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奧運(yùn)會(huì)商場(chǎng)的設(shè)計(jì)與規(guī)劃
摘要
本文主要解決北京市2008年奧運(yùn)會(huì)商場(chǎng)的設(shè)計(jì)與規(guī)劃問(wèn)題。基材選自2004年全國(guó)大學(xué)生數(shù)學(xué)建模競(jìng)賽A題。
首先，根據(jù)題中所附的3次調(diào)查數(shù)據(jù)，統(tǒng)計(jì)計(jì)算大量樣本在出行、用餐、消費(fèi)等方面的比例并畫(huà)出直方圖，總結(jié)出其中規(guī)律；然后解決主體在出行時(shí)選擇最短路徑的情況，采用c++程序計(jì)算出經(jīng)過(guò)各商區(qū)的人次，再乘以去往各目的地的人數(shù)百分比，得到1個(gè)人次數(shù)矩陣。這個(gè)矩陣表達(dá)了經(jīng)過(guò)每個(gè)商區(qū)去往不同目的地的人次數(shù)。橫向相加得到經(jīng)過(guò)每個(gè)商區(qū)的總?cè)肆髁�；最后，建立�?guī)劃方程并求解。以3個(gè)基本要求作為約束條件，針對(duì)人流量和消費(fèi)額分別列出了最大顧客滿(mǎn)意度和最大盈利為目標(biāo)函數(shù)的多目標(biāo)規(guī)劃問(wèn)題。通過(guò)對(duì)目標(biāo)加權(quán)調(diào)節(jié)后，得到結(jié)果。
本文在解題的過(guò)程中進(jìn)行了大量的數(shù)學(xué)運(yùn)算，采用的輔助軟件有Access、Excel和matlab。
關(guān)鍵詞：多目標(biāo)規(guī)劃；最短路徑；加權(quán)計(jì)算；統(tǒng)計(jì)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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