An integrated facility location-inventory model using Lagrangian relaxation approach with a FMCG case study

Supply chain management and distribution network design have attracted the attention of many researchers during recent years. This paper addresses a multi-product system of location problem in distribution network that incorporates inventory decisions for each product into capacitated facility location models. In the development of mathematical model, the data of real case study of fast moving consumer goods company is used. A mixed integer nonlinear mathematical programming model is proposed and due to difficulty of obtaining the optimal solution in real-scaled problems, a heuristic solution approach based on Lagrangian relaxation algorithm and sub-gradient method is presented. The proposed solution method is compared with the optimization software on randomly generated test problems with different size. Computational results show that the performance of proposed solution algorithm is very promising in terms of various indexes including 89.1% of DCs capacity, duality gap average and the worst case 1.14% and 3.12% respectively. The results of considered case study also reduced the number of distribution centers from 17 to 12 centers. Finally, some managerial insights are mentioned.