Excel Solver and AMPL 2.3.1 LP Solution with Excel Solver 2.3.2 LP Solution with AMPL 2.4 Linear Programming Applications 2.4.1 Investment 2.4.2 Production Planning and Inventory Control 2.4.3 Manpower Planning 2.4.4 Urban Development Planning 2.4.5 Blending and Refining 2.4.6 Additional LP Applications References Chapter 3: The Simplex Method and Sensitivity Analysis 3.1 LP Solution Space in Equation Form 3.2 Transition from Graphical to Algebraic Solution 3.3 The simplex Method 3.3.1 Iterative Nature of the Simplex Method 3.3.2 Computational Details of the Simplex Algorithm 3.4 Artificial Starting Solution 3.4.1 M-Method 3.4.2 Two-Phase Method 3.5 Special Cases in Simplex Method Application 3.5.1 Degeneracy 3.5.2 Alternative Optima 3.5.3 Unbounded Solution 3.5.4 Infeasible Solution 3.6 Sensitivity Analysis 3.6.1 Graphical Sensitivity Analysis 3.6.2 Algebraic Sensitivity Analysis-Right-hand Side of the Constraints 3.6.3 Algebraic Sensitivity Analysis-Objective-Function Coefficients 3.6.4 Sensitivity Analysis with TORA, Excel Solver, and AMPL 3.7 Computational Issue in Linear Programming References Chapter 4: Duality and Post-Optimal Analysis 4.1 Definition of the Dual Problem 4.2 Primal-Dual Relationships 4.2.1 Review of Simple Matrix Operations 4.2.2 Simplex Tableau Layout 4.2.3 Optimal Dual Solution 4.2.4 Simplex Tableau Computations 4.3 Economic Interpretation of Duality 4.3.1 Eco
Description: 824 s. : illustrations ; 24 cm
Contents: Chapter 1: What Is Operations Research?1.1 Operations Research Models1.2 Solving the OR Model1.3 Queuing and Simulation Models 1.4 Art of Modeling 1.5 More Than Just Mathematics ... 1.6 Phases of an OR Study 1.7 About This BookReferences Chapter 2: Modeling with Linear Programming2.1 Two-Variable LP Model2.1.1 Properties of the LP Model2.2 Graphical LP Solution 2.2.1 Solution of a Maximization Model 2.2.2 Solution of a Minimization Model2.3 Computer Solution with Excel Solver and AMPL 2.3.1 LP Solution with Excel Solver 2.3.2 LP Solution with AMPL2.4 Linear Programming Applications2.4.1 Investment2.4.2 Production Planning and Inventory Control 2.4.3 Manpower Planning 2.4.4 Urban Development Planning 2.4.5 Blending and Refining 2.4.6 Additional LP ApplicationsReferences Chapter 3: The Simplex Method and Sensitivity Analysis3.1 LP Solution Space in Equation Form3.2 Transition from Graphical to Algebraic Solution3.3 The simplex Method3.3.1 Iterative Nature of the Simplex Method3.3.2 Computational Details of the Simplex Algorithm3.4 Artificial Starting Solution 3.4.1 M-Method 3.4.2 Two-Phase Method3.5 Special Cases in Simplex Method Application 3.5.1 Degeneracy 3.5.2 Alternative Optima 3.5.3 Unbounded Solution 3.5.4 Infeasible Solution3.6 Sensitivity Analysis 3.6.1 Graphical Sensitivity Analysis 3.6.2 Algebraic Sensitivity Analysis-Right-hand Side of the Constraints 3.6.3 Algebraic Sensitivity Analysis-Objective-Function Coefficients 3.6.4 Sensitivity Analysis with TORA, Excel Solver, and AMPL3.7 Computational Issue in Linear ProgrammingReferences Chapter 4: Duality and Post-Optimal Analysis4.1 Definition of the Dual Problem4.2 Primal-Dual Relationships 4.2.1 Review of Simple Matrix Operations 4.2.2 Simplex Tableau Layout 4.2.3 Optimal Dual Solution 4.2.4 Simplex Tableau Computations4.3 Economic Interpretation of Duality 4.3.1 Economic Interpretation of Dual Variables 4.3.2 Economic Interpretation of Dual Constraints4.4 Additional Simplex Algorithms for LP 4.4.1 Dual Simplex Algorithm 4.4.2 Generalized Simplex Algorithm4.5 