A game-theoretical model for green urban logistics coordination: Exact and data-driven methods
Abstract :
This study presents a single-leader, multi-follower game aimed at minimizing carbon emissions in urban
logistics. First-Mile (FM) delivery service providers transport parcels to satellites at city outskirts, after which
Last-Mile (LM) service providers with eco-friendlier vehicles finalize delivery to customers. In this game, FM
and LM delivery service providers are follower players that form a two-echelon logistics network which is
coordinated by a leader player representing a green urban logistics platform. The leader optimally assigns
parcels to satellites and LMs to minimize emissions across both echelons, while FM and LM followers adjust
their operations accordingly. To determine optimal strategies, an exact cutting-plane algorithm is developed
and benchmarked against a scalable data-driven heuristic approach based on constraint learning. To model
followers’ best responses to leader assignment decisions, we implement a network-oriented learning approach
where we learn FM and LM predictive models that can be used with large city-sized network instances. The
proposed approaches are tested on realistic problems instances from Berlin, Madrid and Bologna. Our findings
highlight the potential of the proposed game-theoretical model for reducing emissions while ensuring that
stakeholders’ preferences such as on-time deliveries are taken into account.This study presents a single-leader, multi-follower game aimed at minimizing carbon emissions in urban logistics. First-Mile (FM) delivery service providers transport parcels to satellites at city outskirts, after which Last-Mile (LM) service providers with eco-friendlier vehicles finalize delivery to customers. In this game, FM and LM delivery service providers are follower players that form a two-echelon logistics network which is coordinated by a leader player representing a green urban logistics platform. The leader optimally assigns parcels to satellites and LMs to minimize emissions across both echelons, while FM and LM followers adjust their operations accordingly. To determine optimal strategies, an exact cutting-plane algorithm is developed and benchmarked against a scalable data-driven heuristic approach based on constraint learning. To model followers’ best responses to leader assignment decisions, we implement a network-oriented learning approach where we learn FM and LM predictive models that can be used with large city-sized network instances. The proposed approaches are tested on realistic problems instances from Berlin, Madrid and Bologna. Our findings highlight the potential of the proposed game-theoretical model for reducing emissions while ensuring that stakeholders’ preferences such as on-time deliveries are taken into account.
A. O. Fajemisin, D. Rey, X. Brusset, (2026), European Journal of Operational Research,
doi: 10.1016/j.ejor.2026.07.044.