Last-mile delivery problem with flexible time slot and location options under stochastic customer behavior

The growth of e-commerce has led to a significant rise in daily parcel deliveries, placing increasing pressure on logistics services. Although various delivery options, including home and out-of-home delivery, are offered to enhance customer availability, uncertainty in customer preferences regarding delivery locations and time slots further complicates delivery operations. In this paper, we introduce a last-mile delivery problem with flexible delivery options under stochastic customer behavior, formulated as a two-stage stochastic programming model. The novelty of our model lies in the integration of comprehensive delivery options, including various locations and time slots, with pricing decisions. Furthermore, we incorporate heterogeneous customer preferences across mixed delivery options. To efficiently solve the problem, we develop a hybrid adaptive large neighborhood search (h-ALNS) heuristic based on scenario simulations. Extensive numerical experiments demonstrate the advantages of the mixed delivery strategy and confirm the effectiveness of the proposed algorithm. Our numerical analysis offers important managerial insights for optimizing last-mile delivery assortment and pricing, particularly in addressing customer uncertainty.