mixed programming

Recently, the supply chain of perishable goods, have been considered due to their impact on human life. On the other hand, in the packaging industry, considering paper as a primary and perishable material due to the nature of water absorption, severe rotting in front of sunlight, flammability and turning to ash and finally affecting the final quality of the product produced from this issue. It is not excluded, it has attracted more attention. The high level of speed of changes and ambiguity in decisions has made it impossible to predict the future conditions of supply chains. Therefore, the design and use of a mathematical model for the design of the closed-loop supply chain network, taking into account the optimal pricing of products, the return rate and demand, along with taking into account the wastage of materials in the system, is strongly needed. At first, the supply chain of the paper-cardboard industry was designed and modeled with mixed integer programming, then due to the high volume of calculations and data of the problem, we can't receive exact solution approaches, the innovative approach of searching for harmony was used for the solution. . The problem is a single-objective model that minimizes system costs by considering environmental considerations. The present research shows that the price increase has a positive effect on the product return rate and reducing the level of product corruption. Finally, to validate the model, the numerical solution of a closed loop network has been done in this industry.