In their study, Johannes Gückel, Teodor Gabriel Crainic, and Pirmin Fontaine investigate the economic and environmental savings potentials that can be achieved through collaboration among logistics service providers (LSPs) in two-tier city logistics systems, as well as how these savings can be fairly allocated among the partners. To this end, the authors develop a mixed-integer linear programming model that integrates a service network design formulation on the first tier with a vehicle routing formulation on the second tier.
To efficiently solve large, real-world instances, they propose a two-step large neighborhood search metaheuristic that effectively links decisions across both tiers. The numerical results demonstrate that collaboration among LSPs can lead to average cost savings of 26.9%, primarily driven by cooperation on the first tier.
Furthermore, the study examines how these savings can be fairly distributed among the participating companies using simple proportional and game-theoretical allocation methods (including the Shapley value). The analysis shows that smaller providers benefit disproportionately from collaboration, highlighting the importance of transparent cost allocation mechanisms for stable and sustainable partnerships.
The article is now available online here.