运筹学（36学时）

运筹学是一门定量化决策科学，它利用现代数学、计算机以及其它科学的成果建立模型，研究人类从事各种活动中处理事物的数量化规律，使有限的资源得到合理利用，以获得尽可能满意的经济效益和社会效益。

《运筹学（54学时）》课程主要讲授包括线性规划、整数规划、目标规划、动态规划、图与网络分析、排队论、对策论、决策论在内的经典运筹学分支的基本理论及其实际应用。本课程着重介绍运筹学的基本原理和方法，注重结合经济管理专业实际和其它实际问题，具有一定的深度和广度。

线性规划部分讲授其模型建立、基本定理、主要算法（图解法、单纯形法）、对偶理论（包括影子价格理论、对偶单纯形法理论）、灵敏度分析以及包括运输问题在内的多种应用问题；整数线性规划部分按照递进顺序分别讲授整数规划、0-1规划、指派问题的模型性质、算法（包括割平面法、分支定界法、隐枚举法、匈牙利算法等经典算法）以及实际应用；目标规划部分讲授多目标建模方法、算法以及应用；动态规划部分讲授其最优化原理，确定性的定期多阶段决策问题和不定期多阶段决策问题的算法；图与网络部分讲授图的基本概念，几个经典优化问题（包括最小树、最短路、最大流、最小费用流及最大对集）的理论和主要算法；排队论部分在介绍基本知识的基础上分析无限源排队系统等排队模型，并介绍排队系统的最优化问题；决策分析部分主要讲授基本概念，确定性、风险型和不确定型决策分析的基本条件和方法，以及效用函数在决策中的应用和信息的价值；对策论部分主要讲授基本概念，对策的解，矩阵对策的解法，合作对策。

使用教材：《运筹学》教材编写组. 运筹学（本科版）. 北京：清华大学出版社，2012.

Operations Research (36 class hours)

Operations Research is a quantitative decision science which builds models to study the quantitative law of people’s activities in order to make rational use of the limited resources and to obtain the approving economic and social efficiency based on modern mathematics, computer and other academic achievements.

“Operations research (54 class hours)” course mainly interprets the classical Operational Research branches -- including Linear Programming, Integer Programming, Goal Programming, Dynamic Programming, Graph and Network Analysis, Queuing Theory, Game Theory, Decision Theory. This course mainly introduces the basic principle and method of operational research, with emphasis on the economic management professional practice and other practical problems.

Linear Programming branch focuses on explaining its basic definition, geometric meaning, algorithms (both the Simplex Method and the Graphic Method), Duality Theory (which includes the Shadow Price Theory and the Dual Simplex Method), Sensitivity Analysis and variety of application problems including the Transportation Problem.

Goal Programming Section centralizes on the modeling method, the algorithm and the use of the Multi-object problems.

Integral Linear Programming Section will follow a progressive order which starts from the 0-1 Programming to the Assignment Problem. The property, application and the classic algorithms (namely the Cutting-Plane Method, the Branch and Bound Method, the Implicit Enumeration Method and the Hungary algorithm) of the Assignment Problem will be particularly introduced.

Graph and Network branch will focus on the basic concepts of graph and network, the basic theories and the main algorithms of several classical optimization problems - including the minimum spanning tree, shortest path, maximum flow, minimum cost flow.

Queuing Theory branch will mainly analyze the Queuing Models such as the M/M/1 on the basic of elementary knowledge as well as the Optimization problems.

Decision Analysis branch will mainly introduce the basic concept, basic conditions of the certainty, risk and uncertainty methods and decision analysis, and the value of application and information utility function in decision making.

Game Theory part will follow mainly introduces the basic concept, the solutions of matrix game, cooperative game.

课程教学进度计划