Pseudo Node Insertion Method for Synchronization in Drone-Truck Combined Operations

In this paper, a drone-truck combined last-mile logistics problem is considered, the advantage of which can be summarized in two folds: 1) enabling faster pick-up/delivery of items and 2) expanding operation areas beyond the range that could be achieved by using only one type of vehicle. The drone-truck combined operation (DTCO) solutions are based on truck routes and locations, usually customer nodes, where drones depart from and return to trucks. Since synchronous rendezvous of both vehicles can be very rare, these solutions may contain waste time caused by waiting of one vehicle for the other. In this paper, a pseudo node insertion method is proposed to make DTCO more e cient by resolving the drone-truck asynchronization issue. Pseudo nodes are created at the point where a drone and a truck can meet simultaneously. We present a detailed method to calculate the location of the pseudo node, and provide a detailed analysis for the travel completion time saving conditions. Furthermore, we explore a variety of scenarios to enhance the e ciency of DTCO by way of inserting pseudo nodes. An algorithm for the pseudo node insertion method is provided, and numerical examples are presented to discuss e cacy and e ciency of our proposed approach