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.

In the context of supply chain management, supplier selection plays a key role in reaching desirable production planning. In today & apos; s competitive world, many enterprises have focused on selecting the appropriate suppliers in an attempt to reduce purchasing costs and improve quality products and services. Supplier selection is a multi-criteria decision problem, which includes different qualitative and quantitative criteria such as purchase cost, on time delivery, quality of service, etc. In this study, a fuzzy multi-objective mathematical programming model is presented to select appropriate supplier and assign desirable order to different supplies. The proposed model was implemented for an organization by considering 16 different scenarios and the results are compared with two other existing methods.

The most popular approach for solving fully fuzzy linear programming (FFLP) problems is to convert them into the corresponding deterministic linear programs. Khan et al. (2013) [Khan, I. U., Ahmad, T., & Maan, N. (2013). A simplified novel technique for solving fully fuzzy linear programming problems. Journal of Optimization Theory and Applications, 159(2), 536-546.] claimed that there had been no method in the literature to find the fuzzy optimal solution of a FFLP problem without converting it into crisp linear programming problem, and proposed a technique for the same. Others showed that the fuzzy arithmetic operation used by Khan et al. (2013) had some problems in subtraction and division operations, which could lead to misleading results. Recently, Ezzati et al. (2014) [Ezzati, R., Khorram, E., & Enayati, R. (2014). A particular simplex algorithm to solve fuzzy lexicographic multi-objective linear programming problems and their sensitivity analysis on the priority of the fuzzy objective functions. Journal of Intelligent and Fuzzy Systems, 26(5), 2333-2358.] defined a new operation on symmetric trapezoidal fuzzy numbers and proposed a new algorithm to find directly a lexicographic/preemptive fuzzy optimal solution of a fuzzy lexicographic multi-objective linear programming problem by using new fuzzy arithmetic operations, but their model was not fully fuzzy optimization. In this paper, a new method, by using Ezzati et al. (2014)’s fuzzy arithmetic operation and a fuzzy version of simplex algorithm, is proposed for solving FFLP problem whose parameters are represented by symmetric trapezoidal fuzzy number without converting the given problem into crisp equivalent problem. By using the proposed method, the fuzzy optimal solution of FFLP problem can be easily obtained. A numerical example is provided to illustrate the proposed method.