Joint Optimisation of Sailing Speed and Buffer Times in Liner Shipping



Liner shipping networks consist of fixed ship routes and time schedules that are published beforehand. However, delays are inevitable while executing the timetables, introducing uncertainty in sailing and port times. To maintain schedule reliability and reduce delay cost, liner companies will try to limit the amount of delay with respect to the schedule. Delays can for example be managed by adding buffer times in the timetables (prevention) or by increasing the sailing speed of the ship (recovery). Our goal is to jointly optimize the buffer times and sailing speed. Buffer time allocation is a problem on the tactical planning level, which has to be made in the scheduling problem before routes are executed. Adjusting the sailing speed, on the contrary, is a decision on the operational planning level. Hence, the optimal sailing times given a buffer allocation should already be available when determining the quality of the given buffer allocation, while in practice these decisions are taken much later. In our solution approach, we use that the optimal cost associated with a fixed buffer allocation can be obtained by solving a finite state Markov Decision Process and is convex in the buffer allocation. Hence, we can use a subgradient-based approach to find an optimal solution to the joint problem.

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