Approximate Solutions to a Dynamic Combinatorial Problem in Space

Abstract

A family of important problems in spatial economics may be particularized in the following terms. A set of vehicles, V, exists with elements i = 1, ..., m, each of which carries a given initial supply of product. We identify a sequence of ‘legs’, t = 0, 1, ..., N, during which we assume (fictitiously) that vehicle movement occurs. Finally, we specify a set of stations, S, with elements j = 1, ..., n, located at coordinates [x _j , y _j ] on the plane; for convenience, and without loss of generality, we assume that j = 1, ..., f, f ≤ m, are the initial locations of the vehicles, or the stations at which they are located on Leg 0.

Published originally in the Journal of Regional Science, 8 (1968), pp. 165–80, and reproduced with permission.

This work was initiated while the author was a research associate of the Regional Science Research Institute under National Science Foundation Grant GS-617. He is indebted to Professor Michel L. Balinski, who provided valuable advice at several points during the research.