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Project_Report_Baseball_Problem

# Project_Report_Baseball_Problem - Project IEOR 160 Problem...

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Project IEOR 160 Problem 1: Little League Baseball Scheduling Executive Summary Background A friend of Professor Yyy coaches Little League kids and was trying to set up a competition schedule which had certain requirements and constraints. He could not satisfy all his criteria and

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asked Professor Yyy to try her/his hands at it. Professor Yyy concluded that, indeed, one exception would have to be made in order to set up a schedule. Unfortunately, she/he cannot mathematically prove that the problem, as stated, has no solution and would like to enlist our help in determining whether the problem has, or has no solution. Summary The little leaguers have nine teams, identified by numbers 1 through 9. In the course of a specified period, each team is to play each other team twice. Competitions are conducted every week on Monday through Thursday. No team can play more than once in any four-day time block. In addition to the weekly Monday through Thursday competitions, there is also a weekly Saturday competition. On Saturdays, four competitions are held simultaneously. A team that has played in a given Monday to Thursday competition can participate on the following Saturday's competition. The league starts from March 13, 2006 and ends on May 31, 2006 with certain holiday and vacation periods when no competition can be scheduled on. The question is whether this problem has a perfect solution or, for the aforementioned criteria and constraints. Technical Evaluation Problem Analysis The constraints: 1. Each of the nine teams will compete with one another exactly twice during the league. The total number of required competitions therefore is 72. 2. In a four-day block, no team can play more than once. Therefore, the maximum number of competitions in a block is 4. Moreover, because competitions can be simultaneously
conducted on Saturdays, we can consider each available Saturday a single block on which a maximum number of 4 competitions can be held. 3. In the last block, only two games can be scheduled because the league ends on May 31. The approach: With the above analysis, the question becomes whether we can fit 72 baseball games into 18.5 available blocks, in each of which a maximum of 4 games can be scheduled. Apparently, integer programming has been proven to be the most effective way to solve this sort of problems.

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