Post-optimal Analysis 4.5.1 Changes Affecting Feasibility 4.5.2 Changes Affecting OptimalityReferences Chapter 5: Transportation Model and Its Variants5.1 Definition of the Transportation Model5.2 Nontraditional transportation models5.3 The transportation Algorithm5.3.1 Determination of the Starting Solution 5.3.2 Iterative Computations of the Transportation Algorithm5.4 The Assignment Model 5.4.1 The Hungarian Method 5.4.2 Simplex Explanation of the Hungarian MethodReferences Chapter 6: Network Models6.1 Network definitions6.2 Minimal Spanning tree Algorithm6.3 Shortest-Route Problem 6.3.1 Examples of the Shortest-Route Applications 6.3.2 Shortest-Route Algorithms 6.3.3 Linear Programming Formulation of the Shortest-Route Problem6.4 Maximal flow model 6.4.1 Enumeration of Cuts 6.4.2 Maximal-Flow Algorithm 6.4.3 Linear Programming Formulation of the Maximal Flow Model6.5 CPM and PERT 6.5.1 Network Representation 6.5.2 Critical Path Computations 6.5.3 Construction of the Time Schedule 6.5.4 Linear Programming Formulation of CPM 6.5.5 PERT CalculationsReferences Chapter 7: Advanced Linear Programming7.1 Fundamentals of the Simplex Method 7.1.1 From Extreme Points to Basic Solutions 7.1.2 Generalized Simplex Tableau in Matrix Form7. 2 Revised Simplex Algorithm7.3 Bounded-Variables Algorithm7.4 Duality 7.4.1 Matrix Definition of the Dual Problem 7.4.2 Optimal Dual Solution7.5 Parametric Linear Programming 7.5.1 Parametric Changes in C 7.5.2 Parametric Changes in b7.6 More Linear Programming TopicsReferences Chapter 8: Goal Programming8.1 A Goal Programming Formulation8.2 Goal Programming Algorithms 8.2.1 The Weights Method 8.2.2 The Preemptive MethodReferences Chapter 9: Integer Linear Programming9.1 Illustrative Applications9.2 Integer Programming Algorithms 9.2.1 Branch-and-Bound (B&B) Algorithm 9.2.2 Cutting-Plane AlgorithmReferences Chapter 10: Heuristic and Constraint Programming10.1 Introduction10.2 Greedy (local Search) Heuristics 10.2.1 Discrete Variable Heuristi 10.2.2 Continuous Variable Heuristic10.3 Metaheuristics 10.3.1 Tabu Search Algorithm 10.3.2 Simulated Annealing Algorithm 10.3.3 Genetic Algorithm10.4 Application of metaheuristics to Integer Linear Programs 10.4.1 ILP Tabu Algorithm 10.4.2 ILP Simulated Annealing Algorithm 10.4.3 ILP Genetic Algorithm10.5 Introduction to Constraint ProgrammingReferences Chapter 11: Traveling Salesperson Problem (TSP)11.1 Example Applications of TSP11.2 TSP Mathematical Model11.3 Exact TSP Algorithm 11.3.1 B&B Algorithm 11.3.2 Cutting-plane Algorithm11.4 Local Search Heuristics 11.4.1 Nearest-neighbor Heuristic 11.4.2 Sub-tour Reversal heuristic11.5 Metaheuristic 11.5.1 TSP Tabu Algorithm 11.5.2 TSP Simulated Annealing Algorithm 11.5.3 TSP Genetic AlgorithmReferences Chapter 12: Deterministic Dynamic Programming12.1 Recursive Nature of Computations in DP12.2 Forward and Backward Recursion12.3 Selected DP Applications 12.3.1 Knapsack/Flyaway Kit/Cargo-Loading Model 12.3.2 Workforce Size Model 12.3.3 Equipment Replacement Model 12.3.4 Investment Model 12.3.5 Inventory Models12.4 Problem of DimensionalityReferences Chapter 13: Deterministic Inventory Models13.1 General Inventory Model13.2 Role of Demand in the Development of Inventory Models13.3 Static Economic-Order-Quantity (EOQ) Models 13.3.1 Classic EOQ model 13.3.2 EOQ with Price Breaks 13.3.3 Multi-Item EOQ with Storage Limitation13.4 Dynamic EOQ Models 13.4.1 No-Setup EOQ Model 13.4.2 Setup EOQ ModelReferences Chapter 14: Review of Basic