Disruption Recovery for a Vessel in Liner Shipping

Container vessels in liner shipping are operated on closed-loop routes following a preannounced schedule. In practice, when a vessel embarks on a voyage on the sea, there are lots of uncertain factors that may delay a vessel from its original schedule, even if some uncertainty has been considered in the tactical network design. In this paper, we propose an operational-level solution to recover the disrupted schedule caused by a delay, where we consider different operational actions such as speeding up, port skipping, and port swapping. For the case where only speeding up is allowed, we approach the problem by nonlinear programming and obtain certain structural results of the optimal recovery schedule. It shows that speeding up can effectively handle a delay that is not too large. When there is a large delay, which may be called a major disruption, we study the problem with more options such as port skipping and swapping and develop dynamic programming algorithms on the discretized time space. We also provide a method to estimate a lower bound of the problem that enables us to evaluate the relative error caused by the discretized time space in dynamic programming. Numerical studies are conducted to validate our results and derive managerial insights.