摘要
本文主要解决北京市2008年奥运会商场的设计与规划问题。基材选自2004年全国大学生数学建模竞赛A题。
首先，根据题中所附的3次调查数据，统计计算大量样本在出行、用餐、消费等方面的比例并画出直方图，总结出其中规律；然后解决主体在出行时选择最短路径的情况，采用c++程序计算出经过各商区的人次，再乘以去往各目的地的人数百分比，得到1个人次数矩阵。这个矩阵表达了经过每个商区去往不同目的地的人次数。横向相加得到经过每个商区的总人流量；最后，建立规划方程并求解。以3个基本要求作为约束条件，针对人流量和消费额分别列出了最大顾客满意度和最大盈利为目标函数的多目标规划问题。通过对目标加权调节后，得到结果。
本文在解题的过程中进行了大量的数学运算，采用的辅助软件有Access、Excel和matlab。
关键词：多目标规划；最短路径；加权计算；统计分析
Abstract
This article mainly solves the Olympic Games market design and plan question of Beijing in 2008.The base material elects from the national university student mathematics modeling to compete the A topic in 2004.
According to three investigations data, the statistical computation massive samples are going on a journey, dine, and so on expense proportion and draw the histogram, summarizes rule. Then main body when going on a journey chooses the most short-path the situation, uses the c++ procedure to calculate people who passes through various business area, again multiplies by goes toward various destinations population percentage, obtains a matrix. It expressed who passed through each business area to go toward the different destination human number of times. Crosswise adds together obtains passes through each business area total Stream of people ratio . Finally , set up the equation of planning and ask solving . Regard three basic demand as the condition of restraining, list to flow of the people and amount of consumption most customer satisfaction and most heavy to make profits for goal many target planning equation of function more respectively. After the goal weighting is regulated ,the last result is got to .
This article has carried on the massive mathematics operation in the problem solving process, uses the auxiliary software has Access, Excel and matlab.
Keywords: Much target planning; Short out in the foot-path most; calculated weighting; Statistical analysis
