Minimum Cost Network Flow ProblemsThe 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, letXij= number of units of flow sent from node i to node j through arc(i,j)bi= net supply (outflow-inflow) at node icij= cost of transporting 1 unit of flow from node i to node j via arc(i,j)Lij= lower bound of flow through arc(i,j) (if there is no lower bound, let Lij=0)Uij= upper bound of flow through arc(i,j) (if there is