1 Network Models 1.1 Basic Definitions 1 1.2 Shortest Path Problems 2 1.3 Maximum Flow Problems 8 1.4 CPM and PERT 22 1.5 Minimum Cost Network Flow Problems 42 1.6 Minimum Spanning Tree Problems 49 1.7 The Network Simplex Method 53 2 Decision Making Under Uncertainty 2.1 Decision Criteria 71 2.2 Utility Theory 75 2.3 Decision Trees 89 2.4 Bayes' Rule and Decision Trees I00 2.5 Decision Making with the Normal Distribution 106 3 Decision Making with Multiple Objectives 3.1 Multiattribute Decision Making in the Absence of Uncertainty: Goal Programming 116 3.2 Multiattribute Utility Functions 132 3.3 The Analytic Hierarchy Process 142 3.4 Pareto Optimality and Tradeoff Curves 153 4 Game Theory 4.1 Two-Person Zero-Sum and Constant-Sum Games: Saddle Points 168 4.2 Two-Person Zero-Sum Games: Randomized Strategies, Domination, and Graphical Solution 172 4.3 Linear Programming and Zero-Sum Games 181 4.4 Two-Person Non-Constant-Sum Games 194 4.5 Introduction to n-Person Game Theory 198 4.6 The Core of an n-Person Game 200 4.7 The Shapley Value 204 5 Probabilistic Dynamic Programming 5.1 When Current Stage Costs Are Uncertain, but the Next Period's State Is Certain 214 5.2 A Probabilistic Inventory Model 217 5.3 How to Maximize the Probability of a Favorable Event Occurring 221 5.4 Further Examples of Probabilistic Dynamic Programming Formulations 228 5.5 Markov Decision Processes 235
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