The Importance of Modeling Path Choice Behavior in the Vehicle Routing Problem

Given two pick-up and delivery points, the best path chosen does not necessarily follow the criteria of minimum travel time or generalized minimum cost evaluated with a deterministic approach. Given a criterion, the perceived cost is not deterministic for many reasons (congestion, incomplete information on the state of the system, inexact prediction of the system state, etc.). The same consideration applies to the best-chosen route, assuming that the route is an ordered list of network nodes to visit. The paths and routes perceived and chosen (drivers or companies) could follow different criteria (i.e., minizmum congested travel time for the path and minimum monetary cost for the route). In this context, the paths chosen between two pick-up and delivery points, studied with the path choice problem (PCP), influence the best route, studied with the vehicle routing problem (VRP). This paper reports some considerations on the importance of modelling the path choice behavior in the VRP; the influence of the PCP on the VRP is studied. The considerations are supported by a numerical example in a small network in which the results obtained by adopting the deterministic or probabilistic models for the PCP are compared. To validate the reported thesis, the models are applied in a small test system, and it allows the reader to follow the numerical results step by step.