(The fixed charge net work design problem)

we are given a directed graph G=(N,A) and a demand or supply bi for each i∈N, such that ∑bi=0, i∈N. There are two types of costs:transportation costs cij of shipping one unit from node i to node j,and building costs dij of establishing a link(i,j) between nodes i and node j of capacity uij. We would like to build such a network in order to minimize the total building and transportation costs, so that all demand is met. Formulate the problem as an integer programming problem.

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