With the emerging trend of green supply chain management, supplier selection and order allocation based on green criteria have become very important in this competitive world. During the selection process of the eligible suppliers, qualitative as well as quantitative factors should be considered. In this paper, a novel mathematical model is developed to select a set of suppliers, and assign the order quantity. Due to the importance of environmental concerns, both qualitative and quantitative environmental criteria are taken into account in this research. The proposed model comprises two phases namely a two-stage QFD, and a stochastic multi-objective mathematical model. The stochastic (scenario) approach helps to manage the uncertainty in the order allocation process. Furthermore, trapezoidal fuzzy numbers are utilized to handle the vagueness in human thoughts. The application of the proposed model is shown in beverages industry.