A two stage approach for supplier selection problem in multi-item/multi-supplier environment with quantity discounts

The main structure of the proposed approach.Display Omitted First stage employs Fuzzy AHP to find the relative weights of criteria.Second stage runs the proposed MILP model to select the best suppliers.A case study is performed to select a maximum of 3 among 6 suppliers.Considering 4 criteria: price, quality, delivery time, and after sales performance.To purchase 5 items in case of all-unit quantity discount allowed. Supplier selection, which is the basic process of finding the best supplier/suppliers to procure the items regarding various criteria, is an important decision problem to be studied. It becomes more complicated if there are various items and any supplier cannot provide all types of items individually. Such situations are called multi-item, multi-supplier environments and rarely studied in the literature. In addition, when quantity discounts are also considered, it gets more sophisticated. Although there are several studies dealing with these aspects separately, to the best knowledge of the authors, this study is the first candidate attempting to solve this type of problem with an integrated approach including Fuzzy Analytical Hierarchy Process (F-AHP) and Mixed Integer Linear Programming (MILP) model.This study mainly operates in two stages. In the first stage, the relative weights of each criterion for each type of item are determined via F-AHP technique. In the second stage, these outputs are used as inputs in the MILP model to determine the suppliers and the quantities to be provided. In order to validate the model, an application is performed in a gear motor company and numerical results of the problem are revealed to select the best suppliers among 6 alternatives, for the procurement of 5 items regarding 4 criteria, namely, price, quality, delivery time performance, and after sales performance, in case of quantity discounts.

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