Locating platforms and scheduling a fleet of drones for emergency delivery of perishable items

Motivated by issues dealing with delivery of emergency medical products during humanitarian disasters, this paper addresses the general problem of delivering perishable items to remote demands accessible only by helicopters or drones. Each drone operates out of platforms that may be moved when not in use and each drone has a limited delivery range to service a demand point. Associated with each demand point is a disutility function, or a cost function, with respect to time that reflects preferred delivery clock time for the demanded item, as well as the item's perishability characteristic that models nonincreasing quality with time. The paper first addresses the problem of locating the platforms as well concurrently determining which platform serves which demand points and in what order - to minimize total disutility for product delivery. The second scenario addresses the two period problem where the platforms can be relocated, using useable road network, after the first period. It can be easily proven that continuous time versions of these problems are NP-Hard. However, a practical "time slot" version of the problem, where time is discretized into slots, can be solved by standard optimization software. Extensive computational experiments, using different drone delivery ranges as well as different drone fleet sizes, provide valuable insights on the performance of such drone delivery systems.