The two-echelon routing problem with truck and drones

In this paper, we study novel variants of the well-known two-echelon vehicle routing problem in which a truck works on the first echelon to transport parcels and a fleet of drones to intermediate depots while in the second echelon, the drones are used to deliver parcels from intermediate depots to customers. The objective is to minimize the completion time instead of the transportation cost as in classical two-echelon vehicle routing problems. Depending on the context, a drone can be launched from the truck at an intermediate depot once (single-trip drone) or several times (multiple-trip drone). Mixed-integer linear programming models are first proposed to formulate mathematically the problems and solve to optimality small-sized instances. To handle larger instances, a metaheuristic based on the idea of greedy randomized adaptive search procedure is introduced. The main novel feature of our metaheuristic lies in the design of initial solution construction and local search operators, which can cover all the decision layers of the problems and run in O(1) using additional data structures. Experimental results obtained on instances of different contexts are reported and analyzed.