球赛赛程安排的模型求解

Answers to the Model of the Arrangements of Ball - games' Processes

本文针对n支球队之间举行单循环赛的赛程安排这个实际问题,同时考虑到整个赛程的公平性及优劣情况,对于n的奇偶性不同,根据现行赛程安排方法,提出了相应不同的数学模型。当n为偶数时,我们采用了"循环组合法"进行求解,得到上限为n-4/2,从而得到n=8时的上限为2;当n为奇数时,我们采用了"蛇形回转法"对赛程安排方案求解,得到上限为n-3/2,从而得到n=9时的上限为3。在评价赛程安排公平性方面,我们采用方差检验对模型进行评价,得到相对合理的结果。

This article is aimed at solving the practical problems which are the arrangements of single-round robin among teams. Considering the justice and the quality of the whole process, the model puts forward the corresponding method of the arrangements of processes based on n. when n is even number, we conclude that the upper limit is ( n - 4)/2 by using 'circular technique' . When n is odd number, we conclude that the upper limit is ( n - 3) /2 by using 'S -shaped technique'. At the end of this article, we obtain the reasonable results when we use 'variance analysis' in evaluating the justice of processes.