مدل‌های تصمیم برای ارزیابی و انتخاب تأمین کنندگان در حضور داده‌های اصلی ‏و ترتیبی، محدودیت‌های وزنی و عوامل غیرقابل کنترل: یک رویکرد مبتنی بر ‏DEA‏ با مرز دوگانه

نوع مقاله: مقاله پژوهشی

نویسندگان

1 گروه ریاضی کاربردی، واحد پارس‌آباد مغان، دانشگاه آزاد اسلامی، پارس‌آباد مغان، ایران

2 گروه ریاضی، واحد گرمی، دانشگاه آزاد اسلامی، گرمی، ایران

چکیده

انتخاب تأمین کننده‌ی مناسب برای برون‌سپاری اکنون یکی از مهم‌ترین تصمیمات بخش خرید است. این ‏تصمیمات بخش مهمی از مدیریت تولید و تدارکات برای بسیاری از بنگاه‌ها هستند. بعلاوه، تأمین کنندگان را ‏می‌توان به صورت نسبی از دیدگاه‌های خوشبینانه و بدبینانه ارزیابی و انتخاب کرد. روش تحلیل پوششی ‏داده‌ها برای اندازه‌گیری کارایی سیستم‌های تولیدی به کار می‌رود که ورودی‌های متعددی را مصرف ‏می‌کنند ‏و خروجی‌های متعددی را تولید می‌نمایند. در شرایط نرمال، مطلوب این است که ورودی‌های کمتری ‏مصرف ‏شوند و خروجی‌های بیشتری تولید شوند، زیرا این کار منجر به کارایی بالاتری می‌شود. این مقاله یک رویکرد ‏جدید «تحلیل پوششی داده‌ها با مرز دوگانه» را برای ارزیابی و انتخاب تأمین کنندگان پیشنهاد می‌کند. رویکرد ‏تحلیل پوششی داده‌ها با مرز دوگانه، می‌تواند بهترین تأمین کننده را در حضور محدودیت‌های وزنی، عوامل ‏غیرقابل کنترل، و داده‌های اصلی و ترتیبی شناسایی کند. در این رویکرد، پیشنهاد می‌شود که هر دو کارایی ‏خوشبینانه و بدبینانه نسبی را در قالب یک کارایی میانگین هندسی ادغام کنیم. کارایی میانگین هندسی نشان ‏دهنده‌ی عملکرد کلی هر تأمین کننده می‌باشد. مشاهده می‌شود که کارایی میانگین هندسی قدرت افتراق ‏بیشتری نسبت به هر کدام از دو کارایی خوشبینانه و بدبینانه دارد. یک مثال عددی کاربرد روش پیشنهادی را ‏نشان می‌دهد.‏

کلیدواژه‌ها


عنوان مقاله [English]

Decision models for evaluation and selection of suppliers in the presence of ‎cardinal and ordinal data, weight restrictions, and non-discretionary factors: ‎An approach based on DEA with double frontiers

نویسندگان [English]

  • Hossein Azizi 1
  • Rasul Jahed 2
1 Department of Applied Mathematics, Parsabad Moghan Branch, Islamic Azad University, Parsabad Moghan, Iran.
2 Department of Mathematics, Germi Branch, Islamic Azad University, Germi, Iran
چکیده [English]

Selection of suppliers for outsourcing is now one of the most important decisions of the purchasing ‎department. These decisions constitute an important part of the production and logistics ‎management in many firms. On the other hand, suppliers can be evaluated and selected from ‎optimistic and pessimistic perspectives. There is an argument that both points of view must be ‎considered simultaneously, and any approach that considers only one perspective is biased. This ‎paper proposes a new “data envelopment analysis (DEA) with double frontiers” approach for ‎evaluation and selection of suppliers. The DEA with double frontiers approach can identify the best ‎supplier in the presence of weight restrictions, non-discretionary factors, and cardinal and ordinal ‎data. This paper proposes to integrate both efficiencies in the form of a geometric mean efficiency ‎that measures the overall performance of each supplier. It is shown that geometric mean efficiency ‎has more discriminative power than any of the optimistic and pessimistic efficiencies. A numerical ‎example illustrates the application of the proposed method.‎

کلیدواژه‌ها [English]

  • Data envelopment analysis
  • Supplier selection
  • Weight restriction and Non-discretionary factors
  • ‎Cardinal and ordinal data
  • Optimistic and pessimistic efficiencies‎

      1.            Akarte, M. M., Surendra, N. V., Ravi, B., & Rangaraj, N. (2001). Web based casting supplier evaluation using analytical hierarchy process. Journal of the Operational Research Society, 52, 511-522.

