Drone logistics for uncertain demand of disaster-impacted populations

The paper introduces a stochastic optimization-based approach to address the logistics for the timely delivery of aid packages to disaster-affected areas utilizing a fleet of drones when the set of demand points is unknown. The major problem addressed is to locate a set of drone take-off platforms so that with a specified probability α, the maximum total disutility (or cost) under all realizations of the demand locations is minimized. A set of discrete scenarios defines the uncertainty set of the demand points. A Chance Constrained Programming (CCP) formulation is developed to select a set of platform locations whose disutility distribution produces minimum α percentile. For each platform location set, and each demand scenario, the total disutility is defined as the total delivery time for serving the demand points plus a penalty for unvisited demand points. For every set of drone platform locations, referred to as a candidate combination of platforms, the resultant disutility distribution is obtained by solving a space-time drone scheduling subproblem for all possible demand scenarios. The drone scheduling subproblem optimally schedules and sequences a set of trips for each drone so that the total disutility is minimized. Owing to the computational complexity of the proposed approach, an approximation method is developed that decomposes the problem into three tractable stages. The first stage identifies a set of most preferable platform combinations. The second stage develops an approximation algorithm based on a greedy approach to mitigate the extensive computational requirements for solving the large number of drone scheduling subproblems. The last stage builds upon the properties of a Sample Average Approximation (SAA) method and of the CCP formulation to select the optimum set of platforms. Finally, the performance of the proposed stochastic approach is evaluated through a series of computational experiments and a case study of Central Florida. The results reveal interesting insights and demonstrate the effectiveness of the proposed logistics system for drone delivery of humanitarian aid packages.