毕业论文线性规划在垃圾运输问题的应用

学科分类号 110

黑龙江科技大学

本科学生毕业论文

题 目 线性规划在垃圾运输问题的应用 Linear programming is applied in waste transportation problem 姓 名 *** 学 号 2011*** 院 （系） 理学院 专业、年级 数学与应用数学 指导教师 **** 2015年6月12日

摘 要

我们知道,随着市场经济发展迅速，竞争也随之加快。为了能在这激烈的市场竞争中立足，企业都谋取最大的利润，最少的成本也就是最小的费用。企业通过不断的改进，利用各种方式企图使得费用最少。运输问题关心的是以最低的总配送成本把供应中心的任何产品运送到每 一个接收中心。每一个出发地都有一定供应量配送到目的地，每一个目的地都需要一定的需求量。 运输问题(Transportation Problem)是一个典型的线性规划问题。一般的运输问题就是要解决把某种产品从若干个产地调运到若干个销地，在每个产地的供应量与每个销地的需求量已知，并知道各地之间的运输单价的前提下，如何确定一个使得总的运输费用最小的方案的问题。

本论文运用线性规划的数学模型来解决此运输问题中总费用最小的问题。针对斯特兰运输公司南大西洋办公处的经理雷切尔对于垃圾处理的困惑，对其的三个处理方案进行优化求解，并运用excel电子表格的线性优化来计算各个方案的数学模型。

关键词 最优化 运输问题 线性规划

I

Abstract

As we know, with the market economy has developed rapidly, competition also will speed up. In order to establish oneself in the fierce market competition, enterprises seek maximum profit, the least cost is the minimum cost. Enterprise through continuous improvement, the use of a variety of ways in an attempt to make cost minimum. Transportation problem concerned in the lowest total distribution cost and the supply of any product shipped to each receiving center. Each source has certain supply and distribution to the destination, each destination needs certain demand. Transportation Problem, Transportation Problem) is a typical linear programming Problem. General transportation problem is to solve a product from a number of origin transportation to several Sales site , in each origin of supply and demand for each Sales site known, and know that all the transportation between the unit price under the premise of how to determine a scheme to make the total transportation cost minimum.

In this paper, using the mathematical model of linear programming to solve the transportation problem of minimum total cost. For strenger transport company of south Atlantic office manager Rachel for garbage disposal confusion, three of its treatment scheme optimization solution, and using the excel spreadsheets to calculate the linear optimization mathematical model of each scheme.

Keywords optimization Transportation problem Linear programming

II

目 录

摘 要.......................................................................................................................... I Abstract ...................................................................................................................... II 第1章 绪 论 ........................................................................................................ 1 1.1研究的目的和意义 ......................................................................................... 1 1.2 国内外研究状况 ........................................................................................... 1 1.3 本文的主要工作 ........................................................................................... 5 第2章Excel与线性规划的运输问题 ..................................................................... 6 2.1线性规划............................................................................................................. 6 2.1.1线性规划简介······································································· 6 2.1.2线性规划模型······································································· 6 2.2线性规划与运输问题 ..................................................................................... 7 2.2.1运输问题的基本特征 ····························································· 7 2.2.2运输问题的分类 ··································································· 7 2.3 Excel解决运输问题 .................................................................................... 11 2.3.1软件介绍 ··········································································· 11 2.3.2 运输问题形式 ····································································· 12 2.3.3在excel中的形式 ................................................................................. 12 2.3.4 excel求解步骤 ...................................................................................... 12 第3章 垃圾运输问题 .......................................................................................... 13 3.1问题的提出 ................................................................................................ 13 3.1.1 事例 ················································································· 13 3.1.2对上述问题的几种解决方案 ··················································· 14 3.2实例的分析 ................................................................................................ 15 3.2.1实例的数据分析 .................................................................................... 15 3.2.2对于几种方案的模型建立 ······················································ 15 3.2.3对于几种方案的模型的excel求解 ··········································· 18

待解决问题 ················································· 错误！未定义书签。

结 论 ....................................................................................................................... 25 致 谢 ....................................................................................................................... 26 参考文献................................................................................................................... 27

III

Contents

Abstract ................................................................................. 错误！未定义书签。 Abstract ................................................................................. 错误！未定义书签。 Chapter 1 Introduction ............................................................................................ 1 1.1Research purpose and meaning ...................................................................... 1 1.2 The research status at home and abroad .......................................................... 1 1.3 The main work of this article ........................................................................ 5 Chapter 2 Excel with linear programming transportation question ............................ 6 2.1 Linear programming ........................................................................................... 6 2.1.1 Introduction of linear programming·············································· 6 2.1.2 Linear programming model ······················································· 6 2.2 Linear programming and transportation problem ............................................ 7 2.2.1 The basic characteristics of transportation problem ·························· 7 2.2.2 The classification of the transportation problem ······························ 7 2.3 Excel solve the transportation problem ......................................................... 11 2.3.1 The software is introduced······················································· 11 2.3.2 Form of transportation problem ················································· 12 2.3.3 In the excel form .................................................................................... 12 2.3.4 excel solving steps ................................................................................. 12 Chapter 3 waste transportation problem .................................................................. 13 3.1 raise of problem .......................................................................................... 13 3.1.1 example ··············································································· 13 3.1.2 Several solutions to the problem ··············································· 14 3.2 The analysis of the instance ........................................................................ 15 3.2.1 Example analysis of the data ........................................................ 15 3.2.2 For several solution model is established in this paper ····················· 15 3.2.3 For several kinds of schemes of excel to solve the model ················· 18

待解决问题 ················································· 错误！未定义书签。

conclusions ................................................................................................................ 25 Acknowledgements .................................................................................................. 26 References ................................................................................................................. 27

IV

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