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  《运筹学》(最后更新时间:2007/4/25 14:16:28)

课程编号:35116667

课程名称(中文):运筹学

课程名称(英文):Operational Reasearch

学分数/学时数:4

开课单位/开课学期:信息管理系,第四学期

课程类别:专业选修

面向专业:信息管理与信息系统

课程负责人:路永和

课程内容简介(中文):

绪论:运筹学的起源、发展与分支,运筹学的研究方法。

线性规划:线性规划模型,图解法,单纯形法,计算机求解法。

线性规划的对偶理论与灵敏度分析:对偶问题及其性质,影子价格,灵敏度分析,对偶理论在灵敏度分析上的应用,参数线性规划,目标规划。

运输和指派问题:运输问题及数学模型,运输问题的求解方法,指派问题及求解方法。

图与网络分析:图与网络基本术语,最短路径问题,最大流问题,最小费用问题,网络单纯形法。

动态规划:动态规划的模型、特征,动态规划的解法。

整数规划:整数规划的数学模型,解纯整数规划的割平面法,分枝定界法。

非线性规划:非线性规划的数学模型,图解法,一维搜索,无约束极值问题,约束极值问题。

排队论:排队系统模型,指数分布模型,非指数分布模型。

课程内容简介(英文):

Introduction: The Origins of Operations Research and Its Developments and Branches. The Operations Research modeling Approach.

Linear Programming: The Linear Programming Model. The Interrior-Point Approach. The Simplex Method in Tabular Form. Computer Implementation.

Duality Theory and Sensitivity Analysis: The Essence of Duality Theory.Economic Interpretation of Duality. The Essence of Sensitivity Analysis.The Role of Duality Theory in Sensitivity Analysis. Parametric Linear Programming. Linear Goal Programming and Its Solution Procedures.

The Transportation and Assignment Problems: The Transportation ProblemA Streamlined Simplex Method for the Transportation Problem.The Assignment Problem.

Network Analysis: The Terminology of Networks. The Shortest-Path Problem. The Minimum Spanning Tree Problem. The Maximum Flow Problem. The Minimum Cost Flow Problem. The Network Simplex Method.

Dynamic Programming: A Prototype Example for Dynamic Programming. Characteristics of Dynamic Programming Problems. Solving Dynamic Programming Problems.

Integer Programming: Some Other Formulation Possibilities with Binary Variables. Some Perspectives on Solving Integer Programming Problems. The Branch-and -Bound Technique and Its Application to Binary Integer Programming.

Nonlinear Programming: Graphical Illustration of Nonlinear Programming Problems. Types of Nonlinear Programming Problems. One-Variable Unconstrained Optimization. Multivariable Unconstrained Optimization. The Darush-Duhn-Tucher(KKT)Conditions for Constrained Optimization.

Queuing Theory: Basic Structure of Queuing Models. The Role of the Exponential Distribution.  Queuing Models Involving Non-exponential Distributions. Priority-Discipline Queuing Models.