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Unformatted text preview: Solution problem 4: (questions, comments, suggestions please to Steffen Rebennack, steffen@ufl.edu ) Let x i,j be the flow from node i to node j , if node i and j are connected by an arc, i.e. they are neighbors in the network. Now, we look at the flow problem as follows: Every flow coming from node 1 has to reach flow 7, while meeting the capacity constraints of the network. Hence, we have the flowbalance constraints for nodes 2, 3, 4, 5, and 6. We want to maximize the flow from node 1 to 7, which is the same as saying that we want to maximize the flow into node 7. This yields to the following model: max x 4 , 7 + x 5 , 7 + x 6 , 7 s.t. x 1 , 2 x 2 , 4 x 2 , 5 = 0 x 1 , 3 x 3 , 4 x 3 , 5 = 0 x 2 , 4 + x 3 , 4 x 4 , 6 x 4 , 7 = 0 x 2 , 5 + x 3 , 5 x 5 , 6 x 5 , 7 = 0 x 4 , 6 + x 5 , 6 x 6 , 7 = 0 x i,j ( i, j ) Additional comments: We give some alternative formulations which are all equivalent in some sense (Can you see why?). We refer to the formulation above as formulation 1.(Can you see why?...
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 Fall '09
 VLADIMIRLBOGINSKI

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