Supplying a single location from heterogeneous sources

This paper studies how items with different characteristics, and being demanded at different rates from a finite number of supply points, should be transported to a common destination. The items may differ in size and value, and the origins may differ in their spatial distribution, the kind of items they produce and the production rate. Depending on the application context, the common destination can represent a warehouse, a factory, a military base, a break-bulk terminal, a port or another kind of transportation terminal. Different kinds of items may call for separate transportation treatment if, for example, the items have sharply different inventory carrying costs or their origins are not equally scattered. On the other hand, if their characteristics are not very different, they may be transported together more cheaply because of existing economies of scale. In fact, in most applications it should be optimal to use only a few transportation systems because the economies of scale are quite strong. The paper essentially shows that origins can be ranked according to a simple criterion, and that if two origins are served together, the ones ranked in between should be served with them. A simple method for determining the optimal number of transportation systems and the sources served by each is developed. The technique is illustrated with a numerical example. The results of the paper are developed assuming that supply points do not cluster together by type and that the density of suppliers is slowly varying. In any practical application in which these assumptions are not reasonable approximations, the results of this paper should not be applied too literally. Nevertheless, they can still be used as guidelines in the search for an optimum supply strategy.