Stochastic Programming for Liner Ship Routing and Scheduling under Uncertain Sea Ice Conditions

It is anticipated that in the foreseeable future the Northern Sea Route (NSR) will be able to serve commercial shipping as an alternative transportation shortcut between East Asia and Europe, especially in the summer season. The sailing time, however, is heavily subject to the variation of sea ice conditions along this route. Any participating shipping company must consider how to mitigate the ill effects on itinerary planning caused by sailing time and cost uncertainty. Finding a good trade-off between the benefit from a tight schedule and the risk caused by an unexpected delay is a key element in relevant routing and scheduling decisions, and may be beyond the reach of traditional deterministic planning models. With the aim of maximizing profit over all possible shipping environment scenarios, this article proposes a two-stage stochastic nonlinear integer programming model for liner ship routing and scheduling with uncertain shipping time and cost, the nonlinearity of which arises from the coexistence of schedule-sensitive shipping demand and uncertain arrival time variables in the objective function. The model is converted into an equivalent linear integer programming counterpart by introducing a set of nominal delay variables, and Benders decomposition is applied to solve the linearized problem. Numerical experiments and sensitivity analyses are conducted to validate the efficacy and effectiveness of the model, the results of which suggest several managerial insights that can be used to guide liner ship route and schedule planning under uncertain shipping conditions.