Ship emission monitoring with a joint mode of motherships and unmanned aerial vehicles

Ship emission monitoring is crucial for improving compliance with emission control area (ECA) policies. To address the limitations of traditional base station-based monitoring methods, we propose a highly maneuverable mothership-based unmanned aerial vehicle (UAV) monitoring mode. We develop a mixed integer non-linear programming model to maximize the total profit (i.e., the revenues of ship emission monitoring minus the fixed costs of motherships and UAVs, the fuel cost of motherships, and the electricity cost of UAVs). Three types of integer variables are relaxed to continuous variables based on the model properties. We then design a tailored Benders decomposition algorithm to solve the model. Moreover, to improve the performance of the algorithm, we also present a variety of acceleration strategies, including lower bound limit inequalities and knapsack inequalities. Finally, we verify the effectiveness of the proposed algorithm using experimental instances based on the North American ECA. We also find a relationship between the width of emission inspection area and the total monitoring cost.