An exact method for vessel emission monitoring with a ship-deployed heterogeneous fleet of drones

Abstract

Using drones to monitor vessel emissions has received a lot of attention currently because of its advantages in ensuring compliance with the regulations of Emission Control Areas (ECAs) in the shipping industry. In the existing literature, drones are assumed to be identical and deployed at fixed base stations, resulting in sub-optimal or even infeasible solutions for vessel inspections. This paper investigates a variant of the vessel emission monitoring problem in an ECA, in which drones are deployed on Coastal Patrol Ships (CPSs) to extend their monitoring coverage of vessels, and each drone may have a different flight speed and endurance. We formulate the problem on a time–space network, based on which a mixed-integer linear programming model is presented, aiming to maximize the inspection benefit of the vessels. An exact method is proposed for solving the model. It relies on a structure-based reformulation of the original model, as well as structure enumeration, column generation, and row generation. Computational results show that this exact method can solve large-scale instances with up to 100 vessels, three CPSs, and six drones within one hour, and outperforms the Gurobi solver, the Lagrangian relaxation-based approach developed in the existing literature, and the policies adopted in reality.