Automated picking system employing a drone

We study the possibility of using drones to implement an automated picking system in a warehouse. We imagine a warehouse divided into two contiguous areas: in one area, the drone moves according to the Euclidean distance, while in the other area, the drone moves according to the Manhattan distance. For each customer-order (CO), the automated picking system is in charge of gathering the items requested in the CO to a predefined location where the cart of the drone is positioned. For each item of the order, the drone flies to the location where the item is stored, grasps it, and brings it back to its cart. Our goal is to find the position of the drone's cart that minimizes the sum of the distances traversed by the drone to pick-up all the items of the CO. We propose algorithms to find such a location when the items to be collected are in Euclidean and Manhattan areas. We can prove a √2-approximation factor for our solutions. Moreover, we compare the efficiency of the automated picking system employing a drone with that of a traditional picking system employing a worker that pushes a cart, and we find under which conditions the drone can be more efficient.