礦區(qū)投資動(dòng)態(tài)規(guī)劃分析

摘要
動(dòng)態(tài)規(guī)劃奠基于20世紀(jì)510年代初期，其主要奠基人之1 R.bellman以最優(yōu)性原理為出發(fā)點(diǎn)，建立了動(dòng)態(tài)規(guī)劃理論。在近幾10年來(lái)，動(dòng)態(tài)規(guī)劃獲得了迅速的發(fā)展。在理論和應(yīng)用上都出現(xiàn)了大量的文獻(xiàn)。它正逐步成為國(guó)際學(xué)術(shù)界的重要學(xué)科。
本文詳細(xì)的闡述了動(dòng)態(tài)規(guī)劃。動(dòng)態(tài)規(guī)劃是基于“最優(yōu)性原理”它將1個(gè)復(fù)雜的多維問題分解成若干個(gè)相互依賴、聯(lián)系的易于求解的低維問題。動(dòng)態(tài)規(guī)劃中的1些基本概念有：階段、狀態(tài)、決策、策略、狀態(tài)轉(zhuǎn)移方程、值函數(shù)等。基本算法方程有逆推算法基本方程、順推算法基本方程等。為了求解實(shí)際問題首先必須對(duì)實(shí)際問題建立動(dòng)態(tài)規(guī)劃模型。文中就如何建立模型及應(yīng)注意的1些問題作了說(shuō)明。
它在經(jīng)濟(jì)中的應(yīng)用10分廣泛，涉及工業(yè)、農(nóng)業(yè)、交通運(yùn)輸、投資、通信等各個(gè)領(lǐng)域各個(gè)部門。在本文中，應(yīng)用動(dòng)態(tài)規(guī)劃理論，針對(duì)礦區(qū)建設(shè)的特點(diǎn)，以投資呆滯損失和欠產(chǎn)損失為主要優(yōu)化目標(biāo)，以初期投資少為次優(yōu)化目標(biāo)，建立了礦區(qū)建設(shè)投資最優(yōu)模型，并對(duì)其求解，最后得到了結(jié)論。
關(guān)鍵詞：動(dòng)態(tài)規(guī)劃；投資分析；最短路徑 
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
    在決策過(guò)程中，人類在不斷的探索最優(yōu)決策方法。1方面從橫向入手，即忽略時(shí)間對(duì)決策過(guò)程的影響，從所有可行方案中尋找最優(yōu)方案，實(shí)現(xiàn)最優(yōu)決策。這類問題由于不考慮時(shí)間因素故稱為靜態(tài)規(guī)劃，如：線性規(guī)劃、整數(shù)規(guī)劃等。另1方面從縱向入手，由于問題的復(fù)雜、環(huán)節(jié)多、時(shí)間長(zhǎng)，往往要分階段作多次決策，每次決策都要受其緊前決策的影響，同時(shí)又影響其緊后決策，這類問題是在時(shí)間流動(dòng)過(guò)程中，依次作出決策，以實(shí)現(xiàn)整個(gè)動(dòng)態(tài)過(guò)程的最優(yōu)決策，故稱為動(dòng)態(tài)規(guī)劃。1951年，美國(guó)數(shù)學(xué)家貝爾曼（R.Bellman）等人在研究1類多階段決策問題時(shí)，針對(duì)這類問題的特性，提出了解決動(dòng)態(tài)規(guī)劃問題的核心——最優(yōu)化原理，從而建立了數(shù)學(xué)規(guī)劃的另1新的分支——?jiǎng)討B(tài)規(guī)劃。
本文分為兩大部分。前2章為第1部分，屬于理論范疇。第1章簡(jiǎn)短地介紹了動(dòng)態(tài)規(guī)劃的發(fā)展歷史。第2章詳細(xì)闡述了動(dòng)態(tài)規(guī)劃的基本理論，說(shuō)明了建立動(dòng)態(tài)規(guī)劃模型時(shí)應(yīng)注意的問題，建立動(dòng)態(tài)規(guī)劃的基本方程和算法。第3章為第2部分，屬于實(shí)例部分。根據(jù)前面介紹的理論知識(shí)，建立了礦區(qū)建設(shè)最優(yōu)分配的各階段動(dòng)態(tài)規(guī)劃模型。根據(jù)實(shí)際情況，即現(xiàn)有的內(nèi)部約束條件和外部約束條件，以呆滯損失和欠產(chǎn)損失為主要優(yōu)化目標(biāo)，以前期投資為最少為次優(yōu)化目標(biāo)，建立了動(dòng)態(tài)規(guī)劃模型并求解，得到了礦山最優(yōu)投資方案。
通過(guò)建設(shè)模型并求解，為公司得到了礦山投資最優(yōu)方案，節(jié)約成本，加大利潤(rùn)，為公司提供了正確的決策方法。

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