      2.            Azizi, H. (2011). The interval efficiency based on the optimistic and pessimistic points of view. Applied Mathematical Modelling, 35, 2384-2393.

      3.            Azizi, H. (2013). A note on data envelopment analysis with missing values: an interval DEA approach. The International Journal of Advanced Manufacturing Technology, 66, 1817-1823.

      4.            Azizi, H., & Fathi Ajirlu, S. (2010). Measurement of overall performances of decision-making units using ideal and anti-ideal decision-making units. Computers & Industrial Engineering, 59, 411-418.

      5.            Azizi, H., & Ganjeh Ajirlu, H. (2011). Measurement of the worst practice of decision-making units in the presence of non-discretionary factors and imprecise data. Applied Mathematical Modelling, 35, 4149-4156.

      6.            Azizi, H., & Jahed, R. (2011). Improved data envelopment analysis models for evaluating interval efficiencies of decision-making units. Computers & Industrial Engineering, 61, 897-901.

      7.            Azizi, H., Kordrostami, S., & Amirteimoori, A. (2015). Slacks-based measures of efficiency in imprecise data envelopment analysis: An approach based on data envelopment analysis with double frontiers. Computers & Industrial Engineering, 79, 42-51.

      8.            Azizi, H., & Wang, Y.-M. (2013). Improved DEA models for measuring interval efficiencies of decision-making units. Measurement, 46, 1325-1332.

      9.            Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis. Management Science, 30, 1078-1092.

  10.            Banker, R. D., & Morey, R. C. (1986). Efficiency Analysis for Exogenously Fixed Inputs and Outputs. Operations Research, 34, 513-521.

  11.            Bhutta, K. S. (2002). Supplier selection problem: a comparison of the total cost of ownership and analytic hierarchy process approaches. Supply Chain Management: An International Journal, 7, 126-135.

  12.            Braglia, M., & Petroni, A. (2000). A quality assurance‐oriented methodology for handling trade‐offs in supplier selection. International Journal of Physical Distribution & Logistics Management, 30, 96-112.

  13.            Charnes, A., Cooper, W. W., Wei, Q. L., & Huang, Z. M. (1989). Cone ratio data envelopment analysis and multi-objective programming. International Journal of Systems Science, 20, 1099-1118.

  14.            Chen, C.-T., Lin, C.-T., & Huang, S.-F. (2006). A fuzzy approach for supplier evaluation and selection in supply chain management. International Journal of Production Economics, 102, 289-301.

  15.            Cook, W. D., Kress, M., & Seiford, L. M. (1993). On the Use of Ordinal Data in Data Envelopment Analysis. Journal of the Operational Research Society, 44, 133-140.

  16.            Cook, W. D., Kress, M., & Seiford, L. M. (1996). Data Envelopment Analysis in the Presence of Both Quantitative and Qualitative Factors. Journal of the Operational Research Society, 47, 945-953.

  17.            Cook, W. D., & Zhu, J. (2006). Rank order data in DEA: A general framework. European Journal of Operational Research, 174, 1021-1038.

  18.            Cooper, W. W., Park, K. S., & Yu, G. (1999). IDEA and AR-IDEA: Models for Dealing with Imprecise Data in DEA. Management Science, 45, 597-607.

  19.            Cooper, W. W., Park, K. S., & Yu, G. (2001a). IDEA (Imprecise Data Envelopment Analysis) with CMDs (Column Maximum Decision Making Units). Journal of the Operational Research Society, 52, 176-181.

