Correction to: an efficient environmentally friendly transportation network design via dry ports: a bi-level programming approach

This paper addresses the problem of deciding the locations of dry ports by providing an intermodal rail-road p-hub median model, adopting a bi-level programming approach. In the proposed model, direct transportation and shipment between nodes are allowed instead of transportation merely through the hubs. In the bi-level programming approach, at the top level, the government/authority will decide the locations of the dry ports to increase the utilization of railways and minimize the construction and maintenance costs of dry ports as one of the important transportation infrastructures. Freight forwarders who are considered at the lower level aim to minimize the shipping costs by deciding the optimal shipping routes. A matheuristic approach based on the Genetic Algorithm (GA) is proposed to solve the given problem. Numerical analysis confirms that the proposed algorithm can provide satisfactory solutions for large instances where commercial solvers are not capable of finding the near optimal solutions in a reasonable computational time. Finally, the experimental results show that using the proposed transportation network model can decrease the total transportation costs along with significantly reduction of air pollution.