Going Bunkers: The Joint Route Selection and Refueling Problem

Managing shipping vessel profitability is a central problem in marine transportation. We consider two commonly used types of vessels---“liners” (ships whose routes are fixed in advance) and “trampers” (ships for which future route components are selected based on available shipping jobs)---and formulate a vessel profit maximization problem as a stochastic dynamic program. For liner vessels, the profit maximization reduces to the problem of minimizing refueling costs over a given route subject to random fuel prices and limited vessel fuel capacity. Under mild assumptions about the stochastic dynamics of fuel prices at different ports, we provide a characterization of the structural properties of the optimal liner refueling policies. For trampers, the vessel profit maximization combines refueling decisions and route selection, which adds a combinatorial aspect to the problem. We characterize the optimal policy in special cases where prices are constant through time and do not differ across ports and prices are constant through time and differ across ports. The structure of the optimal policy in such special cases yields insights on the complexity of the problem and also guides the construction of heuristics for the general problem setting.