Composite Variable Formulations for Express Shipment Service Network Design

In this paper we describe a new approach to solving the express shipment service network design problem. Conventional polyhedral methods for network design and network loading problems do not consistently solve instances of the planning problem we consider. Under a restricted version of the problem, we transform conventional formulations to a new formulation using what we term composite variables. By removing flow decisions as explicit decisions, this extended formulation is cast purely in terms of the design elements. We establish that its linear programming relaxation gives stronger lower bounds than conventional approaches. We apply this composite variable formulation approach to the UPS Next Day Air delivery network and demonstrate potential annual cost savings in the hundreds of millions of dollars.