Estimating the optimal number of parcel lockers and their cost structure for last mile distribution: Case study in Barcelona

This paper introduces an analytical model designed to optimise the deployment of parcel lockers for last-mile delivery and determine the cost structure for last mile freight distribution. The model minimizes the total costs associated with traditional home delivery and locker delivery strategies. By integrating a grid search method, this model considers operational and user costs, accommodating specific urban characteristics such as varying demand densities and street layouts. A case study conducted in Barcelona validates the model’s practical applicability, contrasting two scenarios: a cooperative lockers model where the infrastructure is publicly owned and accessible to all carriers, and a private lockers model where the infrastructure is owned and only used by the largest delivery company in the city. Results demonstrate the significant operational efficiency of the locker proposal, with the mean unit cost for traditional deliveries in Barcelona being 4.77€ per item, and the locker model achieving an average cost reduction of over 75%, resulting in a value of 1.12€ per item. This cost reduction holds across all districts, despite variations in demand densities and street patterns. Additionally, the study reveals that high demand densities notably reduce locker operational costs, making the administration-owned locker strategy the most efficient. Conversely, a private locker model leads to significantly higher costs (15.3%) than the public ones due to split demand and lack of cooperation between retailers.