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Disruptions at ports may destroy the planned ship schedules profoundly, which is an imperative operation problem that shipping companies need to overcome. This paper attempts to help shipping companies cope with port disruptions through recovery scheduling.

This paper studies the ship coping strategies for the port disruptions caused by severe weather. A novel mixed-integer nonlinear programming model is proposed to solve the ship schedule recovery problem (SSRP). A distributionally robust mean conditional value-at-risk (CVaR) optimization model was constructed to handle the SSRP with port disruption uncertainties, for which we derive tractable counterparts under the polyhedral ambiguity sets.

The results show that the size of ambiguity set, confidence level and risk-aversion parameter can significantly affect the optimal values, decision-makers should choose a reasonable parameter combination. Besides, sailing speed adjustment and handling rate adjustment are effective strategies in SSRP but may not be sufficient to recover the schedule; therefore, port skipping and swapping are necessary when multiple or longer disruptions occur at ports.

Since the port disruption is difficult to forecast, we attempt to take the uncertainties into account to achieve more meaningful results. To the best of our knowledge, there is barely a research study focusing on the uncertain port disruptions in the SSRP. Moreover, this is the first paper that applies distributionally robust optimization (DRO) to deal with uncertain port disruptions through the equivalent counterpart of DRO with polyhedral ambiguity set, in which a robust mean-CVaR optimization formulation is adopted as the objective function for a trade-off between the expected total costs and the risk.