Factors that impact solution run times of arc - based formulations of the Vehicle Routing Problem ∗

It is well known that the Vehicle Routing Problem (VRP) becomes more difficult to solve as the problem size increases. However little is known about what makes a VRP difficult or easy to solve for problems of the same size. In this paper we investigate the effect of the formulation and data parameters on the efficiency with which we can obtain exact solutions to the VRP with a general IP solver. Our results show that solution run times for arc-based formulations with exponentially many constraints are mostly insensitive to problem parameters, whereas polynomial arc-based formulations, which can solve larger problems because of the smaller memory requirement, are sensitive to problem parameters. For instance, we observe that solution times for polynomial formulations significantly decrease for larger capacities and number of vehicles. ∗Research supported by NSF under grant CMS-0409887 †Corresponding author