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.

在本文中，我们研究了内陆运输系统的内陆仓库选址问题。在内陆集装箱运输中，空集装箱是在仓库和收货人/托运人之间运输的，空集装箱应在满载集装箱进/出集装箱之前/之后进行重新放置。我们建立了一个强大的数学模型，其重点是确定何时将收货人/发货人分配给何处。此外，考虑到需求的不确定性，可以进行场间空集装箱的重新定位。本文提出了一种基于拉格朗日松弛和列生成的分支定价算法。我们展示了定价子问题的最优条件，并在本文中构建了一个更简单的公式。使用模拟现实生活的测试实例进行计算实验。我们的结果还表明，考虑满载和空载集装箱路线的时间兼容性更加接近现实，并提高了仓库中空集装箱的利用率。与CPLEX相比，该算法产生了有希望的解决方案。