Unmanned aerial vehicles, or drones, have the potential to significantly reduce the cost and time of making last-mile deliveries and responding to emergencies. Despite this potential, little work has gone into developing vehicle routing problems (VRPs) specifically for drone delivery scenarios. Existing VRPs are insufficient for planning drone deliveries: either multiple trips to the depot are not permitted, leading to solutions with excess drones, or the effect of battery and payload weight on energy consumption is not considered, leading to costly or infeasible routes. We propose two multitrip VRPs for drone delivery that address both issues. One minimizes costs subject to a delivery time limit, while the other minimizes the overall delivery time subject to a budget constraint. We mathematically derive and experimentally validate an energy consumption model for multirotor drones, demonstrating that energy consumption varies approximately linearly with payload and battery weight. We use this approximation to derive mixed integer linear programs for our VRPs. We propose a cost function that considers our energy consumption model and drone reuse, and apply it in a simulated annealing (SA) heuristic for finding suboptimal solutions to practical scenarios. To assist drone delivery practitioners with balancing cost and delivery time, the SA heuristic is used to show that the minimum cost has an inverse exponential relationship with the delivery time limit, and the minimum overall delivery time has an inverse exponential relationship with the budget. Numerical results confirm the importance of reusing drones and optimizing battery size in drone delivery VRPs.
Publisher Summary This chapter discusses some of the most important vehicle routing problem types. The vehicle routing problem lies at the heart of distribution management. It is faced each day by thousands of companies and organizations engaged in the delivery and collection of goods or people. Because conditions vary from one setting to the next, the objectives and constraints encountered in practice are highly variable. Most algorithmic research and software development in this area focus on a limited number of prototype problems. By building enough flexibility in optimization systems, these can be adapted to various practical contexts. The classical vehicle routing problem (VRP) is one of the most popular problems in combinatorial optimization, and its study has given rise to several exact and heuristic solution techniques of general applicability. The chapter presents a comprehensive overview of the available exact and heuristic algorithms for the VRP, most of which have been adapted to solve other variants. This paper presents a methodology for classifying the literature of the Vehicle Routing Problem (VRP). VRP as a field of study and practice is defined quite broadly. It is considered to encompass all of the managerial, physical, geographical, and informational considerations as well as the theoretic disciplines impacting this ever emerging-field. Over its lifespan the VRP literature has become quite disjointed and disparate. Keeping track of its development has become difficult because its subject matter transcends several academic disciplines and professions that range from algorithm design to traffic management. Consequently, this paper defines VRP's domain in its entirety, accomplishes an all-encompassing taxonomy for the VRP literature, and delineates all of VRP's facets in a parsimonious and discriminating manner. Sample articles chosen for their disparity are classified to illustrate the descriptive power and parsimony of the taxonomy. Moreover, all previously published VRP taxonomies are shown to be relatively myopic; that is, they are subsumed by what is herein presented. Because the VRP literature encompasses esoteric and highly theoretical articles at one extremum and descriptions of actual applications at the other, the article sampling includes the entire range of the VRP literature.