奧運會商場的設計與規(guī)劃

摘要

本文主要解決北京市2008年奧運會商場的設計與規(guī)劃問題�；�材選自2004年全國大學生數學建模競賽A題。
首先，根據題中所附的3次調查數據，統(tǒng)計計算大量樣本在出行、用餐、消費等方面的比例并畫出直方圖，總結出其中規(guī)律；然后解決主體在出行時選擇最短路徑的情況，采用c++程序計算出經過各商區(qū)的人次，再乘以去往各目的地的人數百分比，得到1個人次數矩陣。這個矩陣表達了經過每個商區(qū)去往不同目的地的人次數。橫向相加得到經過每個商區(qū)的總人流量；最后，建立規(guī)劃方程并求解。以3個基本要求作為約束條件，針對人流量和消費額分別列出了最大顧客滿意度和最大盈利為目標函數的多目標規(guī)劃問題。通過對目標加權調節(jié)后，得到結果。
本文在解題的過程中進行了大量的數學運算，采用的輔助軟件有Access、Excel和matlab。

關鍵詞：多目標規(guī)劃；最短路徑；加權計算；統(tǒng)計分析

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

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