Location-routing and cost-sharing models under joint distribution

This article introduces the concept of joint distribution context into the location-routing problem (LRP) to tackle the issue of resource waste and high costs in distribution centers (DCs) for multiple companies. Fixed costs of constructing DCs, fixed costs of hiring vehicles, and routing costs are taken into account when constructing the mixed integer programming (MIP) model. A two-stage algorithm is designed to solve this problem. In the first stage, K-means clustering is used to group demand nodes with vehicle capacity constraints. In the second stage, the simplified LRP model is solved by Lingo, and locations of DCs and routing schemes are obtained. Additionally, a cost-sharing model based on the desirability function is developed to address the cost allocation problem among companies. The results and sensitivity analysis demonstrate that the joint distribution can effectively reduce costs.