1استادیار، گروه ریاضی، واحد پارس‌آباد مغان، دانشگاه آزاد اسلامی، پارس‌آباد مغان، ایران
2استاد، گروه ریاضی، واحد رشت، دانشگاه آزاد اسلامی، رشت، ایران
3استاد، گروه ریاضی، واحد لاهیجان، دانشگاه آزاد اسلامی، لاهیجان، ایران
چکیده
در ارزیابی عینی عملکرد واحدهای تصمیم‌گیری (DMUs)، دو مشکل وجود دارد. مشکل اول نحوه کار با خروجی‌های نامطلوب است که در کنار خروجی‌های مطلوب تشکیل می‌شوند و مشکل دوم نحوه کار با متغیرهای غیرقابل‌کنترل است که غالباً تأثیر محیط عملیاتی را حفظ می‌کنند. با توجه به مشکلات ساخت مدل و دسترس‌پذیری داده‌ها، تعداد کمی از مقالات منتشر شده هر دو مشکل فوق را به‌طور هم‌زمان در نظر گرفته‌اند. هدف از مقاله حاضر، پیشنهاد زوج جدیدی از مدل‌های تحلیل پوششی داده‌ها (DEA) برای اندازه‌گیری کارایی‌های نسبی دی‌ام‌یوها در حضور عوامل غیرقابل‌کنترل، عوامل نامطلوب و داده‌های نادقیق است. در مقایسه با DEA سنتی، رویکرد DEA پیشنهادی، کارایی هر دی‌ام‌یو را نسبت به مرز بدترین عملکرد، که به آن مرز ورودی نیز می‌گویند، اندازه‌گیری می‌کند (بدترین کارایی نسبی یا کارایی بدبینانه). مدل‌های DEA پیشنهادی، داده‌های قطعی، اطلاعات ترجیح ترتیبی، بازه‌ای، عوامل نامطلوب و عوامل غیرقابل‌کنترل را به‌طور هم‌زمان برای اندازه‌گیری کارایی‌های نسبی دی‌ام‌یوها در نظر می‌گیرند. یافته‌های این مقاله نه‌فقط برای روش ارزیابی عملکرد مفید است، بلکه برای محققان صنعتی و دانشگاهی نیز مفید بوده و نتایجی از منظر سیاست‌گذاری را نیز دربردارد. در این مقاله، یک مثال عددی نیز برای نشان دادن کاربرد مدل‌های DEA پیشنهادی ارائه خواهد شد.
1Assistant Professor, Department of Applied Mathematics, Parsabad Moghan Branch, Islamic Azad University, Parsabad Moghan, Iran
2Professor, Department of Applied Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran.
3Professor, Department of Applied Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran.
چکیده [English]
There are two difficulties in implementing an objective evaluation of the performance of decision-making units (DMUs). The first one is how to treat undesirable outputs jointly produced with the desirable outputs, and the second one is how to treat uncontrollable variables, which often capture the impact of the operating environment. Given difficulties in both model construction and data availability, very few published papers simultaneously consider the above two problems. The objective of the present paper is to propose a novel pair of data envelopment analysis (DEA) models for measurement of relative efficiencies of DMUs in the presence of non-discretionary factors, undesirable factors, and imprecise data. Compared to traditional DEA, the proposed DEA approach measures the efficiency of each DMU relative to the worst practice frontier, also called the input frontier, and is called the worst relative efficiency or pessimistic efficiency. The pair of proposed DEA models simultaneously takes into account the crisp data, ordinal preference information, and interval data, as well as undesirable factors and non-discretionary factors, for measurement of relative efficiencies of DMUs. The results of this study are not only useful for the performance evaluation method, but also have policy implications for industrial and academic researchers. A numeric example has been provided to illustrate the applicability of the DEA models.
کلیدواژه‌ها [English]
Data Envelopment Analysis, pessimistic efficiencies, Performance Evaluation, imprecise data
مراجع
[1] Paradi, J.C., Asmild, M., Simak, P.C. Using DEA and worst practice DEA in credit risk evaluation, Journal of Productivity Analysis, 21, 2004, 153–165.
[2] Pendharkar, P.C. A potential use of data envelopment analysis for the inverse classification problem, Omega, 30, 2002, 243–248.
[3] Pille, P., Paradi, J.C. Financial performance analysis of Ontario (Canada) Credit Unions: An application of DEA in the regulatory environment, European Journal of Operational Research, 139, 2002, 339–350.
