The paired pickup and delivery problem with profit in a two-echelon delivery system with multiple trucks and drones

Recently researchers proposed truck and drone coordination to increase delivery efficiency and suggested various truck-drone routing problems. In this paper, we also focused on truck and drone coordination and introduced the paired pickup and delivery problem with profit in a two-echelon delivery system. To solve the problem, we propose a hybrid variable neighborhood search algorithm. For this algorithm, we adapted existing neighborhood search operators from the literature and considering the structure of the proposed problem, developed new neighborhood search operators. Also, we have carried out numerous computational experiments to evaluate the proposed solution methods' performance, where the results show the efficiency of the proposed algorithms. The results highlight that in the paired pickup and delivery problem, for small values of drone operational costs, employing the two-echelon truck and drone routing system increases the profit by up to 5.6 percent in comparison to the vehicle routing system with drones.