Abstract We study barge scheduling for an ocean-river transshipment system with multiple river branches in which containers are unloaded from overseas vessels to the port yard of the ocean container port and subsequently loaded onto heterogeneous barges for final distributions to inland river terminals. Since the arrival times of ocean vessels may vary each week, we construct a pickup-and-delivery vehicle routing model with time windows for the variable weekly barge scheduling problem. For this NP-hard problem, we develop an efficient two-phase approach. First, we solve a sub-problem to optimize the selection of nodes (i.e., orders) for truck transfer to ensure order delivery time constraints. Given the phase-one solution, we solve the model with a hybrid metaheuristic combining adaptive large neighborhood search and variable neighborhood search. Further, to account for container arrival uncertainties, we use a distributionally robust optimization model based on Kullback–Leibler divergence ambiguity sets to quantify risk tolerance. The performance of the algorithms is superior, obtaining optimal solutions for medium-sized samples with a significantly shorter computational time compared to Gurobi and, for large-size samples, reducing the minimum total cost by 5% on average relative to the benchmark algorithms such as SA, VNS, and LNS.
Qu et al. (Sun,) studied this question.