Computational Methods in Engineering

In the recent decades, raw materials and resources have been remarkable issues for researchers; in other words, they play an important role in manufacturing industries or service organizations. On the other hand, the population is increasing every day. An increase in the population means the increased demand for goods or services. Therefore, more resources are needed to deliver services or goods. For this reason, government agencies and environmental agencies have developed and enforced stringent laws against producers and service providers who have exceeded the permissible limits for the environment; in some cases, the use of resources has been even restricted. In the meantime, the supply chain has become one of the major issues that can greatly influence this issue. In this research, the supply chain of the closed loop has been modeled due to uncertainty, disturbances and cost of production. The purpose of this problem has been to minimize the cost of the system in question based on the location decisions, and flow rates between levels and sales. The Lagrangian liberation solution method is used to solve this NP-hard problem. In the end, a numerical example has been employed to test the model and the proposed solution method. The results show that the time of implementation of the large-scale problem with GAMS is higher than that of the proposed method.