The Dantzig-Wolfe Decomposition Principle and Minimum Cost Multicommodity Network Flows.

by Richard D. Wollmer

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A restatement of the problem of meeting required multicommodity network flows at minimum cost. In this Note the problem is shown to be a special case of a second, more general problem in which one is attempting to meet minimum cost multicommodity flows without flow requirements on the individual commodities. An algorithm developed for the original problem, programmed in node-arc and arc-chain forms and adjusted by applying the Dantzig-Wolfe decomposition principle, is then modified to solve the more general problem. The Dantzig-Wolfe principle treats the master program as convex combinations of extreme points of derived subprograms. Subsequently, the subprograms are homogeneous and the master program is a nonnegative combination of independent subprogram solutions. 10 pp. Ref.

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