Integrating fuzzy TOPSIS and multi-period goal programming for purchasing multiple products from multiple suppliers

In this paper, a two-phase approach for supplier selection and order allocation problem under a fuzzy environment is proposed. We investigate a problem in which a single buyer orders multiple products from multiple suppliers in multiple periods. To account for inherent ambiguity and vagueness in most real-world data and information, in the first phase of the approach, a fuzzy multiple criteria decision making (FMCDM) method is used to obtain the overall ratings of alternative suppliers, and to select the most qualified ones for further evaluations. In the second phase, using the goal programming (GP) technique, we construct a multi-objective mixed integer linear programming (MOMILP) model to determine the order quantities of each selected supplier for each product in each period. In the MOMILP model, two goals are considered: 1) total value of purchasing (TVP) and 2) meeting the total available periodic budget. Constructing the approach in this way effectively reduces the risk of purchasing. This is because besides evaluating suppliers with regard to a set of quantitative and qualitative criteria, there is also a systematic way to purchase from more than one supplier. Finally, a numerical example is conducted to clarify the proposed approach and to show its usefulness.