Railcar reallocation optimization on water-rail network under uncertain busyness

Water-rail intermodal transportation can reduce cargo losses and transportation transferring costs. However, the imbalance between the capacity of the scheduled railway network and the large container freight demand greatly reduces operational efficiency. To minimize the total transportation cost and relocation cost, a railcar reallocation stochastic optimization model is formulated to deal with uncertain congestion in the railway network. To capture the uncertain busyness and queuing pattern, a hypercube spatial queue model is embedded in the optimization model by estimating the expected queue length and waiting time. To solve the proposed nonlinear nonconcave stochastic model, an approximate hypercube based iterative algorithm is proposed. A real-world case study is presented to show the effectiveness and efficiency of the proposed method. The proposed model outperforms the comparable deterministic model in the objective value. Sensitivity analyses on the ratio of the unit waiting cost and the unit travel cost for empty cars, and the total number of freight cars show the robustness of the proposed method.