Facility Location and Determination of the Transportation Routes in the Closed-loop Supply Chain Considering the Holding Cost

In recent years, the green supply chain has become a key strategy for the competitiveness of organizations, where the reverse and closed-loop supply chains are one way to achieve it. In the current competitive environment, the closed-loop supply chain helps reduce costs by re-using recyclables and reducing environmental pollution by reducing waste and extending product life. In this study, a closed-loop integrated logistics network is studied in seven levels, and an integer nonlinear-programming model is proposed to minimize the total costs of facility location, transportation, and holding costs of materials and products. By this model, each facility's location in each level, the transportation of materials and products between them are determined by heterogonous vehicles and well-known customer demands. Finally, to validate the proposed model, a numerical example is designed and solved by GAMS software, and its results are analyzed.