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Preface Contents Introduction Introduction The Origins of Operations Research The Nature of Operations Research The Impact of Operations Research Training for a Career in Operations Research The Road A head Mathematical Programming Linear Programming Prototype Example The Linear Programming Model, Assumptions of Linear Programming Additional Examples Principles of the Simplex Method Setting up the Simplex Method The Algebra of the Simplex Method The Simplex Method in fabular Form Tie Breaking in the Simplex Method Adapting to Other Model Forms A Fundamental Insight Duality Theory Conclusions Problems Special Types of Linear Programming Problems The Transportation Problem A Streamlined Simplex Method for the TransportationProblem The Transshipment Problem The Assignment Problem Multidivisional Problems Multitime Period Problems Multidivisional Multitime Period Problems Conclusions Problems The Application of Linear Programming Problem Formulation Computational Considerations Sensitivity Analysis A Case Study-School Rezoning to Achieve Racial Balance Conclusions Problems Network Analysis, Including PERT-CPM Prototype Example The Terminology of Networks The Shortest-Route Problem The Minimal Spanning Tree Problem The Maximal Flow Problem Project Planning and Control with PERT-CPM, Conclusions Problems Dynamic Programming Prototype Example Characteristics of Dynamic Programming Problems Deterministic Dynamic Programming Probabilistic Dynamic Programming Conclusions Problems Game Theory Introduction Solving Simple Games-A Prototype Example Games with Mixed Strategies Graphical Solution Procedure Solving by Linear Programming Extensions Conclusions Problems Probabilistics Models Probability Theory Introduction Sample Space Random Variables Probability and Probability Distributions Conditional Probability and Independent Events Discrete Probability Distributions Continuous Probability Distributions Expectation Moments Bivariate Probability Distribution Marginal and Conditional Probability Distributions Expectations for Bivariate Distributions Independent Random Variables and Random Samples Law of Large Numbers Central Limit Theorem Functions of Random Variables Stoc hastic Process Markov Chains Chapman-Kolmogorov Equations First Passage Time Classification of States of a Markov Chain Long-Run Properties of Markov Chains Abs orption States Continuous Parameter Markov Chains Problems Queueing Theory Prototype Example Basic Structure of Queueing Models Examples of Real Queueing Systems The Role of the Exponential Distribution The Birth-and-Death Process Queueing Models Based on the Birth-and-Death Process Queueing Models Involving Nonexponential Distributions A Priority-Discipline Queueing Model Queueing Networks Conclusions Problems The Application of Queueing Theory Examples Decision Making Formulation of Waiting-Cost Functions Decision Models The Evaluation of Travel Time Estimating Model Parameters Conclusions Problems Inventory Theory Introduction Components of Inventory Models Deterministic Models Stochastic Models Advanced Mathematical Topics in Multiperiod Stochastic Models Forecasting Conclusions Problems Markovian Decision Processes and Applications Introduction Markovian Decision Models Linear Programming and Optimal Policies Policy-Improvement Algorithms for Finding Optimal Policies Criterion of Discounted Costs A Water-Resource Model Inventory Model Conclusions Problems Reliability Introduction Structural Function of a System System Reliability Calculation of Exact System Reliability Bounds on System Reliability Bounds on Reliability Based upon Failure Times Conclusions Problems Decision Analysis Introduction Decision Making without Experimentation Decision Making with Experimentation Decision Trees Utility Function Carnival Example Conclusions Problems Simulation Illustrative Examples Formulating and Implementing a Simulation Model Experimental Design for Simulation The Cycle Method of Statistical Analysis Conclusions Problems Advanced Topics in Mathematical Programming Algorithms for Linear Programmin The Upper Bound Technique The Dual Simplex Method Parametric Linear Programming The Revised Simplex Method The Decomposition Principle for Multidivisional Problems Conclusions Problems Integer Programming Introduction The Branch-and-Bound Technique A Branch-and-Bound Algorithm for Binary Linear Programming A Bound-and-Scan Algorithm for Mixed Integer Linear Programming Formulation Possibilities through Mixed Integer Programming Conclusions Problems Nonlinear Programming The Kuhn-Tucker Conditions, Quadratic Programming Convex Programming Conclusions Problems Operations Research in Perspective Introduction Formulating the Problem Constructing a Mathematical Model Deriving a Solution Testing the Model and Solution Establishing Control over the Solution Implementation Appendixes Convexity Classical Optimization Matrices and Matrix Manipulations Simultanious Linear Equations Tables Answers to Selected Problems Index