Two-Stage Decomposition Algorithms for Single Product Maritime Inventory Routing

We present two decomposition algorithms for single product deep-sea maritime inventory routing problems (MIRPs) that possess a core substructure common in many real-world applications. The problem involves routing vessels, each belonging to a particular vessel class, between loading and discharging ports, each belonging to a particular region. Our algorithms iteratively solve a MIRP by zooming out and then zooming in on the problem. Specifically, in the “zoomed out” phase, we solve a first-stage master problem in which aggregate information about regions and vessel classes is used to route vessels between regions, while only implicitly considering inventory and capacity requirements, berth limits, and other side constraints. In the “zoomed in” phase, we solve a series of second-stage subproblems, one for each region, in which individual vessels are routed through each region and load and discharge quantities are determined. Computational experience shows that an integrated approach that combines these two algorithms is vastly superior to solving the problem directly with a commercial mixed-integer programming solver.