The rapid advancement of e-commerce has driven unprecedented expansion in urban logistics networks, where their sustainability is constrained by multifaceted factors including strict time-bound service requirements, employee’s satisfaction, traffic congestion, and carbon emission regulations. Among these critical elements, employee’s satisfaction reflected by the workload balance not only influences task execution quality but also affects long-term operational sustainability for logistics enterprises, rendering its enhancement an urgent priority in contemporary urban logistics practices. This paper thus investigates a sustainable urban logistics vehicle routing problem mainly focusing on this perspective. Initially, a bi-objective mixed-integer programming model is formulated to simultaneously minimize total delivery cost and workload balance. Subsequently, a hybrid metaheuristic algorithm combining path relinking (PR) with multi-directional local search framework is developed. The adaptive large neighborhood search is adopted to facilitate the intensive local exploration, while PR techniques enhance global search capabilities through systematic solution space diversification. The algorithm’s validity is rigorously verified through comparative analyses with state of art multi-objective optimization algorithms using adapted benchmark instances. Computational results demonstrate the algorithmic effectiveness and efficiency, accompanied by detailed analyses of approximate Pareto front and model’s sensitivity. These findings advance the field of urban delivery and provide practical insights for implementing efficient and sustainable urban logistic systems.
https://doi.org/10.1016/j.jii.2025.100985Cite as:
@article{zhao2025bi,
title={Bi-objective sustainable urban logistics vehicle routing problem with workload balance},
author={Zhao, Wenyan and Yuan, Yaguang and Cheng, Cong and Liu, Wenheng},
journal={Journal of Industrial Information Integration},
pages={100985},
year={2025},
publisher={Elsevier}
}