Coordinating Delivery Service Providers for Greener Two-Echelon Vehicle Routing Via Bilevel Optimization: Exact and Data-Driven Methods
41 Pages Posted: 10 Jul 2024
Abstract
This paper presents a single-leader multi-follower game with two echelons in urban logistics to minimize carbon emissions. The First-Mile (FM) delivery service providers from warehouses outside the city deliver parcels to microhubs at city outskirts so that Last-Mile (LM) service providers with greener vehicles finalize delivery to customers. The leader assigns parcels to microhubs and to LMs minimizing total emissions at both echelons while each FM and LM minimizes cost and respecting time windows. The present study can be viewed as a centralized collaborative logistics approach but differs from the existing literature in its formulation of the collaborative model where the preferences of all players are jointly considered by the leader through a hierarchical game structure and applies bilevel optimization for coordinated routing. To find optimal strategies, an exact cutting-plane algorithm is developed and then compared to a scalable heuristic approach based on constraint learning. The data-driven constraint learning approach solves a single-level reformulation of the bilevel problem where followers' best responses are approximated through predictive models. 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 Madrid and Berlin. Our findings highlight the potential of the proposed game-theoretical model for reducing emissions in urban logistics while ensuring that stakeholders' preferences such as on-time deliveries are taken into account. Our experiments also show that the data-driven method is able to find efficient solutions in competitive time.
Keywords: Bilevel optimization, Constraint learning, Green logistics, Two-echelon vehicle routing, Delivery service providers
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