Schedule Recovery for Liner Shipping Service

Container vessels in liner shipping are operated on closed-loop routes following a pre-announced schedule. In practice, when a vessel is sailed on the sea, there are lots of uncertain events which may delay a vessel from its original schedule, even if some uncertainty has been considered in the tactical network design. In this seminar, I will talk about two issues about schedule recovery.

We first consider the aftermath of a disruption that delays a vessel from its given schedule, aiming to design a scheme for the vessel to catch up with the schedule in an effective way. We consider different operational actions such as speeding up, port skipping, and port swapping. We approach the problem by nonlinear programming and obtain certain structural results of the optimal recovery schedule. For a major disruption, we develop dynamic programming algorithms on the discretized time space and provide a method to estimate a lower bound of the problem, which enables us to evaluate the relative error caused by the discretized time space in dynamic programming.

Then we move on to consider the case where the vessel faces a forecasted incoming disruption. The decision is to make proactive actions for future uncertainties. One important contribution of this work is to explicitly distinguish two types of uncertainties in liner shipping, and propose different strategies to handle them. The problem can be formulated as a multi-stage stochastic control problem that minimizes the total expected fuel cost and delay penalty. For regular uncertainties, we develop the properties of the optimal control policy; then we show how an emerging disruption may change the control policies. We also provide a wide range of numerical studies to verify the analytical results and demonstrate the effectiveness of the model.