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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. |
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