L18_10 - Minimum Cost Network Flow Problems The...

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Minimum Cost Network Flow Problems The transportation, assignment, transshipment, shortest path, and maximum flow problems are all special cases of minimum cost network flow problems (MCNFP) . Any MCNFP can be formulated as an LP. It can be also solved by a generalization of the transportation simplex method called the network simplex method.
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To define MCNFP, let X ij = number of units of flow sent from node i to node j through arc(i,j) b i = net supply (outflow-inflow) at node i c ij = cost of transporting 1 unit of flow from node i to node j via arc(i,j) L ij = lower bound of flow through arc(i,j) (if there is no lower bound, let L ij =0) U ij = upper bound of flow through arc(i,j) (if there is
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