摘要
动态规划奠基于20世纪510年代初期，其主要奠基人之1 R.bellman以最优性原理为出发点，建立了动态规划理论。在近几10年来，动态规划获得了迅速的发展。在理论和应用上都出现了大量的文献。它正逐步成为国际学术界的重要学科。
本文详细的阐述了动态规划。动态规划是基于“最优性原理”它将1个复杂的多维问题分解成若干个相互依赖、联系的易于求解的低维问题。动态规划中的1些基本概念有：阶段、状态、决策、策略、状态转移方程、值函数等。基本算法方程有逆推算法基本方程、顺推算法基本方程等。为了求解实际问题首先必须对实际问题建立动态规划模型。文中就如何建立模型及应注意的1些问题作了说明。
它在经济中的应用10分广泛，涉及工业、农业、交通运输、投资、通信等各个领域各个部门。在本文中，应用动态规划理论，针对矿区建设的特点，以投资呆滞损失和欠产损失为主要优化目标，以初期投资少为次优化目标，建立了矿区建设投资最优模型，并对其求解，最后得到了结论。
关键词：动态规划；投资分析；最短路径
Abstract
The dynamic programming lays a foundation in the 1950th. R.bellman is one of its main founders that he has taken optimality principle as a starting point, established the dynamic programming theory. In the recent several dozens years, the dynamic programming has get rapid development, some literatures in the theory and the application have appeared. It is gradually becoming the important discipline of international academic circles.
Dynamic programming has been elaborated in this article. The dynamic programming is based on “the optimality principle”, which makes a complex multi-dimensional question into an easy lower question with relation to it. In dynamic programming, some basic concepts include: Stage, state, policy, strategy, equation of state shift, value function and so on. The basic algorithm equation has tow: counter projection method and along projection method. In order to solve the actual problem, we establish dynamic programming model first. In this paper, it gives some explanations to establish some dynamic programming model.
It is extremely widespread in the economical application, involves the industry, the agriculture, the transportation, the investment, and so on. In this paper, in apply of dynamic programming theory, in view of the mining area construction characteristic, take of delay loss and the shortfall in output loses as the main optimized goal, take the initial investment few as the sub optimization goal, established construction investment most superior model in the mining area, and get model solution. We get the conclusion at last.
Keywords: Dynamic programming；Investment analysis； Most short-path
前言
在决策过程中，人类在不断的探索最优决策方法。1方面从横向入手，即忽略时间对决策过程的影响，从所有可行方案中寻找最优方案，实现最优决策。这类问题由于不考虑时间因素故称为静态规划，如：线性规划、整数规划等。另1方面从纵向入手，由于问题的复杂、环节多、时间长，往往要分阶段作多次决策，每次决策都要受其紧前决策的影响，同时又影响其紧后决策，这类问题是在时间流动过程中，依次作出决策，以实现整个动态过程的最优决策，故称为动态规划。1951年，美国数学家贝尔曼（R.Bellman）等人在研究1类多阶段决策问题时，针对这类问题的特性，提出了解决动态规划问题的核心——最优化原理，从而建立了数学规划的另1新的分支——动态规划。通过建设模型并求解，为公司得到了矿山投资最优方案，节约成本，加大利润，为公司提供了正确的决策方法。
