A branch-and-price heuristic algorithm for the bunkering operation problem of a liquefied natural gas bunkering station in the inland waterways

Liquefied natural gas (LNG) bunkering stations are areas for bunkering LNG-powered ships via a flexible hose from either a shoreside facility, shore-based/pontoon tank, or an LNG truck. The operation management of LNG bunkering stations is complex because many factors affect the operational performance, including station layout, bunkering technology, and frequent interactions among trucks, tanks, and ships. In this study, we consider the bunkering operation problem (BOP) of an LNG bunkering station in the inland waterways. The problem involves decisions of assigning ships to tanks, managing the inventory of the tanks, and scheduling LNG trucks for bunkering ships and replenishing tanks. We first formulate the problem as a mixed-integer linear programming (MILP) model that aims to minimize the cost incurred by the bunkering operations. As the BOP is NP-hard, the MILP model for the problem with practical size is generally difficult to solve. We thus reformulate it into an equivalent task-based model and develop a tailored branch-and-price heuristic (BPH) algorithm to solve the new model. Several enhancement techniques are also presented to improve the solution efficiency of the BPH algorithm. Numerical experiments demonstrate the satisfactory performance of the solution algorithm. Some managerial implications are also obtained to provide scientific guidance for station operators to make operational decisions. In particular, our model can help determine the best combination of bunkering modes and replenishment modes as well as the optimal truck fleet.