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.

中文翻译：

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干船坞调度问题

干船坞是船舶维护的重要设施，因此是造船厂的重要资产。在本文中，我们研究了造船厂运营和管理中出现的干船坞调度问题。该问题涉及将船舶分配到一组干船坞以及对每个干船坞中的船舶进行排序的决策，这些决策受到复杂但现实的操作约束（例如并行船舶服务、与顺序相关的设置时间以及船舶与干船坞之间的兼容性）的影响最大限度地减少船舶总离港延误成本。由于船舶必须安装在干船坞的放置块上并经过详细检查后才能获得准确的船舶服务时间，因此在干船坞调度时应考虑船舶服务时间的不确定性。该问题的结构使我们能够开发一个两阶段稳健优化模型来捕获船舶服务时间的不确定性。我们表明，给定第一阶段决策，即船舶分配和排序，最佳第二阶段决策，即最坏情况下船舶的服务开始时间、准备时间、服务时间和出发迟到时间，可以通过在伪多项式时间内运行的动态规划算法获得。我们将这种动态规划算法融入迭代求解方法中，以生成两阶段鲁棒优化模型的最优解。通过对新加坡一家造船厂运营数据生成的问题实例进行计算实验，我们表明，稳健的优化方法确保了造船厂运营商对不确定的船舶服务时间的弹性，并显着优于当前的干船坞调度实践。