We study a typical daily drayage problem concerning the last-mile logistics at seaports for inland container supply chains. A set of trucks available at an inland container terminal must fulfil shippers’ requests of transporting containers within time windows and, to do so, can perform multiple daily trips. A request may entail picking up or delivering containers either at the shippers’ premises, the inland terminal or the seaport. Demand for empty containers can be satisfied by either using the available limited stock at the inland terminal, by street-turning or, ultimately, by retrieving them at a local depot for empties resulting in extra mileage. Hence, the minimization of routing costs also entails synchronizing trucks’ trips that retrieve and add empty containers to the inland terminal stock to avoid unnecessary visits to the empty depot. After modelling the problem mathematically, we develop an exact column-and-row generation approach embedded in a branch-and-price framework. To accelerate the solving process of the pricing problem, we propose effective strategies by combining a set of tailored pricing algorithms. These strategies perform well on a set of adapted Solomon's instances up to 100 nodes and against a standard branch-and-cut solver. Finally, experiments on real-world instances, inspired by a case study of an inland terminal at the Port of Rotterdam region, provide insights into current planning practices.@en

In this paper, we will study a typical problem in inland container shipping, concerning the barge transportation of maritime containers between a dry port and a set of seaport terminals. The barges depart from the dry port and visit a set of sea terminals, where containers need either to be dropped off or picked up. The goal is to achieve economies of scale with barges and avoid trucking as much as possible. The decision thus involves finding the best allocation of containers to barges in order to guarantee on-time delivery and meet capacity restrictions. The problem will be modeled as a variant of the split vehicle routing problem with simultaneous pickups and deliveries coupled with time features. The model includes parameters that can be tuned to improve barge utilization and travelling distance. A hybrid local search meta-heuristic algorithm, combined with a branch-and-cut solver, will be developed to solve the model. Numerical experiments have been conducted to test the performance of the algorithm and provide solution analysis for practical insights. Real-world data has been collected from a local barge operator based in the Port of Rotterdam region and will be used as input for the experiments. This will result in an in-depth analysis into current planning practices. The proposed framework complements existing models in the literature and contributes to the development of a comprehensive set of decision support tools, which help in the decision-making process for inland terminals.

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