Evaluation of flow dependent external costs in freight logistics networks

In this paper we face a distribution problem arising in a freight logistics context. More precisely, we are involved with the containerized flow originating from maritime terminals and going to inland destinations using the road transportation network. The goal is the minimization of the total shipping costs, given by the travelled distance, vehicles and external cost components. In particular, we consider accidental and polluting costs as external negative costs. Note that the proposed externality costs depend on the amount of flow through the selected arcs in the route and their capacity; therefore, a novel stepwise function is proposed and analyzed. A deep analysis is performed for evaluating the impact of environmental externalities on the choice of the route in terms of costs and distances depending on the density of the traffic. Results of an extensive computational experimentation performed with randomly generated instances of different size and capacity values of the arcs are reported. A real case instance related to the logistics network connecting the main ports of the Liguria County (Italy) to the main inland destinations is finally proposed and analyzed.