خوشه بندی و انتخاب تامین کنندگان بر اساس الگوریتم های آنیل شبیه سازی شده

This study proposes two optimization mathematical models for the clustering and selection of suppliers. Model 1 performs an analysis of supplier clusters, according to customer demand attributes, including production cost, product quality and production time. Model 2 uses the supplier cluster obtained in Model 1 to determine the appropriate supplier combinations. The study additionally proposes a two-phase method to solve the two mathematical models. Phase 1 integrates kk-means and a simulated annealing algorithm with the Taguchi method (TKSA) to solve for Model 1. Phase 2 uses an analytic hierarchy process (AHP) for Model 2 to weight every factor and then uses a simulated annealing algorithm with the Taguchi method (ATSA) to solve for Model 2. Finally, a case study is performed, using parts supplier segmentation and an evaluation process, which compares different heuristic methods. The results show that TKSA+ATSA provides a quality solution for this problem.

Global competition means that companies must integrate with upstream and downstream supply chain partners efficiently to increase market opportunities and competitiveness and to adapt to rapid changes in market trends and customer demands. To satisfy customer demand and to lower internal cost and risk, companies select appropriate suppliers to make more competitive products and distribute these products to customers, according to the varied demands of those customers. Nonetheless, for a supply chain with a large number of suppliers, each supplier has a different product strategy and therefore a different level of competitiveness and customer demands are varied, in accordance with their preferences. If customer demand is not considered, then product types that are incompliant with customer expectations are produced, causing members of the supply chain system to suffer great losses. He et al. [1] mentioned that good supply chain management requires that companies select appropriate suppliers, according to the nature of the product purchased and the upstream market. Sun et al. [2] pointed out that the process of supplier evaluation is a process where both parties seek optimally balanced decisions in accordance with actual supplier manufacturability and serviceability. Appropriate incentives or punishments ensure a win–win situation for both parties. Wang and Wang [3] suggested that cluster analysis could be used to cluster all suppliers and to establish a supplier evaluation index, to effectively manage suppliers. Bottani and Rizzi [4] pointed out that suppliers with similar characteristics could be clustered by using cluster analysis to reduce supplier combinations. Sung and Ramayya [5] stated that cluster analysis could effectively differentiate supplier types. Therefore, this paper proposes a two-phase model to find the appropriate supplier combinations, which ensure that customer demand is fulfilled. In Model 1, suppliers are divided into several clusters, depending on the characteristics of customers’ demands. In Model 2, the more efficient supplier combinations are determined with respect to customer demand in the specific cluster determined by Model 1. Maria [6] and Kanungo et al. [7] pointed out that, for unsupervised learning, kk-means is the fundamental and most widely used clustering algorithm. However, Kanungo et al. [7] stated that selection of the initial cluster centroid for kk-means has a great influence on clustering result. If selection of the initial cluster centroid is flawed, the quality of the clustering is compromised. Liu et al. [8] also pointed out that kk-means is subject to initial weighting, which yields an unsatisfactory clustering result. A clustering solution that uses kk-means is usually confined to a local optimum, during the optimization clustering process. Wang et al. [9] proposed that the probabilistic acceptance of local minima, for SA, could provide strong local search capabilities and avoid confinement to a local optimum. Bandyopadhyay [10] applied SA to clustering and obtained good quality clustering results, as determined through experiments with artificial and real data sets. Wu et al. [11] applied SA to the clustering of incomplete data and the results showed a reduction in clustering errors. Hence, Model 1 uses SA to combine kk-means, for supplier clustering. Supplier evaluation and selection procedures in Model 2 include a quantity discount. Wang et al. [9] stated that when quantity discounts are used in planning, the associated problems are very complex and not easily solved through ordinary commercial software. Tsai [12] pointed out that it is difficult to find a global optimal solution for a nonlinear model with quantity discount variables. As already mentioned, SA provides a strong local search capability, so it is also used to solve for supplier selection for Model 2. The Taguchi method is used to set the proper level for each parameter of SA to yield a quality solution. The major aims of this study are as follows. (1) Create two optimization mathematical models for the clustering and selection of suppliers. In Model 1, suppliers are clustered with minimal total within cluster variation (TWCV), according to customer demands for the product type. Model 2 uses the results of Model 1 to determine the optimal supplier combination with consideration to quantity discount and customer demands. AHP is used, in this model, to weight each factor. (2) Create a two-phase method to solve Models 1 and 2. Phase 1 develops the TKSA method, which consists of the Taguchi method, kk-means and simulated annealing to solve for Model 1, and Phase 2 uses an ATSA method, which consists of an analytical hierarchy process, Taguchi method and simulated annealing to solve for Model 2. (3) Compare the quality of the solutions for different heuristic methods in each phase and verify that the proposed method TKSA+ATSA provides the best quality solution to the proposed problem.

This study presents a systematic methodology for the clustering and selection of suppliers. The methodology consists of two optimization mathematical models, which help decision makers to select the quality suppliers from the potential suppliers pool, and a two-phase method to solve the mathematical models effectively. The main results and contributions of this study are as follows. (1) The development of two optimization mathematical models for clustering and selection of suppliers: Model 1 is based on the customer demands to cluster suppliers with TWCV. Using the results from Model 1, Model 2 is primarily to evaluate the candidate suppliers with consideration to quantity discount and customer demands in the specific supplier cluster. (2) The development of the two-phase method for solving the mathematical models: the first phase uses the TKSA method, which consists of the Taguchi method, kk-means and a simulated annealing algorithm to solve Model 1 for the clustering of potential suppliers. The second phase uses the ATSA method, which consists of an analytic hierarchy process, the Taguchi method, and a simulated annealing algorithm to solve Model 2 and identify the combinations of quality suppliers. (3) A case study of notebooks in supplier clustering and selection, to compare the quality of the solution provided by different heuristic methods. With regard to the performance of the solutions, the results show that TKSA is better than TKGA and TKPSO in Phase 1, that ATSA is better than ATGA and ATPSO in Phase 2. In addition, the supplier selection result using Phase 1 and Phase 2 is better than that without Phase 1.