Probability14.1 Laws of Probability 14.1.1 Addition Law of Probability 14.1.2 Conditional Law of Probability14.2 Random Variables and Probability Distributions14.3 Expectation of a Random Variable 14.3.1 Mean and Variance (Standard Deviation) of a Random Variable 14.3.2 Mean and Variance of Joint Random Variables14.4 Four Common Probability Distributions 14.4.1 Binomial Distribution 14.4.2 Poisson Distribution 14.4.3 Negative Exponential Distribution 14.4.4 Normal Distribution14.5 Empirical DistributionsReferences Chapter 15: Decision Analysis and Games15.1 Decision Making under Certainty-Analytic Hierarchy Process (AHP)15.2 Decision Making under Risk 15.2.1 Expected Value Criterion 15.2.2 Variations of the Expected Value Criterion15.3 Decision under Uncertainty15.4 Game Theory 15.4.1 Optimal Solution of Two-Person Zero-Sum Games 15.4.2 Solution of Mixed Strategy GamesReferences Chapter 16: Probabilistic Inventory Models16.1 Continuous Review Models 16.1.1 "Probabilitized" EOQ Model 16.1.2 Probabilistic EOQ Model16.2 Single-Period Models 16.2.1 No Setup Model 16.2.2 Setup Model (s-S Policy)16.3 Multiperiod ModelReferences Chapter 17: Markov Chains17.1 Definition of a Markov Chain17.2 Absolute and n-Step Transition Probabilities17.3 Classification of the States in a Markov Chain17.4Steady-State Probabilities and Mean Return Times of Ergodic Chains17.5 First Passage Time17.6 Analysis of Absorbing StatesReferences Chapter 18: Queuing Systems18.1 Why Study Queues?18.2 Elements of a Queuing Model18.3 Role of Exponential Distribution18.4 Pure Birth and Death Models (Relationship Between the Exponential and Poisson Distributions) 18.4.1 Pure Birth Model 18.4.2 Pure Death Model18.5 Generalized Poisson Queuing Model18.6 Specialized Poisson Queues 18.6.1 Steady-State Measures of Performance 18.6.2 Single-Server Models 18.6.3 Multiple-Server Models 18.6.4 Machine Servicing Model-(M/M/R) :(GD/K/K),R18.7 -Pollaczek-Khintchine (P-K) Formula18.8 Other Queuing Models18.9 Queuing Decision Models 18.9.1 Cost Models 18.9.2 Aspiration Level ModelReferences Chapter 19: Simulation Modeling19.1 Monte Carlo Simulation19.2 Types of Simulation19.3 Elements of Discrete-Event Simulation 19.3.1 Generic Definition of Events 19.3.2 Sampling from Probability Distributions19.4 Generation of Random Numbers19.5 Mechanics of Discrete Simulation 19.5.1 Manual Simulation of a Single-Server Model 19.5.2 Spreadsheet-Based Simulation of the Single-Server Model 19.6 Methods for Gathering Statistical Observations 19.6.1 Subinterval Method 19.6.2 Replication Method19.7 Simulation LanguagesReferences Chapter 20: Classical Optimization Theory20.1 Unconstrained Problems 20.1.1 Necessary and Sufficient Conditions 20.1.2 The Newton-Raphson Method20.2 Constrained Problems 20.2.1 Equality Constraints 20.2.2 Inequality Constraints-Karush-Kuhn-Tucker (KKT) ConditionsReferences Chapter 21: Nonlinear Programming Algorithms21.1 Unconstrained Algorithms 21.1.1 Direct Search Method 21.1.2 Gradient Method21.2 Constrained Algorithms 21.2.1 Separable Programming 21.2.2 Quadratic Programming 21.2.3 Chance-Constrained Programming 21.2.4 Linear Combinations Method 21.2.5 SUMT AlgorithmReferencesAppendix A: Statistical TablesAppendix B: Partial Answers to Selected Problems On the CD-ROM Chapter 22-CD: Additional Network and LP algorithms22.1 Minimum-Cost Capacitated Flow Problem 22.1.1 Network Representatio 22.1.2 Linear Programming Formulation 22.1.3 Capacitated Network Simplex Algorithm Model 22.2 Decomposition