A matheuristic approach for the Pollution-Routing Problem

This paper deals with the Pollution-Routing Problem (PRP), a Vehicle Routing Problem (VRP) with environmental considerations, recently introduced in the literature by Bektaş and Laporte (2011) [Transportation Research Part B: Methodological 45 (8), 1232-1250]. The objective is to minimize operational and environmental costs while respecting capacity constraints and service time windows. Costs are based on driver wages and fuel consumption, which depends on many factors, such as travel distance and vehicle load. The vehicle speeds are considered as decision variables. They complement routing decisions, impacting the total cost, the travel time between locations, and thus the set of feasible routes. We propose a method which combines a local search-based metaheuristic with an integer programming approach over a set covering formulation and a recursive speed-optimization algorithm. This hybridization enables to integrate more tightly route and speed decisions. Moreover, two other “green” VRP variants, the Fuel Consumption VRP (FCVRP) and the Energy Minimizing VRP (EMVRP), are addressed, as well as the VRP with time windows (VRPTW) with distance minimization. The proposed method compares very favorably with previous algorithms from the literature, and new improved solutions are reported for all considered problems.