Hao Ji's research while affiliated with Xi’an International Studies University and other places

The rapid growth of e-commerce has heightened the importance for express delivery companies to ensure timely deliveries. Consequently, it is essential to explore ways to deliver more packages to customers while simultaneously reducing costs through the adoption of a joint distribution mode. This study presents a two-level delivery location selection model within the joint distribution mode, considering factors such as delivery station capacity and the number of transport vehicles, with the objective of minimizing the total cost associated with selecting delivery station locations. The proposed model is addressed using a combination of the k-means algorithm and the improved discrete firefly algorithm. In addition, to facilitate equitable cost allocation among enterprises, the Shapley value method is introduced in this study. A case study based on real data from an urban distribution network in the city of Hebei Province, China, is adopted to perform the experiments. The results of this study indicate that the improved algorithm not only improves solution accuracy but also reduces solution time when compared to both the particle swarm optimization and artificial bee colony methods. Furthermore, the application of the Shapley value method demonstrates the efficacy of a rational allocation of costs.