Operations Research: An Introduction

Includes Index

Chapter 1: What is Operations Research?1.1 Operations Research Models1.2 Solving the OR Model1.3 Queueing and Simulation Models1.4 Art of Modeling1.5 More than Just Mathematics1.6 Phases of an OR Study1.7 About this Book Problems References Chapter 2: Modeling with Linear Programming2.1 Two-Variable LP Model2.2 Graphical LP Solution2.3 Selected LP Applications2.4 Computer Solution with Solver and AMPL Problems References Chapter 3: The Simplex Method and Sensitivity Analysis3.1 LP Model in Equation Form3.2 Transition from Graphical to Algebraic Solution3.3 The Simplex Method3.4 Artificial Starting Solution3.5 Special Cases in the Simplex Method 3.6 Sensitivity Analysis Problems References Chapter 4: Duality and Post-Optimal Analysis4.1 Definition of the Dual Problem4.2 Primal-Dual Relationships4.3 Economic Interpretation of Duality4.4 Additional Simplex Algorithms 4.5 Post-Optimal Analysis Problems References Chapter 5: Transportation Model and its Variants5.1 Definition of the Transportation Model5.2 Nontraditional Transportation Models5.3 The Transportation Algorithm5.4 The Assignment Model5.5 The Transshipment Model Problems References Chapter 6: Network Models6.1 Scope and Definition of Network Models6.2 Minimal Spanning Tree Algorithm6.3 Shortest-Route Problem6.4 Maximal Flow Model6.5 CPM and PERT Problems References Chapter 7: Advanced Linear Programming7.1 Simplex Method Fundamentals 7.2 Revised Simplex Method7.3 Bounded Variables Algorithm7.4 Duality7.5 Parametric Linear Programming Problems References Chapter 8: Goal Programming8.1 A Goal Programming Formulation8.2 Goal Programming Algorithms Problems References Chapter 9: Integer Linear Programming9.1 Illustrative Applications9.2 Integer Programming Algorithms9.3 Traveling Salesperson (TSP) Problem Problems References Chapter 10: Deterministic Dynamic Programming10.1 Recursive Nature of Computations in DP10.2 Forward and Backward Recursion10.3 Selected DP Applications10.4 Problem of Dimensionality Problems References Chapter 11: Deterministic Inventory Models11.1 General Inventory Model11.2 Role of Demand in the Development of Inventory Models11.3 Static Economic-Order-Quantity (EOQ) Models11.4 Dynamic EOQ Models Problems References Chapter 12: Review of Basic Probability12.1 Laws of Probability12.2 Random Variables and Probability Distributions12.3 Expectation of a Random Variable 12.4 Four Common Probability Distributions12.5 Empirical Distributions Problems References Chapter 13: Decision Analysis and Games13.1 Decision Making under Certainty-Analytic Hierarchy Process (AHP)13.2 Decision Making under Risk13.3 Decision under Uncertainty13.4 Game Theory Problems References Chapter 14: Probabilistic Inventory Models14.1 Continuous Review Models14.2 Single-Period Models14.3 Multiperiod Model Problems References Chapter 15:Queueing Systems15.1 Why Study Queues?15.2 Elements of a Queuing Model15.3 Role of Exponential Distribution15.4 Pure Birth and Death Models (Relationship between the Exponential and Poisson Distributions)15.5 Generalized Poisson Queuing Model15.6 Specialized Poisson Queues15.7 (M/G/1):(GD/Inf/Inf)-Pollaczek-Khintchine (P-K) Formula15.8 Other Queuing Models15.9 Queueing Decision Models Problems References Chapter 16: Simulation Modeling16.1 Monte Carlo Simulation16.2 Types of Simulation16.3 Elements of Discrete-Event Simulation16.4 Generation of Random Numbers16.5 Mechanics of Discrete Simulation16.6 Methods for Gathering Statistical Observations16.7 Simulation Languages Problems References 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 States Problems References Chapter 18: Classical Optimization Theory18.1 Unconstrained Problems18.2 Constrained Problems Problems References Chapter 19: Nonlinear Programming Algorithms19.1 Unconstrained Algorithms19.2 Constrained Algorithms Problems References Appendix A: AMPL Modeling LanguageA.1 Rudimentary AMPL ModelA.2 Components of AMPL ModelA.3 Mathematical Expressions and Computed ParametersA.4 Subsets and Indexed SetsA.5 Accessing External FilesA.6 Interactive CommandsA.7 Iterative and Conditional Execution of AMPL CommadsA.8 Sensitivity Analysis Using AMPL Reference Appendix B: Statistical Tables Appendix C: Partial Answers to Selected Problems Index On the CD Chapter 20: Additional Network and LP Algorithms20.1 Minimim-Cost Capacitated Flow Problem20.2 Decomposition Alogrithm20.3 Karmarkar Interior-Point Method Problems References Chapter 21: Forecasting Models21.1 Moving Average Technique21.2 Exponential Smoothing21.3 Maximization of the Event of Achieving a Goal Problems References Chapter 22: Probabilistic Dynamic Programming22.1 A Game of Chance22.2 Investment Problem22.3 Maximization of the Event of Achieving a Goal Problems References Chapter 23: Markovian Decision Process23.1 Scope of the Markovian Decision Problem23.2 Finite-Stage Dynamic Programming Model23.3 Infinite-Stage Model23.4 Linear Programming Solution Problems References Chapter 24: 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 Assignments 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 of a Computer Integrated Manufacturing (CIM) FacilityCase 10: Booking Limits in Hotel ReservationsCase 11: Casey's Problem: Interpreting and Evaluating a New TestCase 12: 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 Airways Appendix D: Review of Vectors and MatricesD.1 VectorsD.2 MatricesD.3 Quadratic FormsD.4 Convex and Concave Functions Problems References Appendix E: Case Studies