Robust Multi-Period Maximum Coverage Drone Facility Location Problem Considering Coverage Reliability

Abstract

This study proposes a multi-period facility location formulation to maximize coverage while meeting a coverage reliability constraint. The coverage reliability constraint is a chance constraint limiting the probability of failure to maintain the desired service standard, commonly followed by emergency medical services and fire departments. Further, uncertainties in the failure probabilities are incorporated by utilizing robust optimization using polyhedral uncertainty sets, which results in a compact mixed-integer linear program. A case study in the Portland, OR metropolitan area is analyzed for employing unmanned aerial vehicles (UAVs) or drones to deliver defibrillators in the region to combat out-of-hospital cardiac arrests. In the context of this study, multiple periods represent periods with different wind speed and direction distributions. The results show that extending to a multi-period formulation, rather than using average information in a single period, is particularly beneficial when either response time is short or uncertainty in failure probabilities is not accounted for. Accounting for uncertainty in decision-making improves coverage significantly while also reducing variability in simulated coverage, especially when response times are longer. Going from a single-period deterministic formulation to a multi-period robust formulation boosts the simulated coverage values by 57%, on average. The effect of considering a distance-based equity metric in decision-making is also explored.