Time-Dependent Green Location-Routing Problem with the Consideration of Spatio-Temporal Variations

Urban logistics systems are under mounting pressure to decarbonize while meeting growing freight demand. This study addresses this dual challenge by formulating a novel Time-Dependent Green Location-Routing Problem with Spatio-Temporal Variations (TDGLRP-STV). Our proposed framework integrates a dynamic carbon emission calculation method that explicitly links real-time traffic dynamics with the energy consumption patterns of electric logistics vehicles (ELVs), enabling precise, spatio-temporally resolved emission quantification. To tackle the NP-hard complexity arising from the coupling of emission objectives with location-routing decisions, we devise a Two-Stage Interactive Optimization Algorithm (TSI-LR-IACO). This algorithm synergizes Lagrangian Relaxation (LR) and an Improved Ant Colony Optimization (IACO) through a bidirectional feedback mechanism, effectively coordinating strategic facility location with tactical vehicle routing. Numerical experiments based on real-world metropolitan road network data from Beijing demonstrate the efficacy of our approach. The TSI-LR-IACO achieves a 5% reduction in total carbon emissions with a merely 0.01% increase in total system cost, validating its ability to balance environmental and economic objectives. This research provides a scalable and scientifically robust decision-support framework for advancing low-carbon urban logistics.