A variable neighborhood search algorithm for locker-based drone delivery makespan minimization problem

This article studies a novel makespan minimization problem for locker-based drone delivery in which several automatic drones take lockers as launching and landing platforms. It is a vehicle routing and machine scheduling hybrid problem with formulation and solution challenges. Firstly, we formally define the problem and analyze its complexity. Secondly, we formulate an integer linear program model based on a time-expanded network. Thirdly, we develop a variable neighborhood search algorithm that embeds a translation heuristic. The translation heuristic first constructs a rough solution and then improves the solution by solving a linear program. Numerical tests are conducted on simulated instances. The results show that the algorithm finds solutions with an average gap of 7% for small-scale uniform instances and demonstrates good scalability, with CPU time growing nearly linearly as the instance size increases.