چكيده به لاتين
COVID-19 was one of the remarkable health threats facing the world in the 21st century that caused severe humanitarian crises worldwide. In spite of efforts to curtail the spread of the disease, the pandemic continued to pose a significant strain on healthcare systems worldwide. Hence, in response to a pressing need to limit viral transmission, the virus responsible for coronavirus disease sparked a race toward accelerating the Covid-19 vaccine's last-mile delivery. Taking this into account, the Covid-19 vaccine delivery was made within a given time frame consisting of distinct periods to distribute varied types of single-dose vaccines as well as the double-dose ones. On that account, with the goal of deploying drones in conjunction with a truck to capture the propounded scenario, once the vaccines are delivered in each period, either of the vehicles may visit the serviced nodes recursively in subsequent periods. Not only to satisfy the existing primary demand of each vaccination center but also to fulfill the demand for succeeding doses. In addition, with respect to the double-dose vaccine type previously delivered to each node and the required interval between every dose in succession, the recursive visits can be scheduled at each node. Accordingly, in light of the illumination perceived from the Covid-19 pandemic vaccine delivery, this paper presents two frameworks of novel Vehicle Routing Problem (VRP) called "Vehicle Routing Problem with Interchangeable multivisit drones" (VRP-ImD) and the "Recursive delivery Vehicle Routing Problem with multiple Drones" (R-VRPmD) that can be classified as a new branch of VRP. (VRP-ImD) presents an approach to optimize last-mile delivery. In this scenario, multiple trucks are equipped with a fleet of drones capable of launching from a truck, delivering parcels to one or more customers per flight, and returning to either their originating truck or any available alternative regarding its flightrange. In addition, the presented novel R-VRPmD is an application captured from the enlightenments of Covid-19 vaccine delivery that can be applied to many other scenarios such as home healthcare, equipment maintenance and repair, in which, with a glance at the kind of services supplied in previous periods and their required time interval, the same service must recursively be provided in following periods after its specific time interval passes. We formulate the R-VRPmD as a mixed integer linear programming (MILP) model. The objective of the presented optimization models are to minimize the total transportation costs to service nodes. In addition, due to the limitations of the solver's performance when applied to large-scale instances, we have developed a heuristic approach based on several algorithms to solve real-world problems. Furthermore, we have incorporated a lower bound to compare the proposed heuristic's performance to the results of the solver.
