Robust schedule design for liner shipping services

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This paper examines the design of liner ship route schedules that can hedge against the uncertainties in port operations, which include the uncertain wait time due to port congestion and uncertain container handling time. The designed schedule is robust in that uncertainties in port operations and schedule recovery by fast steaming are captured endogenously. This problem is formulated as a mixed-integer nonlinear stochastic programming model. A solution algorithm which incorporates a sample average approximation method, linearization techniques, and a decomposition scheme, is proposed. Extensive numerical experiments demonstrate that the algorithm obtains near-optimal solutions with the stochastic optimality gap less 1.5% within reasonable time.