The transportation problem with optimization of the origins

Abstract

This dissertation presents solution procedures for two related location/allocation problems. Two algorithms which mathematically guarantee global optimality are described for the first problem which considers the optimal positioning of an origin set and associated optimal quotas given a known destination set. For the second problem which requires the optimal positioning of a 'serving center' set given a known origin set and destination set, an efficient exhaustive scanning procedure and a modified version of an algorithm given for the first problem are presented. Both of these techniques guarantee a global optimum. For large problems which have both limited capacities and geographic restrictions placed on the optimal positioning of the serving centers, a two-phase iterative procedure not guaranteeing global optimality is described. Example problems are provided to illustrate selected algorithms.