Optimization of Bunkering Logistics at Sea, Taking into Account Cost, Time and Technical Constraints

This study examines the organization of offshore bunkering operations with the aim of improving their economic and logistical efficiency. A mathematical model is proposed that minimizes the total cost of fleet refueling while accounting for technical limitations of vessels, service time windows, and external operational constraints. The formulation extends classical vehicle routing approaches by incorporating fixed and variable costs as well as penalties for delays. A case study based on the Sea of Okhotsk fleet illustrates the application of the model to ten client vessels and four bunkering ships. Using mixed-integer programming combined with heuristic route construction, optimal routing solutions were obtained and tested under varying fuel prices, demand volumes, and fleet sizes. In a stylized one-day case study with ten client vessels located within a 100 km radius around Magadan, the results indicate that reducing the number of active bunkering vessels from four to three can lower overall operating costs while maintaining service quality, yielding indicative savings of approximately 12–18% relative to a simple sequential baseline policy in which bunkering vessels serve customers in a fixed order and the client set is partitioned roughly equally among vessels. The proposed approach provides a practical framework for decision-makers to enhance planning, resource allocation, and operational reliability in marine fuel supply chains.