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An efficient decision making model was developed to select suppliers using Multi-Layer Feed Forward Neural Networks. Both types of criteria: qualitative and quantitative, were considered in the model. Fuzzy techniques were applied to convert qualitative data to quantitative data. The model structure was designed and tested. The results of the neural network model indicated that the proper structure of the model had a crucial effect on its performance. The selection of appropriate initial weights, learning rate and momentum were critical in improving the model performance. The applied genetic algorithm showed better performance in comparison with backpropagation. The genetic algorithm was applied in the neural network model to generate weights and to design the architecture of the network. Several methods were applied to improve backpropagation, and the results showed that the difference between these two techniques was not significant. To prove the capability of the proposed model, suppliers of three products were ranked based on the proposed model and the results were compared with the managers' ranking. The Grey method was also applied as one decision making model to rank suppliers of these three products. The results of suppliers' rank based on the proposed applied genetic algorithm model showed a better performance than Grey method. Application of pairwise comparisons matrices for the weight assignment in Grey method indicated an improvement in the results. The proposed applied genetic algorithm model can use historical data of suppliers to evaluate their performance in the vendor supplier selection decision. The vendor can update the suppliers' database information over time for future decisions.