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Given a set of a spatially distributed demand for a specific commodity, potential facility locations, and drones, an agency is tasked with locating a pre-specified number of facilities and assigning drones to them to serve the demand while respecting drone range constraints. The agency seeks to maximize the demand served while considering uncertainties in initial battery availability and battery consumption. The facilities have a limited supply of the commodity being distributed and also act as a launching site for drones. Drones undertake one-to-one trips (from located facility to demand location and back) until their available battery energy is exhausted. This paper extends the work done by Chauhan et al. and presents an integer linear programming formulation to maximize coverage using a robust optimization framework. The uncertainty in initial battery availability and battery consumption is modeled using a penalty-based approach and gamma robustness, respectively. A novel robust three-stage heuristic (R3SH) is developed which provides objective values which are within 7% of the average solution reported by MIP solver with a median reduction in computational time of 97% on average. Monte Carlo simulation based testing is performed to assess the value of adding robustness to the deterministic problem. The robust model provides higher and more reliable estimates of actual coverage under uncertainty. The average maximum coverage difference between the robust optimization solution and the deterministic solution is 8.1% across all scenarios. 

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.