Chapter 0 Introduction 0.1 The definitions of Operations Research 0.2 The development history of Operations Research 0.3 The nature of Operations Research Chapter 1 Linear Programming 1.1 Linear programming problems 1.2 Graphical LP solution 1.3 The standard form of the LP model 1.4 The theory of the simplex method 1.5 Simplex method and simplex tableau 1.6 Determining an initial basic feasible solution 1.7 Degenerate problem 1.8 The revised simplex algorithm Exercises Chapter 2 Dual Programming 2.1 Dual programming problem and its mathematical model 2.2 Duality theory 2.3 Dual simplex method 2.4 Shadow price 2.5 Sensitivity analysis 2.6 Parameter linear programming Exercises Chapter 3 The Transportation Problem 3.1 The transportation problem model 3.2 The tableau operation method 3.3 The unbalanced transportation problem Exercises Chapter 4 Goal Programming 4.1 The mathematical model of goal programming 4.2 Simplex method Exercises Chapter 5 Integer Programming 5.1 Mathematical model of integer programming 5.2 Branch-and-bound algorithm 5.3 Cutting-plane algorithm 5.4 The assignment problem and Hungarian Algorithm Exercises Chapter 6 Graph Theory 6.1 Graphs and subgraphs 6.2 Trees 6.3 The shortest path problem 6.4 Transportation networks 6.5 Network plan Exercises Chapter 7 Dynamic Progamming 7.1 Decision problems with multiple stages 7.2 Forward and backward recursion Exercises Chapter 8 Game Theory 8.1 The mathematical model of matrix game
8.2 The optimal strategy 8.3 Linear programming Exercises Indexes
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