A Network Design Problem

Abstract

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.