A Bi-Objective Green Vendor Inventory model for a Two-echelon Supply Chain

According to the literature of vendor managed inventory, less attention to environmental pollution or green emissions of supply chain systems has been considered. This study aims to probe the issue of green backorder vendor managed inventory in a two-echelon supply chain system for the first time. In view of customer facing, staff shortages in the supply chain, two-echelon warehouse and limits the number of orders are 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 developed problem as a model of bi-objective, non-convex and non-linear, by GAMS and 𝜺-constraint method on some samples which studies in the related articles, the problem has been solved. Also, 𝜺-constraint method is used to obtain the Pareto front. Finally, results confirms that allowed the shortage situation, the lack of cost 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.