A priori performance measures for arc-based formulations of the Vehicle Routing Problem ∗

Abstract

The Vehicle Routing Problem (VRP) is a central problem for many transportation applications, and although it is well known that it is difficult to solve, how much of this difficulty is due to the formulation of the problem is less understood. In this paper we experimentally investigate how the solution times to solve a VRP with a general IP solver are affected by the formulation of the VRP used. The different formulations are evaluated by examining solution efficiency as a function of several a priori performance measures based on the data parameters. Our experimental results show how the solution run times are sensitive to problem parameters; in particular the sensitivity of formulations to the coefficient of variation of the cost matrix of travel times is explained by two interacting factors