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Recently, much attention has been given to Stochastic demand due to uncertainty in the real -world. In the literature, decision-making models and suppliers\' selection do not often consider inventory management as part of shopping problems. On the other hand, the environmental sustainability of a supply chain depends on the shopping strategy of the supply chain members. The supplier selection plays an important role in the green chain. In this paper, a multi-objective nonlinear integer programming model for selecting a set of supplier considering Stochastic demand is proposed. while the cost of purchasing include the total cost, holding and stock out costs, rejected units, units have been delivered sooner, and total green house gas emissions are minimized, while the obtained total score from the supplier assessment process is maximized. It is assumed, the purchaser provides the different products from the number predetermined supplier to a with Stochastic demand and the uniform probability distribution function. The product price depends on the order quantity for each product line is intended. Multi-objective models using known methods, such as Lp-metric has become an objective function and then uses genetic algorithms and simulated annealing meta-heuristic is solved.