Optimizing last-mile delivery through crowdshipping on public transportation networks

In this paper, we explore an innovative last-mile delivery paradigm that leverages commuters on public transportation (PT) networks as crowdshippers, creating a low-impact delivery model that minimizes environmental footprint while taking advantage of technological advancements, improved infrastructure, and the widespread use of electronic devices. At the beginning of each delivery service period, parcels are routed to selected PT stations by a delivery company, and assigned to a set of crowdshippers (commuters). These crowdshippers collect and deliver the parcels as part of their regular journeys through the PT network, without deviating from their usual routes. The delivery company ensures, through a backup service, the final delivery of parcels that do not reach their final destination. The problem looks for the optimal schedule and route for each parcel while minimizing overall delivery expenses. We call this problem the Public Transportation-based Crowdshipping Problem (PTCP). We propose a compact Mixed Integer Linear Programming formulation strengthened with valid inequalities and develop an Adaptive Large Neighborhood Search to address large-scale instances. The experimental analysis, conducted on a large set of instances, shows the effectiveness of the proposed heuristic method when compared to the exact model solution. Sensitivity analysis reveals that crowdshipping and backup delivery costs significantly influence the total system cost.