[4] Cielen, A., Peeters, L., Vanhoof, K. Bankruptcy prediction using a data envelopment analysis, European Journal of Operational Research, 154, 2004, 526–532.
[5] Sueyoshi, T. DEA-discriminant analysis: Methodological comparison among eight discriminant analysis approaches, European Journal of Operational Research, 169, 2006, 247–272.
[6] Charnes, A., Cooper, W.W., Rhodes, E. Measuring the efficiency of decision making units, European Journal of Operational Research, 2, 1978, 429–444.
[7] Jahanshahloo, G.R., Afzalinejad, M. A ranking method based on a full-inefficient frontier, Applied Mathematical Modelling, 30, 2006, 248–260.
[8] Liu, F.F., Chen, C.L. The worst-practice DEA model with slack-based measurement, Computers & Industrial Engineering, 57, 2009, 496–505.
[9] Cook, W.D., Kress, M., Seiford, L. On the use of ordinal data in data envelopment analysis, Journal of the Operational Research Society, 44, 1993, 133–140.
[10] Cook, W.D., Kress, M., Seiford, L. Data envelopment analysis in the presence of both quantitative and qualitative factors, Journal of the Operational Research Society, 47, 1996, 945–953.
[11] Cooper, W.W., Park, K.S., Yu, G. IDEA and AR-IDEA: models for dealing with imprecise data in DEA, Management Science, 45, 1999, 597–607.
[12] Cooper, W.W., Park, K.S., Yu, G. An illustrative application of IDEA (imprecise data envelopment analysis) to a Korean mobile telecommunication company, Operations Research, 49, 2001, 807–820.
[13] Cooper, W.W., Park, K.S., Yu, G. IDEA (Imprecise Data Envelopment Analysis) with CMDs (Column Maximum Decision Making Units), Journal of the Operational Research Society, 52, 2001, 176–181.
[14] Wang, Y.-M., Greatbanks, R., Yang, J.-B. Interval efficiency assessment using data envelopment analysis, Fuzzy Sets and Systems, 153(3), 2005, 347–370.
[15] Parkan, C., Wang, Y.-M. Worst Efficiency Analysis Based on Inefficient Production Frontier, Working Paper, Department of Management Sciences, City University of Hong Kong, 2000.
[16] Azizi, H., Ganjeh Ajirlu, H. Measurement of the worst practice of decision-making units in the presence of non-discretionary factors and imprecise data, Applied Mathematical Modelling, 35, 2011, 4149–4156.
[17] Charnes, A., Cooper, W.W. Programming with fractional functionals, Naval Research Logistics Quarterly, 9, 1962, 181–186.
[18] Dyckhoff, H., Allen, K. Measuring ecological efficiency with data envelopment analysis (DEA), European Journal of Operational Research, 132, 2001, 312–325.
[19] Moore, R.E. Method and Application of Interval Analysis, SIAM, Philadelphia, 1979.
[20] Shabani, A., Farzipoor Saen, R., Torabipour, S.M.R. A new benchmarking approach in Cold Chain, Applied Mathematical Modelling, 36, 2012, 212–224.
[21] Azizi, H. Efficiency assessment in data envelopment analysis using efficient and inefficient frontiers, Management Research in Iran, 16(3), 2012, 153–173. (In Persian)
[22] Azizi, H., Bahari, A., Jahed, R. A new approach for the selection of advanced manufacturing technologies: A new approach based on double frontiers data envelopment analysis, Journal of Applied Mathematics, 10, 2014, 99–117. (In Persian)
[23] Azizi, H., Wang, Y.-M. Improved DEA models for measuring interval efficiencies of decision-making units, Measurement, 46(3), 2013, 1325–1332.
[24] Azizi, H., Amirteimoori, A. Flexible measures in production process: A new approach based on double-frontier DEA, Modern Researches in Decision Making, 2(2), 2017, 197–216. (In Persian)
[25] Azizi, H., Jafari Shaerlar, A., Farzipoor Saen, R. A new approach for considering a dual-role factor in supplier selection problem: DEA with efficient and inefficient frontiers, Journal of Production & Operations Management, 6(2), 2016, 129–144. (In Persian)
[26] Azizi, H., Jahed, R. Suppliers selection in volume discount environments in the presence of both cardinal and ordinal data: A new approach based on double frontiers DEA, Management Research in Iran, 19(3), 2015, 191–217. (In Persian)
ابتدای صفحه