On a Class of Capacitated Transportation Problems

Transportation models (ordinary and transhipment) having certain types of capacity constraints on the flows between origins and destinations are studied from the point of view of transforming them into enlarged standardized (non-capacitated) models. Specifically constraints on the flow from disjoint and/or nested sets of origins to all destinations, and from any single origin to disjoint and/or nested sets of destinations are considered. Dual formulations are indicated for constraints on the flow to destinations from origins. In the case of a set of capacity constraints on the flow from each origin to each destination, the models proposed are easily seen to be of minimal dimension for any “standardized” version of such a capacitated problem.