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Unformatted text preview: ORIE 321/521 RECITATION 4 Spring 2007 Consider the following AMPL model file maxflow.mod for the maximum flow problem, which can be found in the MODELS folder within the amplcml folder on your desktop. set nodes; param orig symbolic in nodes; param dest symbolic in nodes, <> orig; set arcs within (nodes diff {dest}) cross (nodes diff {orig}); param cap {arcs} >= 0; var Flow {(i,j) in arcs} >= 0, <= cap[i,j]; maximize Total_Flow: sum {(orig,j) in arcs} Flow[orig,j]; subject to Balance {k in nodes diff {orig,dest}}: sum {(i,k) in arcs} Flow[i,k] = sum {(k,j) in arcs} Flow[k,j]; Again, change this model so that the capacity constraints are explicit con straints of the model, rather than just upper bounds on the variable Flow . This week you will be using the max flow model to solve the socalled baseball elimination problem, which will be introduced in recitation. The data for this problem consists of a collection of teams: team 1, team 2, through team n ; each pair of teams i and j has been scheduled to play each other a given number of times; of these, g ( i, j ) games currently remain, and team i has won a total of w ( i ) games thus far. For simplicity, we assume that each team plays the same total number of games in the entire season. We would like to determine if team n 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...
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 Spring '07
 SHMOYS/LEWIS
 Flow network, Maximum flow problem, Maxflow mincut theorem, Team New York Baltimore Boston Toronto Detroit

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