A primary commodity such as wheat, rice, coffee, oil, etc., is shipped from m locations where it was grown or pumped to n manufacturers. Each manufacturer processes, packages, advertises, and distributes the commodity under a consumer product brand name. The resulting heterogeneous good is sold at a sealed bid auction, in competition with the other manufacturers of the consumer product, to k final customers. The problem to be considered in this paper is to find a way of determining prices for the goods produced and the physical exchanges between seller and buyer which satisfy flow conditions and which take into account the evaluations of the goods by both sellers and buyers. The first model for doing this is given in section 1, which combines the idea of a sealed bid auction due to Shapley, Shubik and Thompson, with a conventional trnsportation system. The sealed bid auction is used to determine the exchange prices, and the transportation system is used to calculate the production and transportation costs. It is suggested that the resulting model type can also be applied in a wide range of problems that arise in the marketing of goods sold under brand names (i.e., heterogeneous goods) regardless of whether they are actually exchanged at formal auctions. The authors show in section 6 that the present model is a generalization of the transshipment model in a recent paper by Dubey and Shapley. In their model they considered a number of oligopolists engaged in transshipping and trading goods. Their oligopolists set their prices in order to maximize profits rather than having them determined by an auction process as is done in our model. In section 7, the authors extend the model to one in which the wholesalers are permitted to make positive profits. They show how to calculate the values of coalitions of the various players in the model.