Algorithm22.3 Karmarkar Interior-Point Method 22.3.1 Basic Idea of the Interior-Point Algorithm 22.3.2 Interior-Point AlgorithmReferences Chapter 23-CD: Forecasting Models23.1 Moving Average Technique23.2 Exponential Smoothing23.3 RegressionReferences Chapter 24-CD: Probabilistic Dynamic Programming24.1 A Game of Chance24.2 Investment Problem24.3 Maximization of the Event of Achieving a GoalReferences Chapter 25-CD: Markovian Decision Process25.1 Scope of the Markovian Decision Problem25.2 Finite-Stage Dynamic Programming Model25.3 Infinite-Stage Model 25.3.1 Exhaustive Enumeration Method 25.3.2 Policy Iteration Method Without Discounting 25.3.3 Policy Iteration Method with Discounting25.4 Linear Programming SolutionReferences Chapter 26-CD: Case AnalysisCase 1: Airline Fuel Allocation Using Optimum TankeringCase 2: Optimization of Heart Valves ProductionCase 3: Scheduling Appointments at Australian Tourist Commission Trade EventsCase 4: Saving Federal Travel DollarsCase 5: Optimal Ship Routing and Personnel Assignment for Naval Recruitment in ThailandCase 6: Allocation of Operating Room Time in Mount Sinai HospitalCase 7: Optimizing Trailer Payloads at PFG Building GlassCase 8: Optimization of Crosscutting and Log Allocation at WeyerhaeuserCase 9: Layout Planning for a Computer Integrated Manufacturing (CIM) FacilityCase 10: Booking Limits in Hotel ReservationsCase 11: Casey's Problem: Interpreting and Evaluating a New TestCase 14: Ordering Golfers on the Final Day of Ryder Cup MatchesCase 13: Inventory Decisions in Dell's Supply ChainCase 14: Analysis of an Internal Transport System in a Manufacturing PlantCase 15: Telephone Sales Manpower Planning at Qantas AirwaysAppendix C-CD: AMPL Modeling LanguageC.1 Rudimentary AMPL ModelC.2 Components of AMPL ModelC.3 Mathematical Expressions and Computed ParametersC.4 Subsets and Indexed SetsC.5 Accessing External Files C.5.1 Simple Read Files C.5.2 Using Print or Printf to Retrieve Output C.5.3 Input Table Files C.5.4 Output Table Files C.5.5 Spreadsheet Input/Output TablesC.6 Interactive CommandsC.7 Iterative and Conditional Execution of AMPL Commands C.8 Sensitivity Analysis using AMPLC.9 Selected AMPL Models Reference Appendix D-CD: Review of Vectors and MatricesD.1 Vectors D.1.1 Definition of a Vector D.1.2 Addition (Subtraction) of Vectors D.1.3 Multiplication of Vectors by Scalars D.1.4 Linearly Independent VectorsD.2 Matrices D.2.1 Definition of a Matrix D.2.2 Types of Matrices D.2.3 Matrix Arithmetic Operations D.2.4 Determinant of a Square Matrix D.2.5 Nonsingular Matrix D.2.6 Inverse of a Nonsingular Matrix D.2.7 Methods of Computing the Inverse of Matrix D.2.8 Matrix Manipulations Using ExcelD.3 Quadratic FormsD.4 Convex and Concave Functions ProblemsReferencesAppendix E: Case StudiesIndex
Responsibility: Hamdy A. Taha

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<http:\/\/www.worldcat.org\/title\/-\/oclc\/900473152#PublicationEvent\/upper_saddle_river_n_j_pearson_prentice_hall_2011<\/a>>\u00A0\u00A0\u00A0\u00A0a \nschema:PublicationEvent<\/a> ;\u00A0\u00A0\u00A0\nschema:location<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/5218866225#Place\/upper_saddle_river_n_j<\/a>> ; # Upper Saddle River, N.J.<\/span>\n\u00A0\u00A0\u00A0\nschema:organizer<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/5218866225#Agent\/pearson_prentice_hall<\/a>> ; # Pearson\/Prentice Hall<\/span>\n\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n\n

Content-negotiable representations<\/p>\n