Out-of-kilter algorithm

The out-of-kilter algorithm is an algorithm that computes the solution to the minimum-cost flow problem in a flow network. It was published in 1961 by D. R. Fulkerson  and is described here. The analog of steady state flow in a network of nodes and arcs may describe a variety of processes. Examples include transportation systems & personnel assignment actions. Arcs generally have cost & capacity parameters. A recurring problem is trying to determine the minimum cost route between two points in a capacitated network. The idea of the algorithm is to identify out-of-kilter arcs and modify the flow network until all arcs are in-kilter and a minimum cost flow has been reached. The algorithm can be used to minimize the total cost of a constrained flow in an oriented network.