Probabilistic Analysis of the Capacitated Transportation Problem

We consider the capacitated transportation problem defined by sets of supplies a i , i (in) I , demands b j , j (in) J , and capacities c ij , i (in) I , j (in) J . Assuming that the capacities are random variables, we prove asymptotic conditions on the supplies and demands which assure that a feasible solution exists almost surely. The proof is constructive and supplies an algorithm whose running time is O (| I | | J |). We then apply the results to the maximum flow problem.

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