The dry dock scheduling problem

Dry docks are essential facilities for ship maintenance and thus are critical assets of a shipyard. In this paper, we study a dry dock scheduling problem that arises from shipyard operations and management. The problem involves decisions on assigning ships to a set of dry docks and sequencing the ships in each dry dock, subject to complicated but realistic operational constraints such as parallel ship service, sequence-dependent setup times, and compatibility between ships and dry docks, to minimize the total departure tardiness cost of ships. Because accurate ship service times are not available until ships have been mounted on the placing blocks of dry docks and have undergone detailed inspections, the uncertainty of ship service times should be taken into account in dry dock scheduling. The structure of the problem enables us to develop a two-stage robust optimization model to capture ship service time uncertainty. We show that given the first-stage decisions, i.e., ship assignment and sequencing, the optimal second-stage decisions, i.e., the service start times, setup times, service times, and departure tardiness of the ships in the worst-case scenario, can be obtained by a dynamic programming algorithm that runs in pseudo-polynomial time. We incorporate this dynamic programming algorithm into an iterative solution method to generate an optimal solution to the two-stage robust optimization model. Through computational experiments on problem instances generated from the operational data of a shipyard in Singapore, we show that the robust optimization approach ensures the shipyard operator’s resilience against uncertain ship service times and significantly outperforms the current practice for dry dock scheduling.