An integrated modeling for supplier selection and optimal lot sizing: A case study of four-echelon supply chain

Supply chain management is one of the new approaches that are considered significantly by variety of experts and enterprises in today competitive world. Supply chain refers to the network of facilities, supply centers, production centers and distribution centers which encompass various tasks such as providing raw materials, transforming raw materials to components or finished products and distributing them among customers. Regarding this issue, studying literature indicates on this fact that multi-level, multi-product, multi-period models in multi-sourcing situation by considering the supply capacity have not been taken into account notably and just few mathematical models are proposed for the analysis of such decisions. In this paper, it is attempted to investigate and delve into the supply chain planning issue in multi-level, multi-product, multi-period situation. In the proposed model, simultaneously optimization of two objectives is considered which entails maximizing the service level related to giving agreeable services to customers at each retailer´s site and minimizing the overall costs of supply chain. As the proposed mixed integer non-linear model has specific complexity, branch and bound solver is utilized and has been applied for a data set in an automotive supply chain. In this way, a model has been presented which determines the lot size of ordering among various members in a supply chain, the amount of holding inventory at each elements of supply chain´s site, optimal combination of selecting potential suppliers and the amount of ordering components to suppliers.