Contents Front Page Models Methods Computation Problems Instruction Text Contents Supplements
 Contents
 Text Contents 1 Problem Solving with Operations Research 1.1 The Problem Solving Process 1.2 Problems, Models and Methods 1.3 About the Book 1.4 Exercises Bibliography 2 Linear Programming Models 2.1 A Manufacturing Example 2.2 Computational Considerations 2.3 Terminology 2.4 Solution Characteristics 2.5 Solutions and Sensitivity Analysis 2.6 Problem Classes 2.7 Exercises Bibliography 3 Linear Programming Methods 3.1 Standard Form of Model 3.2 Preparing the Model 3.3 Geometric Properties of a Linear Program 3.4 Simplex Tableau 3.5 Information from the Simplex Form 3.6 Simplex Method Using Tableaus 3.7 Special Situations 3.8 The Initial Basic Feasible Solution 3.9 Dual Simplex Algorithm 3.10 Simplex Method Using Matrix Notation 3.11 Revised Simplex Method 3.12 Exercises Bibliography 4 Sensitivity Analysis, Duality, and Interior Point Methods 4.1 Sensitivity Analysis 4.2 The Dual Linear Program 4.3 Interior Point Methods 4.4 Exercises Bibliography 5 Network Flow Programming Models 5.1 Classical Models 5.2 Extensions of the Basic Models 5.3 Linear Programming Model 5.4 Minimum Cost Flow Problem 5.6 Exercises Bibliography 6. Network Flow Programming Methods 6.1 Transportation Problem 6.2 Shortest Path Problem 6.3 Maximum Flow Problem 6.4 Pure Minimum Cost Flow Problem 6.5 Exercises Bibliography 7 Integer Programming Models 7.1 Site Selection Example 7.2 General Considerations 7.3 System Design with Fixed Charges 7.4 Facility Location Problem 7.5 Covering and Partitioning Problems 7.6 Distance Problems 7.7 Examples 7.8 Nonlinear Objective Function 7.9 Exercises Bibliography 8 Integer Programming Methods 8.1 Greedy Algorithms 8.2 Solution by Enumeration 8.3 Branch and Bound 8.4 Cutting Plane Methods 8.5 Additional Cuts 8.6 Exercises Bibliography 9 Nonlinear Programming Models 9.1 Manufacturing Example 9.2 General Considerations 9.3 Determining Convexity 9.4 Applications 9.5 Problem Classes 9.6 Exercises Bibliography 10 Nonlinear Programming Methods 10.1 Classical Optimization 10.2 Equality Constraints 10.3 Inequality Constraints 10.4 Separable Programming 10.5 Quadratic Programming 10.6 One-Dimensional Search Methods 10.7 Multidimensional Search Methods 10.8 Exercises Bibliography 11 Models for Stochastic Processes 11.1 Continuous-Time Markov Chains 11.2 Realization of the Process 11.3 Discrete-Time Markov Chains 11.4 Examples of Stochastic Processes 11.5 Assessment of Stochastic Models 11.6 Exercises Bibliography 12 Discrete-Time Markov Chains 12.1 Transition Matrix 12.2 Multi-Step Transitions 12.3 Steady-State Solutions 12.4 Economic Analysis 12.5 Applications 12.6 Exercises Bibliography 13 Mathematics of Discrete-Time Markov Chains 13.1 State-Transition Probabilities 13.2 Classification of States 13.3 Multi-Step Transition Matrix 13.4 Transient Probability Vector 13.5 Steady-State Probabilities 13.6 Economic Analysis 13.7 First Passage Times 13.8 Absorbing State Probabilities 13.9 Exercises Bibliography 14 Continuous-Time Markov Chains 14.1 Markovian Property 14.2 Model Components 14.3 Transient Solutions 14.4 Steady-State Solutions 14.5 Design Alternatives for ATM 14.6 Birth and Death Processes 14.7 Probabilistic Transitions 14.8 Exercises Bibliography 15 Mathematics of Continuous-Time Markov Chains 15.1 Embedded Discrete-Time Markov Chain 15.2 Steady-State Probabilities 15.3 Economic Analysis 15.4 First Passage Times 15.5 Birth-Death Processes 15.6 Exercises Bibliography 16 Queueing Models 16.1 System Characteristics 16.2 Markov Queueing Systems 16.3 Non-Markov Systems 16.4 Exercises Bibliography 17 Queueing Networks and Decision Models 17.1 Jackson Networks 17.2 Network Examples 17.3 Expected Flow Time through Network 17.4 Non-Poisson Networks 17.5 Optimal Design of Queues 17.6 Systems with Travel Times 17.7 Exercises Bibliography 18 Simulation 18.1 Nature and Motivation for Simulation 18.2 Model Components 18.3 Inverse Transformation Method for Generating Random Variates 18.4 Simulating Complex Random Variables 18.5 Discrete Event Dynamic Simulation 18.6 Simulation of Inventory System 18.7 Steps in a Simulation Study 18.8 Implementation Issues 18.9 Analysis of Simulation Output 18.10 Assessment of Methodology 18.11 Exercises Bibliography

Operations Research Models and Methods
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by Paul A. Jensen
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