A production-transportation problem with stochastic demand and concave production costs

Abstract

The problem of transporting goods from a set of supply points (factories) to a set of demand points (customers) so as to minimize linear transportation costs is well known and very efficient solution methods exist. In the well-known facility location problem one also includes fixed charges for the supply points. On the other hand, in ordinary transportation problems, stochastic demand has been introduced and modelled by convex costs, yielding the Stochastic Transportation Problem, [STP], solved by for example the methods in Cooper and LeBlanc (1977) and Holmberg and Jornsten (1984). However, the simultaneous use of these generalizations has recieved little attention until now. Only a few suggestions for solution methods can be found, LeBlanc (1977), Franca and Luna (1982). In this paper we consider generalizing this problem even further, by introducing general concave costs at the supply points, as well as convex costs at the demand points. Fixed charges are not the only cost structures that occur when producing goods at a factory. Economies of scale very often yield other concave cost functions.