انتخاب تامین کننده با معیارهای چندگانه در محیط های سطح تخفیف

Supplier selection is a multi-criteria decision making problem which includes both qualitative and quantitative factors. In order to select the best suppliers it is necessary to make a trade-off between these tangible and intangible factors some of which may conflict. When business volume discounts exist, this problem becomes more complicated as, in these circumstances, buyer should decide about two problems: which suppliers are the best and how much should be purchased from each selected supplier. In this article an integrated approach of analytical hierarchy process improved by rough sets theory and multi-objective mixed integer programming is proposed to simultaneously determine the number of suppliers to employ and the order quantity allocated to these suppliers in the case of multiple sourcing, multiple products, with multiple criteria and with supplier's capacity constraints. In this context, suppliers offer price discounts on total business volume, not on the quantity or variety of products purchased from them. A solution methodology is presented to solve the multi-objective model, and the model is illustrated using two numerical examples.

Supplier selection decisions are an important component of production and logistics management for many firms. Such decisions entail the selection of individual suppliers to employ, and the determination of order quantities to be placed with the selected suppliers. Selecting right suppliers significantly reduces the material purchasing cost and improves corporate competitiveness, which is why many experts believe that the supplier selection is the most important activity of a purchasing department [1] and [2]. Many factors affect a supplier's performance. Dickson [3] identified 23 criteria that have been considered by purchasing managers in various supplier selection problems. More recently, a review of supplier selection criteria and methods by Weber et al. [4] found that 47 of the 76 articles reviewed addressed more than one criterion. Hence supplier selection problem (SSP) is a multiple criteria problem and it is necessary to make a trade-off between conflicting tangible and intangible factors to find the best suppliers. SSP is complicated by the fact that various criteria must be considered in the decision making process. SSP is further complicated by the fact that individual suppliers may have different performance characteristics for different criteria. For example, the supplier who can supply an item for the lowest per unit price may not have the best quality or service performance among the competing suppliers. Supplier selection is therefore an inherent multi-objective decision that seeks to minimize procurement cost, maximize quality and service performance concurrently. Often complicating the SSP for the buyer is the presence of price discounts, offered by supplier, that depend on the total value of sales volume, not on the quantity or variety of products purchased over a given period of time. In traditional quantity discount pricing schedules, price breaks are a function of the order quantity which existed for each product, irrespective of the total purchasing volume over a given period of time. With the advent of just-in-time (JIT) purchasing, the strategy that calls for ordering smaller lot-size is more practical and feasible. So suppliers are finding it more meaningful to give discounts based on the total value of multi-product orders (i.e. total business volume) placed by a given buyer. The remainder of this paper is organized as follows. The Section 2 cites the relevant literature to SSP. The improved analytic hierarchy process (AHP) by rough sets theory is introduced in Section 3. Formulation of the multi-objective mathematical model is presented in Section 4. Section 5 describes the experimental design and solution methodology to multi-objective optimization. Finally, concluding remarks are provided in Section 6.

Little attention is given in the literature to decisions on the appropriate selection of suppliers, and on assigning order quantities to these suppliers, in the case of multiple sourcing, with multiple criteria and with supplier's capacity constraints. Increasing attention toward supplier partnership not only raises the importance of supplier selection but also increases the significance of considering qualitative factors in this decision making process. AHP can be very useful in involving several decision-makers with different conflicting objectives to arrive at a consensus decision. By improving AHP with rough sets theory in this paper, the qualitative judgment can be quantified to make comparison more intuitionistic and reduce or eliminate assessment bias in pairwise comparison process. Taking the supplier's capacity constraints and price discounts into account makes SSP complicated. This paper introduced a multi-objective mixed integer programming model to support supplier selection decisions between conflicting tangible and intangible factors. The AHP-based model offers viable approach to supplier selection with price discounts because of the availability of MATLAB software packages that provide flexible and efficient computational tools for solving the model. Results of two computational examples suggest that the model can help a buyer determine the optimal set of suppliers to employ and make order quantity allocation among suppliers. The use of the proposed model indicates that it can be applied to improve the group decision making in selecting suppliers. Also, it is found that the decision process is systematic and that supplier selection with price discounts can be performed at the fingertips of buyer.