An integrated supply chain production–distribution planning with stochastic demands

•A new comprehensive hierarchical model for designing production–distribution network.•Inventory decisions have been incorporated in the production planning.•In the location/allocation model multi-level capacitated warehouses is considered.•A novel and efficient solution procedure is based on the LR method and GA.•Results indicated that the model yields high-quality solutions.

In this paper a three echelon supply chain with multiple distribution centers, production sites and suppliers is modeled. For this supply chain several commodities with defined items is produced. The model is categorized as a capacitated facility location model. The hierarchical approach is used to modeling and based on decision types the model is divided into two levels. The solution approach is based on the Lagrangian Relaxation approach, improved by an efficient heuristic to solve complex sub-problems. Computational results indicated that the proposed method yields high-quality solutions within a reasonable computational time for various real size problems.