Hybrid Vehicle-drone Routing Problem For Pick-up And Delivery Services Mathematical Formulation And Solution Methodology

The fast growth of online retail and associated increasing demand for same-day delivery have pushed online retail and delivery companies to develop new paradigms to provide faster, cheaper, and greener delivery services. Considering drones’ recent technological advancements over the past decade, they are increasingly ready to replace conventional truck-based delivery services, especially for the last mile of the trip. Drones have significantly improved in terms of their travel ranges, load-carrying capacity, positioning accuracy, durability, and battery charging rates. Substituting delivery vehicles with drones could result in $50M of annual cost savings for major U.S. service providers. The first objective of this research is to develop a mathematical formulation and efficient solution methodology for the hybrid vehicle-drone routing problem (HVDRP) for pick-up and delivery services. The problem is formulated as a mixed-integer program, which minimizes the vehicle and drone routing cost to serve all customers. The formulation captures the vehicle-drone routing interactions during the drone dispatching and collection processes and accounts for drone operation constraints related to flight range and load carrying capacity limitations. A novel solution methodology is developed which extends the classic Clarke and Wright algorithm to solve the HVDRP. The performance of the developed heuristic is benchmarked against two other heuristics, namely, the vehicle-driven routing heuristic and the drone-driven routing heuristic. Anticipating the potential risk of using drones for delivery services, aviation authorities in the U.S. and abroad have mandated necessary regulatory rules to ensure safe operations. The U.S. Federal Aviation Administration (FAA) is examining the feasibility of drone flights in restricted airspace for product delivery, requiring drones to fly at or below 400-feet and to stay within the pilot’s line of sight (LS). Therefore, a second objective of this research is considered to develop a modeling framework for the integrated vehicle-drone routing problem for pick-up and delivery services considering the regulatory rule requiring all drone flights to stay within the pilot’s line of sight (LS). A mixed integer program (MIP) and an efficient solution methodology were developed for the problem. The solution determines the optimal vehicle and drone routes to serve all customers without violating the LS rule such that the total routing cost of the integrated system is minimized. Two different heuristics are developed to solve the problem, which extends the Clarke and Wright Algorithm to cover the multimodality aspects of the problem and to satisfy the LS rule. The first heuristic implements a comprehensive multimodal cost saving search to construct the most efficient integrated vehicle-drone routes. The second heuristic is a light version of the first heuristic as it adopts a vehicle-driven cost saving search. Several experiments are conducted to examine the performance of the developed methodologies using hypothetical grid networks of different sizes. The capability of the developed model in answering a wide variety of questions related to the planning of the vehicle-drone delivery system is illustrated. In addition, a case study is presented in which the developed methodology is applied to provide pick-up and delivery services in the downtown area of the City of Dallas. The results show that mandating the LS rule could double the overall system operation cost especially in dense urban areas with LS obstructions