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

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Unformatted text preview: 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 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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This note was uploaded on 06/01/2008 for the course ENGRI 1101 taught by Professor Trotter during the Spring '05 term at Cornell University (Engineering School).

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

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