A two-echelon location-routing model for designing a pooled distribution supply chain

In literature, the majorities of paper on the subject of modeling pooled distribution supply chain (SC) are based on vehicle routing problem and propose models for, only, the operational level of the supply chain. Modeling pooled SC is a problem including a strategic decision consisting of designing a network by locating a number of logistical platforms and tactical /operational decisions dealing with the customer allocation and vehicle routing. So, it will be interesting to propose and study a model as two echelons Location Routing problem (2E-LRP) for this type of chain for a more comprehensive resolution that separate decision levels. We opt for a multi-sourcing and multi-products 2E-LRP in which routes can end at different depots than the starting one in contrary of classical formulations. We add to usual constraints of 2E-LRP those specific to pooling. We propose a mixed integer linear programming (MILP) formulation for this problem. To measure the performance of our method, we have used Matlab solver to solve the MILP using extended known 2E-LRP instances and different configurations of costumers. The results obtained by comparing a collaboration scenario and non-collaboration one, show that collaboration leads to a reduction in transport costs, travel distances, and CO2 emissions in addition to the improvement of the vehicle load rate. This work opens up new lines of research in this area.