Evaluating Decision Making Units with Multi-Periodic Data Using DEA-R Models

Subject Areas : تحقیق در عملیات

Mahsa Torkavannejad ¹ , Behrouz Daneshian ² , Ghasem Tohidi ³ , Mahnaz Maghbouli ⁴ , Farzin Modarres Khiyabani ⁵

1 - Islamic Azad University, Tabriz Branch, Tabriz, Iran
2 - Islamic Azad University, Central Tehran Branch, Tehran, Iran
3 - Islamic Azad University, Central Tehran Branch, Tehran, Iran
4 - Islamic Azad University, Aras Branch, , Jolfa, Iran
5 - Islamic Azad University. Tabriz Branch. Tabriz. Iran

Received: 2022-04-20 Accepted : 2023-02-06 Published : 2024-01-18

Keywords: سیستم‌های چند دوره‌ای, وزن‌های غیرصفر, تحلیل پوششی داده‌ها مبتنی بر تحلیل کسری (DEA-R), کارآیی کلی,

Abstract :

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.

References:



[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.