Freight vehicle routing with reliable link travel times: a method based on network fundamental diagram

This paper presents a procedure for the solution of the Vehicle Routing Problem (VRP) based on reliable link travel times. They are obtained as a combination of spatially disaggregated and aggregated data about simulated traffic conditions on an urban road network. The disaggregated data concern the congested link travel times, which are traditionally used as variable to be minimized in VRP. The novelty of this research article consists in the introduction of spatially aggregated data, which are estimated by means of the Network Fundamental Diagram (NFD). In a within-day dynamic context, they are a measure of reliability of travel times because they could anticipate the latter ones’ variation in the short term. The equation of reliable link travel times is composed of a congestion term, expressing the traditional congested link travel times (or generalized costs), and a reliability term, which depends on the fundamental diagram of the link and the NFD of the homogeneous cluster of adjacent links. The proposed procedure has been validated and applied for two real test cases. NFDs data are used in the proposed link travel time function to calculate reliable travel times. The reliable link travel times are used for the solution of VRP to obtain optimal routes of freight vehicles.