Liner ship route schedule design with sea contingency time and port time uncertainty

This paper deals with a tactical-level liner ship route schedule design problem which aims to determine the arrival time of a ship at each portcall on a ship route and the sailing speed function on each voyage leg by taking into account time uncertainties at sea and at port. It first derives the optimality condition for the sailing speed function with sea contingency and subsequently demonstrates the convexity of the bunker consumption function. A mixed-integer non-linear stochastic programming model is developed for the proposed liner ship route schedule design problem by minimizing the ship cost and expected bunker cost while maintaining a required transit time service level. In view of the special structure of the model, an exact cutting-plane based solution algorithm is proposed. Numerical experiments on real data provided by a global liner shipping company demonstrate that the proposed algorithm can efficiently solve real-case problems.