A risk-averse two-stage stochastic programming model for vessel schedule recovery in liner shipping service

Significant delays caused by disruption events, coupled with regular uncertainties, pose challenges to risk avoidance and vessel schedule recovery problem (RA-VSRP) in liner container shipping services. To address this, we propose a new optimization framework that incorporates a hybrid risk aversion measure with three recovery strategies, including sailing speed adjustment, port skipping, and transshipment. The framework systematically combines ex-ante decision-making and in-progress decision-making. The former helps shorten vessel schedule recovery time and costs by quickly responding to disruption events, while the latter improves the flexibility of selecting vessel schedule recovery strategies. By adopting a scenario-based approach to jointly capture regular uncertainties and disruption events, RA-VSRP is formulated as a chance-constrained two-stage stochastic programming model, where conditional value-at-risk (CVaR) is used as the risk measure. An exact Benders decomposition-based branch-and-cut algorithm is employed to efficiently solve the computationally challenging model. We develop two algorithmic variants based on alternative representations of CVaR. Extensive numerical experiments demonstrate the applicability of the model and the computational efficiency of the algorithm. The results show that the proposed framework can provide reliable vessel schedule recovery solutions through sailing speed adjustments, port skipping, and transshipment. The findings provide managerial insights for shipping companies regarding schedule recovery, risk aversion, and cost control.