Traveling salesman problem with drone and bicycle: multimodal last-mile e-mobility

Recently, the multimodal last-mile e-mobility concept has been at the center of attention for cleaner, greener, and more accessible urban deliveries. As part of sustainable transportation systems, multimodal e-mobility is proper for a variety of logistics operations as well as medical applications. This work tries to address a novel application of multimodal e-mobility through introducing and modeling the traveling salesman problem with drone and bicycle (TSP-D-B). Therefore, a novel mixed integer linear programming model is developed to formulate the problem wherein the total traveling time is minimized. As part of the last-mile delivery, a fleet of three vehicles including a truck, a drone, and a bicycle is taken into account to serve the customers in a single visit. The truck is considered as the main vehicle, while the drone and bicycle can be preferred in case of emergencies such as traffic or route failures. In order to assess the complexity, validity and applicability of the offered model, a dataset including 64 different benchmarks is generated, and according to the findings, the model is able to efficiently solve the benchmarks for up to 50 customers in 685 s maximum. A comparison is also made between TSP-D-B, the classic version of the TSP and the TSP-D, which reveals that TSP-D-B provides appropriate service time savings in all benchmarks. Finally, another comparative analysis is made using several instances adapted from the literature. It is revealed that TSP-D-B leads to significant time savings in most instances.