公平合理获奖名额分配

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1、公平合理的获奖名额分配姓名：庄佳彬学号：090602113姓名：劳伟东学号：090602114姓名：陈辉东学号：0906021152011年12月15日1目录摘要·······································································1关键词·····································································11、问题重述····························

2、····································12、模型假设································································13、符号说明································································24、模型建立与分析··························································24.1问题分析······

3、·······················································24.2模型建立·····························································24.3引入Q值公式························································45、模型求解·······························································

4、·56、结论····································································67、模型推广与改进··························································68、附录····································································7参考文献········································

5、···························72【摘要】近年来，各高校数学建模活动蓬勃发展。对于以往的奖项分配存在不合理现象，为了进一步促进数学建模的发展提高同学们的积极性，对此进行了公平合理的评奖办法。通过Q值法，公平席位进行建模得到更加优化的奖项分配。【关键词】合理分配；Q值法；公平席位1.问题重述近年来，各高校数学建模活动蓬勃发展。某综合性大学数学建模竞赛参赛人数近两年连年翻番。现行的评奖办法是对所有参赛队伍一视同仁，按两轮评阅成绩由高到低确定前20%的队伍获一等奖，处于20%到前45%之间的队伍获

6、二等奖。现行评奖办法的主要问题是可能会挫伤一年级同学和经济、医学、管理类同学的参赛积极性。为了进一步促进数学建模发展，数学建模俱乐部竞赛培训管理中心研究决定从2009年该大学数学建模竞赛开始，采用兼顾学院均衡、兼顾年级均衡的评奖办法。因此，向大家提出了以下的问题：如果总获奖队伍为100队，如何分配获奖名额？对获奖名额的分配需要兼顾学院均衡，同时也要保护主力学院同学的参赛热情。对获奖名额的分配需要兼顾年级均衡，同时也要保护主力年级同学的参赛热情。通过这样的分配，2009年该大学数学建模竞赛将可能有多少队伍报名参加？2

7、.模型假设1)参加不存在院系间交叉。2)不存在中途退出。13.符号说明符号符号说明A某学院获奖队数B某学院参赛队数C获奖总队数D总参赛队数Qii学院席位分配Q值pii学院队伍数nii学院席位数4.模型的建立与分析4.1问题分析通常分配结果的公平与否以每个代表席位所代表的人数相等或接近来衡量。目前沿用的惯例分配方法为按比例分配方法，即：BACD如果按上述公式参与分配的一些单位席位分配数出现小数,则先按席位分配数的整数分配席位,余下席位按所有参与席位分配单位中小数的大小依次分配之。参赛院系数理管理海科船建石化总数队

8、伍数17852402628324队伍比例0.550.160.120.080.091按比例席54.9416.0512.358.028.64100位分配4.2模型建立假设由两个单位公平分配席位的情况，设人数席位数单位Ap1n1单位Bp2n22pp要公平，应该有12，但这一般不成立。注意到等式不成立时有nn12pp12若，则说明单位A吃亏(即对单位A不公平)n