فرآیند تحلیلی یکپارچه و برنامه ریزی ریاضی برای مشکل انتخاب تامین کننده با تخفیف کمیت

In this article an integration of analytical hierarchy process and non-linear integer and multi-objective programming under some constraints such as quantity discounts, capacity, and budget is applied to determine the best suppliers and to place the optimal order quantities among them. This integration-based multi-criteria decision making methodology takes into account both qualitative and quantitative factors in supplier selection. While the analytical hierarchy process matches item characteristics with supplier characteristics, non-linear integer programming model analytically determines the best suppliers and the optimal order quantities among the determined suppliers. The objectives of the mathematical models constructed are maximizing the total value of purchase (TVP), minimizing the total cost of purchase (TCP) or maximizing TVP and minimizing TCP simultaneously. In addition, several “what if” scenarios are facilitated and the quality of the resulting models is evaluated on real-life data.

The selection of suppliers plays a key role in an organization because the cost of raw material constitutes the main cost of the final product. A typical manufacturer spends 60% of its total sales on purchased items such as raw materials, parts, subassemblies and components [1]. In automotive industries, these costs may be more than 50% of the total revenues. That can go up to 80% of the total product costs for high technology firms [2]. Many experts believe that the supplier selection is the most important activity of a purchasing department [3]. Therefore, the supplier link in the supply chain appears to have significant cost-cutting opportunities. Determining selection criteria and selection techniques are the most important sides of supplier selection.

Little attention is given in the literature to decisions on the appropriate selection of suppliers, and on assigning order quantities to these suppliers in case of discounted cost. Taking into account the demand, supplier’s and manufacturer’s capacity, minimum order quantity, limitation on the number of selected suppliers, total capacities of selected suppliers and discounted cost makes the supplier selection process more complicated. We have suggested an integrated AHP and non-linear integer programming and multi-objective integer programming models for maximizing TVP, minimizing TCP and maximizing TVP and minimizing TCP simultaneously. The integrated method presented in this paper apply the AHP which uses pair wise comparison to make trade-offs between tangible and intangible factors and calculate a weight of suppliers. Applying these weights as coefficients of an objective function in the proposed models determines the best suppliers and assigns optimal order quantities to the determined suppliers under constraints such as quantity discounts and the total capacity of the selected suppliers. In addition, we have demonstrated the use of integrated approach on purchasing a frame in a prominent automotive manufacturer firm in Turkey and several “what if” scenarios are facilitated and the corresponding solutions are compared.