# MINIMUM-COSTNetwork-flow problem

**DOI:**https://doi.org/10.1007/1-4020-0611-X_618

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In a directed, capacitated network with supply and demand nodes, the problem is to determine the flows of a single, homogeneous commodity from the supply nodes to the demand nodes that minimizes a linear cost function. In its general form, when the network contains transshipment or intermediate nodes, that is, nodes that are neither supply nor demand nodes, the problem is called the transshipment problem. Conservation of flow through each node is assumed. Due to its special mathematical structure, this problem has a solution in integer flows, given that the data that define the network are integers. It is a linear-programming problem whose major constraints form a node-arc incidence matrix. Conservation of flow; Maximum-flow network problems; Network optimization.