  20.            Cooper, W. W., Park, K. S., & Yu, G. (2001b). An Illustrative Application of Idea (Imprecise Data Envelopment Analysis) to a Korean Mobile Telecommunication Company. Operations Research, 49, 807-820.

  21.            Despotis, D. K., & Smirlis, Y. G. (2002). Data envelopment analysis with imprecise data. European Journal of Operational Research, 140, 24-36.

  22.            Ebrahimi, B., & Toloo, M. (2019). Efficiency bounds and efficiency classifications in imprecise DEA: An extension. Journal of the Operational Research Society, 1-14.

  23.            Farzipoor Saen, R. (2006a). An algorithm for ranking technology suppliers in the presence of nondiscretionary factors. Applied Mathematics and Computation, 181, 1616-1623.

  24.            Farzipoor Saen, R. (2006b). A decision model for selecting technology suppliers in the presence of nondiscretionary factors. Applied Mathematics and Computation, 181, 1609-1615.

  25.            Farzipoor Saen, R. (2007). Suppliers selection in the presence of both cardinal and ordinal data. European Journal of Operational Research, 183, 741-747.

  26.            Farzipoor Saen, R. (2009). Supplier selection by the pair of nondiscretionary factors-imprecise data envelopment analysis models. Journal of the Operational Research Society, 60, 1575-1582.

  27.            Farzipoor Saen, R. (2009). A decision model for ranking suppliers in the presence of cardinal and ordinal data, weight restrictions, and nondiscretionary factors. Annals of Operations Research, 172, 177-192.

  28.            Forker, L. B., & Mendez, D. (2001). An analytical method for benchmarking best peer suppliers. International Journal of Operations & Production Management, 21, 195-209.

  29.            Humphreys, P. K., Wong, Y. K., & Chan, F. T. S. (2003). Integrating environmental criteria into the supplier selection process. Journal of Materials Processing Technology, 138, 349-356.

  30.            Jahed, R., Amirteimoori, A., & Azizi, H. (2015). Performance measurement of decision-making units under uncertainty conditions: An approach based on double frontier analysis. Measurement, 69, 264-279.

  31.            Kao, C., & Lin, P.-H. (2011). Qualitative factors in data envelopment analysis: A fuzzy number approach. European Journal of Operational Research, 211, 586-593.

  32.            Kao, C., & Lin, P.-H. (2012). Efficiency of parallel production systems with fuzzy data. Fuzzy Sets and Systems, 198, 83-98.

  33.            Kao, C., & Liu, S.-T. (2009). Stochastic data envelopment analysis in measuring the efficiency of Taiwan commercial banks. European Journal of Operational Research, 196, 312-322.

  34.            Kim, S.-H., Park, C.-G., & Park, K.-S. (1999). An application of data envelopment analysis in telephone officesevaluation with partial data. Computers & Operations Research, 26, 59-72.

  35.            Liu, F.-H. F., & Hai, H. L. (2005). The voting analytic hierarchy process method for selecting supplier. International Journal of Production Economics, 97, 308-317.

  36.            Liu, J., Ding, F. Y., & Lall, V. (2000). Using data envelopment analysis to compare suppliers for supplier selection and performance improvement. Supply Chain Management: An International Journal, 5, 143-150.

  37.            Liu, W., & Wang, Y.-M. (2018). Ranking DMUs by using the upper and lower bounds of the normalized efficiency in data envelopment analysis. Computers & Industrial Engineering, 125, 135-143.

  38.            Liu, W., Wang, Y.-M., & Lyu, S. (2017). The upper and lower bound evaluation based on the quantile efficiency in stochastic data envelopment analysis. Expert Systems with Applications, 85, 14-24.

  39.            Moore, R. E., & Bierbaum, F. (1979). Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.): Soc for Industrial & Applied Math.

  40.            Park, K. S. (2004). Simplification of the transformations and redundancy of assurance regions in IDEA (imprecise DEA). Journal of the Operational Research Society, 55, 1363-1366.

  41.            Seyedalizadeh Ganji, S., Rassafi, A. A., & Bandari, S. J. (2019). Application of evidential reasoning approach and OWA operator weights in road safety evaluation considering the best and worst practice frontiers. Socio-Economic Planning Sciences.

