الگوریتم جستجوی پراکنده برای انتخاب تامین کننده و "تعیین اندازه دسته تولید" تحت محیط تخفیف قیمت متعدد

Supplier selection is one the most important elements of supply chain management. This function involves evaluation of many factors such as, cost of parts/materials, size of order, quality, and delivery performance. Therefore, this problem is categorized as multi-criteria decision making problems. Different approaches have been applied in order to assess and select the suppliers when suppliers offer discount on the unit price. In practical conditions, buyers may face a situation where different types of discount may be offered by candidate suppliers. None of the previous studies have considered different discount schemes simultaneously. In this article a mathematical model is introduced which consider different types of discount (all-unit cost, incremental discount, and total business volume discount) through multi-objective formulation for single item purchasing problem. In addition, constraints such as suppliers’ capacity and demand are taken into consideration in the model. Due to the complexity of the problem a proposed scatter search algorithm (SSA) is presented to solve this problem. Finally several sample problems have been solved by the proposed SSA and the exact (branch and bound) method. The results illustrate slight relative errors to compare with reasonable saving in computational times.

Supplier selection is one the most important components of production and logistics management in the competitive environment of the global market. As organizations become more dependent on their suppliers the direct and indirect consequences of poor decisions become more severe [4]. Such decisions involve the selection of individual suppliers to employ and the determination of order quantities to be placed with the selected suppliers. Practitioners need to follow strategies to achieve higher quality, reduced costs and shorter lead times to be able to compete in the global market. Within new strategies for purchasing and manufacturing, suppliers play a key role in achieving corporate competition [1], [9] and [27]. Many attributes affect a supplier’s performance. Dickson [8] identified 23 criteria that have been considered by purchasing managers in various supplier selection problems. Also Weber et al. [26] found that 47 out of 76 articles which they reviewed, addressed more than one criterion for supplier selection decision making. Hence supplier selection problem is a multiple criteria decision making (MCDM) problem and it is necessary to make a trade off between conflicting quantitative and qualitative criteria to select the best suppliers. Suppliers sometimes offer discounts. The motivation for using discount schemes stems from the fact that it tends to encourage buyers to procure larger quantities and to obtain operating advantages (such as economies of scale or reducing the cost of transportation) for the buyer. From a coordination perspective, it has been shown that both the buyer and the supplier can realize higher overall profits if discounting schemes are used to set transfer prices [25]. Various kinds of discount schemes which are usually offered by suppliers are discussed in relevant studies. So, the multi-objective supplier selection problem in presence of discount schemes becomes more complicated. Usually, two types of discounts—all-units discount and incremental discount—are used for cost reduction [3]. All-units model divides the range of possible order quantities into intervals with progressively lower unit costs. The unit cost corresponding to the size of a particular order is applied to every unit in the order. Dolan [10] and others argue, however, that the supplier is often better served by the incremental discount model, which applies a lower unit price only to those units purchased in excess of each successive breakpoint [21]. Finally total business volume discount model, described by Xia and Wu [28], is usually used when more than one item is to be purchased. In this paper we propose a mathematical model for a single item purchasing problem considering various discount schemes simultaneously. Considering both qualitative and quantitative criteria in this model and in addition, permitting various types of discount schemes by suppliers, make this model more practical in comparison with other previous studies. The remainder of this paper is organized as follows. In Section 2, some previous studies and researches on supplier selection problem in presence of discount offers are reviewed. In Section 3, the developed model of supplier selection problem when suppliers may offer various discount models is presented. In this model qualitative criteria are considered as well as quantitative criteria. In Section 4, the complexity of the problem is discussed and then a scatter search algorithm is proposed and in Section 5 the described problem and the impacts of varying situations on both formulation and optimum results are analyzed through some examples. In Section 6 the performance of the proposed SSA is evaluated by solving some sample problems. Finally in Section 7, conclusions achieved from this research are discussed.

In supplier selection decision making there are tangible and intangible conflicting factors that affect this decision making problem. Furthermore, in many real situations, suppliers may offer different discount schemes according to their selling policies. Hence, buyers face a complex decision making problem. This paper introduced a linear integer programming model in which qualitative and quantitative factors are considered. Furthermore, an extended cost objective function is modeled as a part of the main decision making model in which suppliers are allowed to offer any of the three discount schemes which are all-unit discount, incremental discount and total business volume discount. We discussed that for a single-item supplier selection problem the total business volume discount and all-unit discount are the same. The weighted sum of objective functions is used in development of the mathematical model to consider the importance of objectives and also obtaining a unique optimal decision for the problem. Since this problem is NP-hard, we proposed a scatter search algorithm (SSA) by which this problem can be solved. The performance of this SSA is evaluated through comparing its outputs with exact optimal solutions while solving 24 sample problems. For computing exact optimal solutions LINGO package version 8 is used. Results obtained from this evaluation showed that the proposed SSA can find solutions with high quality but in a short computational time.