Projection results for vehicle routing

A variety of integer programming formulations have been proposed for Vehicle Routing Problems (VRPs), including the so-called two- and three-index formulations, the set partitioning formulation, and various formulations based on extra variables representing the flow of one or more commodities. Until now, there has not been a systematic study of how these formulations relate to each other. An exception is a paper of Luis Gouveia, which shows that a one-commodity flow formulation of Gavish and Graves yields, by projection, certain `multistar' inequalities in the two-index space. We give a survey of formulations for the capacitated VRP, and then present various results of a similar flavour to those of Gouveia. In particular, we show that:

• Type: Journal
• Year: 2006
• Where: MP
• Authors: Adam N. Letchford, Juan José Salazar González
• Keywords: Flow Formulation, Formulations, Inequalities, MP 2006