Semi-liner Shipping Service Design

Abstract

Semi-liner shipping transports various types of cargo, such as containers, break-bulk cargo, and heavy-lift project cargo, between different ports. Similar to liner shipping, semi-liner shipping publishes shipping routes for customers’ reference. However, it does not strictly follow the published route and usually makes some adjustments for each ship voyage by adding some port calls to transport more cargo considering the excess ship capacity. This study first proposes the semi-liner shipping service design (SLSSD) problem that aims to maximize the shipping profit by determining a shipping route subject to the potential adjustments. The proposed SLSSD problem is subsequently formulated as a two-stage stochastic mixed integer programming model with integer recourse variables. The first stage determines the visit sequence of a set of compulsory ports under shipping demand uncertainty. The second stage decides whether to add or remove some ports in the route in view of the realized shipping demand for each ship voyage. To effectively solve the model, two decomposition methods are developed, namely, the stage decomposition method and the scenario decomposition method, that decompose the problem by stage and demand scenario, respectively. In addition, two novel acceleration techniques are also provided to expedite the scenario decomposition method. Numerical experiments reveal satisfactory efficiency of these two methods to solve the semi-liner shipping service design problem, especially the scenario decomposition method, which is generally better than the stage decomposition method and can be thousands of times faster than the classic branch-and-cut algorithm.