运筹学（72学时）课程简介

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（72学时）主要讲授规划论的各个分支，包括线性规划、目标规划、整数线性规划、非线性规划等部分的理论及其实际应用，另外还包括排队论。线性规划部分讲授其基本定理、几何意义、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、参数规划以及包括运输问题在内的多种应用问题，其中在一类特殊的线性规划问题——运输问题部分讲授表上作业法及其应用；目标规划部分讲授多目标建模方法、算法以及应用；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；非线性规划包括无约束极值问题与约束极值问题，前者在讲授函数性质的基础上讨论下降迭代算法，包括确定搜索方向的梯度法、共轭梯度法、变尺度法等以及确定步长的一维搜索算法（包括斐波那契法、0.618法等）；后者在讨论K-T条件理论的基础上分别讲授可行方向法、制约函数法等算法以及一类特殊的非线性规划——二次规划的求解及应用。排队论部分在介绍基本知识的基础上分析M/M/1等排队模型，并介绍排队系统的最优化问题。

使用教材：《运筹学》教材编写组. 运筹学（第四版）. 北京：清华大学出版社，2012.

Operations Research (72 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 (72 class hours) mainly interprets the embracement of Programming Theory which includes Linear Programming, Goal Programming, Integral Linear Programming, Non-Linear Programming with their applications and Queuing theory.

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, Parameter Programming and variety of application problems including the Transportation Problem. As the Transportation Problem being described as a special kind of Linear Programming, the Table Dispatching Method will be primarily introduced beside its applications. 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.

Non-Linear Programming branch will be divided into Extreme-Value problems with both constrains and not. The Descent Iterative Algorithm will be discussed based on the function properties, which includes both the direction-searching methods (such as the Gradient Method, the Conjugate Gradient Method and the Variable-Metric Method) and the step-size determination methods (such as the Fibonacci Method and the 0.618 Method) during the Unconstrained Minimizations Section. As for the Constrained Extreme-Value Problem section, algorithms like the Feasible Direction Method and the Constraint function method will be introduced based on the KT condition theory. And the solution and the application of a specific Non-Linear Programming problem namely the Quadratic Programming will also be interpreted.

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.

《运筹学》课程教学进度计划