An exact algorithm for inland container transportation network design

In this paper, we investigate the inland depot location problem of the inland transportation system. In inland container transportation, empty containers are transported between depots and consignees/shippers, and empty containers should be repositioned after/before inbound/outbound full containers. We build a robust mathematical model that focuses on determining when and where consignees/shippers are assigned to. In addition, inter-depots empty container repositioning is implemented considering demand uncertainty. This paper proposes a branch-and-price algorithm that is based on Lagrangian relaxation and column generation. We show the optimality condition of the pricing subproblem and construct a simpler formulation in this paper. Computational experiments are performed with test instances that mimic real life. Our results also show that considering time compatibility of full and empty container routes is closer to reality and increases the utilization of empty containers in depots. The proposed algorithm yields promising solutions compared with CPLEX.