A Network Design Problem

We consider the problem of designing a distribution network to facilitate the repeated movement of shipments from many origins to many destinations. A sufficient number of the origin-destination shipments require less than the capacity of a vehicle, so that consolidation of shipments is economical. We consider the case in which consolidation takes place at terminals, and we assume each shipment moves through exactly one terminal on its way from its origin to its destination. Then, a major design decision is to determine the best number of terminals. We develop a continuous approximation method to estimate transportation costs as a function of the number of terminals. We use the continuous approximation method to choose the number of terminals that minimizes the sum of terminal cost and transportation cost. Numerical results indicate that the design resulting from the continuous approximation method facilitates operations with lower cost than those resulting from a widely used integer programming based design