A continuous approximation model for time definite many-to-many transportation

Time definite freight transportation carriers provide very reliable scheduled services between origin and destination terminals. They seek to reduce transportation costs through consolidation of shipments at hubs, but are restricted by the high levels of service to provide less circuitous routings. This paper develops a continuous approximation model for time definite transportation from many origins to many destinations. We consider a transportation carrier serving a fixed geographic region in which demand is modeled as a continuous distribution and time definite service levels are imposed by limiting the maximum travel distance via the hub network. Analytical expressions are developed for the optimal number of hubs, hub locations, and transportation costs. Computational results for an analogous discrete demand model are presented to illustrate the behavior observed with the continuous approximation models.