ارزیابی واحدهای تصمیم گیری با داده‌های چند مرحله‌ای با استفاده از مدل‌های DEA-R
محورهای موضوعی : تحقیق در عملیات
مهسا ترکاوان نژاد
1
(گروه ریاضی، واحد تبریز، دانشگاه آزاد اسلامی، تبریز، ایران)
بهروز دانشیان
2
(گروه ریاضی، واحد تهران مرکزی، دانشگاه آزاد اسلامی، تهران، ایران)
قاسم توحیدی
3
(گروه ریاضی، واحد تهران مرکزی، دانشگاه آزاد اسلامی، تهران، ایران)
مهناز مقبولی
4
(گروه ریاضی، واحد ارس، دانشگاه آزاد اسلامی، جلفا، ایران)
فرزین مدرس خیابانی
5
(گروه ریاضی، واحد تبریز، دانشگاه آزاد اسلامی، تبریز، ایران)
کلید واژه: non-zero weights, Overall efficiency, Multi-Periodic Production Process, lower bound, Ratio Data Envelopment Analysis(DEA-R),
چکیده مقاله :
در اندازه‌گیری کارآیی مجموعه‌ای از واحدها در یک بازه زمانی که چند دوره را پوشش می‌دهد، مدل‌های مبتنی بر تکنیک DEA استاندارد، وضعیت هر واحد در هر دوره را نادیده می‌گیرند که این باعث نتایج گمراه‌کننده می‌شود. این مقاله مدل‌های DEA-R را در حضور داده‌های چند دوره‌ای به گونه‌ای توسعه می‌دهد که روش پیشنهادی می‌تواند کارآیی کلی را با توجه به کارآیی کلی و دوره‌ای همه واحدها ارزیابی کند. روش پیشنهادی با ارائه یک کران پایین در وزن‌های بدست آمده از دوره‌ها، به اولویت‌بندی واحدها پرداخته و با ایجاد بینش‌های ارزشمند به تصمیم‌گیرندگان کمک می‌کند تا یافته‌های یک فرآیند ارزیابی عملکرد را بهتر درک کنند. این مقاله دارای چهار ویژگی است: (1) کارآیی کلی محاسبه شده از روش پیشنهادی به عملکرد تمام واحدها در تمام دوره‌ها بستگی دارد، (2) روش پیشنهادی، کارآیی کلی را با تحمیل یک کران پایین به دست آمده از تمام دوره‌ها بر روی وزن‌ها ارزیابی می‌کند، (3) این رویکرد دارای قدرت تشخیص بالا در تمییز واحدهایی است که در مدل‌های چند دوره‌ای موجود به عنوان کارآ ارزیابی می‌شوند، (4) برای روشن شدن جزئیات روش پیشنهادی، مقایسه‌ای بین مدل‌های موجود و مدل DEA-R چند دوره‌ای پیشنهادی، برای اندازه گیری کارآیی 22 بانک تجاری تایوانی در دوره زمانی 2009-2011 انجام شده است.
In measuring the efficiency of a set of units over a period of time covering multiple periods, models based on the standard DEA technique ignore the status of each unit in each period that causes misleading results. This paper develops DEA-R models in the presence of multi-periodic data in such a way that the proposed method can evaluate the overall efficiency with respect to the overall and periodic efficiencies of all units. By providing a lower bound on the weights derived from periods, the proposed method prioritizes the units for yielding valuable insights that aid decision makers to better understand the findings from a performance evaluation process. The contribution of this paper is fourfold: (1) the overall efficiency calculated from the proposed method depends on the unit performance of all units in all periods, (2) the proposed method determines the overall efficiency by imposing a lower bound obtained from all periods on the weights, (3) this method endowed with a high discriminatory power in differentiating the units which are evaluated as efficient in the existing multi-period models, (4) To elucidate the details of the proposed method, a comparison is made between the existing models in the literature and the proposed multi-period DEA-R method to measure the efficiency of 22 Taiwanese commercial banks for the period of 2009–2011.
[1] Farrell, M. J. (1957) ‘The measurement of productivity efficiency’, Journal of The Royal Statistical Society Series A: General, Vol. 120, No. 3, pp. 253–281.
[2] Charnes, A., Cooper, W. W. and Rhodes, E. (1978) ‘Measuring the efficiency of decision making units’, European Journal of Operational Research, Vol. 2, pp. 429-444.
[3] Cooper, W. W., Seiford, L. M., & Tone, K. (2002) Data Envelopment Analysis – A comprehensive text with models, applications, references and DEA-solver software. Massachusetts: Kluwer, 68–74.
[4] Banker, R. D., Charnes, A. and Cooper, W. W.. (1984) ‘Some models estimating technical and scale inefficiencies in data envelopment analysis’, Management Science, Vol. 30, pp. 1078-1092.
[5] Paradi, J.C. and Zhu, H. (2013) ‘A survey on bank branch efficiency and performance research with data envelopment analysis’, Omega International Journal of Management Science , Vol. 41 pp. 61–79.
[6] Asmild, M., Bogetoft, P. and Hougaard, J.L (2013) ‘Rationalizing inefficiency: staff utilization in branches of a large Canadian bank’, Omega International Journal of Management Science, Vol. 41, pp. 80–87.
