MILP-based cost and time-competitive vehicle routing problem for last-mile delivery service using a swarm of UAVs and UGVs

There are numerous studies on the unmanned vehicle routing problem (VRP) considering battery constraints in the areas of 1) path-planning problem based on intelligent task allocation and 2) determination of routes according to defined objectives and constraints. However, in most previous literature, only a simple linear approximation of battery energy consumption is considered, producing unrealistic results. In this study, a cost and time-competitive VRP is established and solved using mixed-integer linear programming (MILP), considering the relationship between the cost and electricity consumption of unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs). In particular, the maximum flyable and drivable ranges of the UAV and UGV were calculated by setting a linear capacity degradation equation based on the state of health, considering a limited number of (dis)charge cycles. This approach guarantees more realistic optimization results due to the adaptation of the detailed characteristics of battery-related information. Numerical analyses using two solvers based on MILP, 1) COIN-OR Branch and Cut (CBC) and 2) Gurobi, were performed with four different scenarios and four corresponding cases for each scenario by varying the number of demanders. The results show that using a combination of UAVs and UGVs slightly reduces the cost by approximately 1% but significantly reduces the delivery completion time by approximately 79%. The simulation running time was approximately 1.1Â s for all the cases, and the CBC solver operates faster than the Gurobi solver by approximately 0.93%.