Green Vendor Managed Inventory with Backorder in Two Echelon Supply Chain with Epsilon-Constraint and NSGA-II Approach

In the articles that have been investigated by the vendor managed inventory less attention to environmental pollution or emission of green logistics is considered. In this paper, the issue of green backorder vendor managed inventory in two-echelon supply has been considered. But innovation in green conditions of this article or reducing the amount of pollution is as a function intended purpose. In view of customer facing staff shortages in the supply chain, two-echelon warehouse and limits the number of orders is considered. The first objective is to maximize profit of vendor, which includes sales minus production and distribution costs and facing to shortage cost. The second objective function is minimizing the amount of pollution caused by the movement of goods. According to the model as a model of bi-objective, non-convex and non-linear algorithms is solved by GAMS and Epsilon-Constraint on a small scale can be used to obtain the Pareto front and compare with traditional inventory management in shortage state and for large scale non-dominated sorting genetic algorithm (NSGA-II) was used to solve the model. To adjust the algorithm parameters NSGA-II Taguchi method has been exploited in this article. The results of this research is that allowed the shortage situation, the lack of cost reduction and environmental pollution reduction, the greater the amount of shipping and orders as well as the lack of a less optimal to reduce the cost of inventory shortages.