  42.            Seyedalizadeh Ganji, S., Rassafi, A. A., & Xu, D.-L. (2019). A double frontier DEA cross efficiency method aggregated by evidential reasoning approach for measuring road safety performance. Measurement, 136, 668-688.

  43.            Shabani, A., Visani, F., Barbieri, P., Dullaert, W., & Vigo, D. (2019). Reliable estimation of suppliers’ total cost of ownership: An imprecise data envelopment analysis model with common weights. Omega, 87, 57-70.

  44.            Smirlis, Y. G., Maragos, E. K., & Despotis, D. K. (2006). Data envelopment analysis with missing values: An interval DEA approach. Applied Mathematics and Computation, 177, 1-10.

  45.            Talluri, S., & Baker, R. C. (2002). A multi-phase mathematical programming approach for effective supply chain design. European Journal of Operational Research, 141, 544-558.

  46.            Talluri, S., Narasimhan, R., & Nair, A. (2006). Vendor performance with supply risk: A chance-constrained DEA approach. International Journal of Production Economics, 100, 212-222.

  47.            Talluri, S., & Sarkis, J. (2002). A model for performance monitoring of suppliers. International Journal of Production Research, 40, 4257-4269.

  48.            Thompson, R. G., Langemeier, L. N., Lee, C.-T., Lee, E., & Thrall, R. M. (1990). The role of multiplier bounds in efficiency analysis with application to Kansas farming. Journal of Econometrics, 46, 93-108.

  49.            Wang, G., Huang, S. H., & Dismukes, J. P. (2004). Product-driven supply chain selection using integrated multi-criteria decision-making methodology. International Journal of Production Economics, 91, 1-15.

  50.            Wang, Y.-M., & Chin, K.-S. (2009). A new approach for the selection of advanced manufacturing technologies: DEA with double frontiers. International Journal of Production Research, 47, 6663-6679.

  51.            Wang, Y.-M., Chin, K.-S., & Yang, J.-B. (2007). Measuring the performances of decision-making units using geometric average efficiency. Journal of the Operational Research Society, 58, 929-937.

  52.            Wang, Y.-M., Greatbanks, R., & Yang, J.-B. (2005). Interval efficiency assessment using data envelopment analysis. Fuzzy Sets and Systems, 153, 347-370.

  53.            Wang, Y.-M., Luo, Y., & Liang, L. (2009). Ranking decision making units by imposing a minimum weight restriction in the data envelopment analysis. Journal of Computational and Applied Mathematics, 223, 469-484.

  54.            Wang, Y.-M., Yang, J.-B., & Xu, D.-L. (2005a). Interval weight generation approaches based on consistency test and interval comparison matrices. Applied Mathematics and Computation, 167, 252-273.

  55.            Wang, Y.-M., Yang, J.-B., & Xu, D.-L. (2005b). A preference aggregation method through the estimation of utility intervals. Computers & Operations Research, 32, 2027-2049.

  56.            Weber, C. A. (1996). A data envelopment analysis approach to measuring vendor performance. Supply Chain Management: An International Journal, 1, 28-39.

  57.            Weber, C. A., Current, J., & Desai, A. (2000). An optimization approach to determining the number of vendors to employ. Supply Chain Management: An International Journal, 5, 90-98.

  58.            Zhou, X., Wang, Y., Chai, J., Wang, L., Wang, S., & Lev, B. (2019). Sustainable supply chain evaluation: A dynamic double frontier network DEA model with interval type-2 fuzzy data. Information Sciences, 504, 394-421.

  59.            Zhu, J. (2003a). Efficiency evaluation with strong ordinal input and output measures. European Journal of Operational Research, 146, 477-485.

  60.            Zhu, J. (2003b). Imprecise data envelopment analysis (IDEA): A review and improvement with an application. European Journal of Operational Research, 144, 513-529.

  61.            Zhu, J. (2004). Imprecise DEA via Standard Linear DEA Models with a Revisit to a Korean Mobile Telecommunication Company. Operations Research, 52, 323-329.