最优化方法课程简介

最优化方法是运筹学（72学时）课程的延续，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。

最优化方法主要讲授动态规划、图与网络优化以及存储论。动态规划部分讲授其最优性原理、最优性定理、动态规划在求解静态规划中的应用以及动态规划在多种实际问题中的应用包括资源分配问题、生产计划问题、不确定性采购问题、背包问题、复合系统工作可靠性问题、设备更新问题等；图与网络优化部分在讲授图的基本概念的基础上分别探讨最小支撑树、最短路、最大流、最小费用流等问题的算法以及匹配问题、染色问题的算法等；存储论部分分别介绍确定性存储问题以及随机性存储问题，前者根据生产是否需要一定时间以及是否允许缺货探讨了4个模型以及价格有折扣的存储问题的最优解，后者分别讨论了离散型随机存储模型（报童问题）以及连续型随机存储模型等。

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.

Optimization Method

Optimization Method is the continue class of Operations Research. This 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.

Optimization Method mainly expresses Dynamic Programming, Graph Theory, Network Optimization and Inventory Theory.

Dynamic Programming branch introduces optimality principle, optimality theorem, the application of the dynamic programming under the static programming situation and the solution to plenty of practical problems which includes resource allocation problem, production planning problem, uncertain purchase problem, the knapsack problem, the reliability problem of compound system, the equipment replacement problem and so on.

Graph Theory and Network Optimization branch introduces the algorithm of minimum spanning tree, shortest path, max-flow, minimum cost maximum flow, matching problems and chromosome problems.

Inventory Theory branch mainly interprets inventory problems under both definite and uncertain situations. The definite inventory problem discusses the optimal solution of four models whether includes the time, out of stock, price discount conditions while the uncertain situation focuses on the discrete random storage model (newspaper-boy problem) and continuous stochastic storage model problems.

《最优化方法》课程教学进度计划