A capacitated biobjective location problem with uniformly distributed demands in the UAV-supported delivery operation

Abstract

In recent years, small unmanned aerial vehicles have been used to deliver medicine and goods as a solution to severe traffic jams and to serve the purpose of fast and effective delivery, especially for medical and emergency applications where time is vital. On the other hand, in the competitive market of today, retailers are considering the use of drones to minimize the customers' waiting times and as a way to lower their transportation costs. This study aims to develop a biobjective mathematical model to account for the optimum number and spatial location of facilities among a set of candidate locations such that the total travel distance, costs, and lost demand are minimized simultaneously. It is assumed that the demand occurrence follows a Poisson distribution and is uniformly distributed along the network edges. The proposed biobjective capacitated facility location model is NP-hard, thus nondominated sorting genetic algorithm II and reference-point based nondominated sorting genetic algorithm are applied to solve the problem. The performance of the algorithms, quality of solutions, and the results are investigated and discussed.