Capacitated transportation problem with convex polygonal costs
A consideration of an extension of the classical transportation problem. In such problems, a minimal cost schedule is derived for shipping a commodity from a set of origins to a set of destinations. In the classical model, however, the only constraints permitted are total capacities at origins and destinations, and the cost is strictly a linear function of the amount shipped on any route. The extension presented here enables one to put an upper bound on each individual route, and permits the imposition of increased or penalty costs for excessive amounts shipped on any individual route. This greater realism should be of value in many transportation problems. Constructive proofs leading to a machine-oriented algorithm are given for the extension. The basic technique is a labeling process similar to that used by Ford and Fulkerson for the general network problem, and by Balinski and Gomory for the standard transportation problem. The objective of this work is to trade off some of the generality of the network problem for increased computational efficiency. It is conjectured, from limited hand calculations and certain theoretical features, that the present algorithm will also be useful for the standard transportation problem. 48 pp. Bibliog.