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
محورهای موضوعی : مدیریت صنعتی
Hossein Azizi
1
(Department of Applied Mathematics, Parsabad Moghan Branch, Islamic Azad University, Parsabad Moghan, Iran.)
Rasul Jahed
2
(Department of Mathematics, Germi Branch, Islamic Azad University, Germi, Iran)
کلید واژه: محدودیت وزنی, انتخاب تأمین کنندگان, عوامل غیرقابل کنترل و داده‌های اصلی و ترتیبی, کارآیی‌های خوشبینانه و بدبینانه, تحلیل پوششی داده‌ها,
چکیده مقاله :
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.
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.‎
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.
_||_
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.
