This paper presents a mathematical model to solve a multi-objective decision making supplier selection problem. The proposed problem considers three objective functions: the first objective function minimizes the cost of purchasing the products while the second objective function minimizes the due dates and finally the third objective function maximizes the customer satisfaction. The resulted problem is formulated as mixed integer programming and, therefore, we use invasive weed optimization technique to solve the resulted problem. The performance of the proposed model is compared with NSGA II based on different criteria such as mean ideal distance and quality matrix. The preliminary results indicate that the proposed model performs relatively well compared with alternative method.