Maximum coverage capacitated facility location problem with range constrained drones

Given a set of demand and potential facility locations and a set of fully available charged drones, an agency seeks to locate a pre-specified number of capacitated facilities and assign drones to the located facilities to serve the demands. The facilities serve as drone launching sites for distributing the resources. Each drone makes several one-to-one trips from the facility location to the demand points and back until the battery range is met. The planning period is short-term and therefore the recharging of drone batteries is not considered. This paper presents an integer linear programming formulation with the objective of maximizing coverage while explicitly incorporating the drone energy consumption and range constraints. The new formulation is called the Maximum Coverage Facility Location Problem with Drones or simply MCFLPD. The MCFLPD is a complex problem and even for relatively small problem sizes a state of the art MIP solver may require unacceptably long running times to find feasible solutions. Computational efficiency of MCFLPD solutions is a key factor since conditions associated with customer demands or weather conditions (e.g., wind direction and speed) may change suddenly and require a fast global reoptimization. To better balance solution quality and running times novel greedy and three-stage heuristics (3SH) are developed. The 3SH is based on decomposition and local exchange principles and involves a facility location and allocation problem, multiple knapsack subproblems, and a final local random search stage. On average the 3SH solutions are within 5% of the best Gurobi solutions but at a small fraction of the running time. Multiple scenarios are run to highlight the importance of changes in drone battery capabilities on coverage.