A Mixed Integer Nonlinear Programming Model for a Green Closed-Loop Supply Chain Optimization (Case Study: Kalleh Dairy Company)

In this research, a mixed integer nonlinear programming (MINLP) model is presented to optimize a closed loop supply chain in dairy industry. The mentioned supply chain includes production, distribution and sales. The proposed model contains two objective functions. The first one is economic and seeks to maximize total profit and the second one is aiming to minimize CO2 emissions and COD as environmental objective function. Also, a green vehicle routing problem is presented to addresses the relationship between distributor and customers. This problem includes several products, several warehouses, several types of vehicles and several time periods. Due to complexity and NP-hardness of this problem, the NSGAII algorithm has been applied to resolve the problem. In order to evaluate the validity of this algorithm, some small problems have been designed and solved in Lingo software. The results also were compared with the outcomes of the meta-heuristic method. Finally, the effect of fat loss, as one of the most affecting factors on dairy wastewater pollution, was also investigated. The results showed the efficiency of NSGAII algorithm and the direct effect of fat loss rate on wastewater pollution.