# HW5Q4Key - Solution problem 4(questions comments...

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Unformatted text preview: Solution problem 4: (questions, comments, suggestions please to Steffen Rebennack, [email protected] ) 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 flow-balance 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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HW5Q4Key - Solution problem 4(questions comments...

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