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lab5 - ENGRI 115 Engineering Applications of OR Fall 2007...

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ENGRI 115 Engineering Applications of OR Fall 2007 The Baseball Elimination Problem Lab 5 Name: Objectives: Introduce students to a sophisticated formulation using the maximum flow problem. Demonstrate how to solve the application by the Ford-Fulkerson algorithm. Key Ideas: integrality property max-flow min-cut theorem the baseball elimination problem Prelab Exercise: Look around the RIOT (Remote Interactive Optimization Tool) homepage at http://riot.ieor.berkeley.edu/ (look for Major League Baseball under Ian Adler). You do not need to hand in anything. 1
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You have seen an example for the Baseball Elimination Problem in class. Recall that the data for this problem consists of the following: a collection of teams 1, 2, ... ,n , at the beginning of the season each pair of teams i,j is scheduled to play each other a given number of times, of all the games between teams i and j , g ij currently remain to be played, team i has already won w i games. We would like to determine if team n (our favorite) has been eliminated already: that is, even if team n wins all of its remaining games, no matter how the games between the other teams turn out, there will always be some team with more wins than team n at the end of the season. We have considered the following data for a 4 team league. Team Wins 1 8 2 10 3 10 4 1 Games Remaining vs. 1 2 3 4 1 3 3 6 2 3 6 3 3 3 6 3 4 6 3 3 Our team (team 4 ) didn’t do very well so far. We would like to determine whether it still has a chance to finish first at the end of the season (we are satisfied with a tie for the first place as well). How many games can team 4 possibly win during the season? Call this number W .
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