A new formulation for the multi-period vessel-drone routing problem

To address the limitations of conventional offshore oil-and-gas field inspections, such as high cost, low frequency, and high risk, a new method called vessel-drone collaborative inspection is proposed. This approach involves a drone-carrying vessel departing from the port and sailing to a designated distance from the oil-and-gas field. The drones are then released to conduct field inspections. Once the drones complete their tasks, the vessel retrieves them at a specific location. This paper focuses on addressing the multi-period "vessel-drone" collaborative inspection route planning problem. The objective is to minimize the fixed cost of the vessel over the planning horizon while considering the overall path cost of both the vessel and the drone. The planning model takes into account various factors, including the coordination of space and time between the vessel and drone, drone endurance limitations, and the inspection cycle limitations for each period. To solve the problem, a mixed-integer second-order cone optimization formulation is proposed, along with several valid inequalities. Through empirical research and sensitivity analyses, the effectiveness of the proposed method is demonstrated. It is shown that the method can provide a cost-effective plan for oilfield inspections, offering potential value in guiding offshore oil-and-gas field inspection operations.