[7] Saljoughian, M., Shirouyehzad, H., Khajeh, E. and Dabestani, R. (2019) ‘Evaluating the efficiency of the commercial banks admired in Fortune 500 list; using data envelopment analysis’, International Journal of Productivity and Quality Management, Vol. 26, No. 1, pp. 58-73
[8] Hwang, S. N., Chen, C. L., Chen, Y., Lee, H. S. and Shen, P. D. (2013) ‘Sustainable design performance evaluation with applications in the automobile industry: focusing on inefficiency by undesirable factors’, Omega International Journal of Management Science, Vol. 41, pp. 553–558.
[9] Chang, S. J., Hsiao, H. C. and Huang, L. H. (2011) ‘Taiwan quality indicator project and hospital productivity growth’, Omega International Journal of Management Science , Vol. 39, pp. 14–22.
[10] Assaf, A. G., Barros, C. and Sellers-Rubio, R. (2011) ‘Efficiency determinants in retail stores: A Bayesian framework’. Omega International Journal of Management Science, Vol. 9, pp. 283–292.
[11] Nemoto, J. and Goto, M. (1999) ‘Dynamic data envelopment analysis: Modeling intertemporal behavior of a firm in the presence of productive inefficiencies’, Economics Letters, Vol. 64, pp. 51–56.
[12] Kao, C. (2009) ‘Efficiency measurement for parallel production systems’, European Journal of Operational Research, Vol. 196, pp. 1107‐1112.
[13] Tone, K., & Tsutsui, M. (2014). ‘Dynamic DEA with network structure’. Omega , Vol. 42, No, 1, pp 124–131.
[14] Mariz, F. B. A. R., Almeida, M. R. and Aloise, D. (2017) ‘A review of Dynamic Data Envelopment Analysis: state of the art and applications’, International Transaction in Operation
Research, 1-37, DOI: 10.1111/itor.12468.
[15] Kao, C. and Liu, S.T. (2014) ‘Multi-period efficiency measurement in data envelopment analysis: The case of Taiwanese Commercial banks’, Omega, Vol. 47, pp. 90-98.
[16] Wei, X. Y., Jun, Z. H., Kai, C., Xuan, Z. Z. and Tian, C. Y. (2021) ‘Efficiency measurement in multi-period network DEA model with feedback’, Expert Systems with Applications, Vol. 175, 114815
[17] Despic, O., Despic, M. and Paradi, J. C. (2007) ‘DEA-R: Ratio-based comparative efficiency model, its mathematical relation to DEA and its use in applications’, Journal of Productivity Analysis, Vol. 28, pp. 33–44.
[18] Wei, C. K., Chen, L. C., Li, R. K. and Tsai, C. H. (2011a) ‘Using the DEA-R model in the hospital industry to study the pseudo-inefficiency’, Expert Systems with Applications, Vol. 38, pp. 2172-2176.
[19] Wei, C. K., Chen, L. C., Li, R. K. and Tsai, C. H. (2011b) ‘Exploration of efficiency underestimation of CCR model: Based on medical sectors with DEA-R model’, Expert Systems with Applications, Vol. 38, pp. 3155–3160.
[20] Wei, C. K., Chen, L. C., Li, R. K. and Tsai, C. H. (2011c) ‘A study of developing an input- oriented ratio-based comparative efficiency model’, Expert Systems with Applications, Vol. 38, pp. 2473–2477.
[21] Liu, W. B., Zhang, D. Q., Meng, W., Li, X. X. and Xu, F. A. (2011) ‘Study of DEA models without explicit inputs’, Omega, Vol. 39, pp. 472–480.
[22] Mozaffari, M. R., Kamyab, P., Jablonsky, J. and Gerami, J. (2014b) ‘Cost and revenue efficiency in DEA-R models’, Computers & Industrial Engineering, Vol. 78, pp. 188-194.
[23] Mozaffari, M. R., Gerami, J. and Jablonsky, J. (2014a) ‘Relationship between DEA models without explicit inputs and DEA models without explicit inputs and DEA-R models’, Central European Journal of Operation Research, Vol. 22, pp. 1-12.
[24] Mozaffari, M. R., Dadkhah, F., Jablonsky, J. and Wanke, P. F. (2020) ‘Finding Efficient surface in DEA-R models’, Applied Mathematics and Computation, Vol. 386, pp. 125497.
[25] Olesen, O. B., Petersen, N. C. and Podinovski, V. (2015) ‘Efficiency analysis with ratio measures’, European Journal of Operational Research, Vol. 245, pp. 446-462.
[26] Kamyab, P., Mozaffari, M. R., Gerami, J. and Wankei, P. F. (2021), ‘Two-stage incentives system for commercial banks based on centralized resource allocation model in DEA-R’, International Journal of Productivity and Performance Management, Vol. 70 No. 2, pp. 427-458.
[27] Mozaffari, M. R., Gerami, J., Wanke, P. F., Kamyab, P and Peyvas, M. (2022) ‘Ratio-based data envelopment analysis: An interactive approach to identify benchmark’, Results in Control and Optimization, Vol. 6, 100081.
[28] Park, K. S. and Park, K. (2009) ‘Measurement to multipored aggregative efficiency’, European Journal of Operational Research, Vol. 193, pp. 567–580.
[29] Olesen, O. B., Petersen, N. C. and Podinovski, V. (2017) ‘Efficiency measures and computational approaches for data envelopment analysis models with ratio inputs and outputs’, European Journal of Operational Research, Vol. 261, pp. 640–655.
[30] Färe, R. and Grosskopf, S. (2000) ‘Network DEA’, Socio-Economic Planning Sciences, Vol. 34, pp. 35–49.