Document Type : Original Article
Authors
- Mahsa Torkavannezhad 1
- Ghasem Tohidi 2
- Behrouz Daneshian 2
- Mahnaz Maghbouli 3
- Farzin Moddarres Khiyabani 4
1 Department of Mathmatic, Tabriz Branch, Islamic Azad University, Tabriz, Iran.
2 Department of Mathmatic, Central Tehran Branch, Islamic Azad University, Tehran, Iran.
3 Department of Mathmatic, Aras Branch, Islamic Azad University, Jolfa, Iran.
4 Department of Mathmatic, Tabriz Branch, Islamic Azad University, Tabriz, Iran/
Abstract
Purpose: Standard Data Envelopment Analysis (DEA) models measure the efficiency of Decision-Making Units (DMUs) over a period. In actual occasions, multiple periods are presented. In the presence of a multi-period system, overall efficiency depends on the performance of the DMU in all periods. That is to say, periodic efficiencies must be calculated. Also, the overall efficiency is dependent on periodic efficiencies. In other words, a DMU cannot be efficient overall, but it is considered an efficient unit in each separate period. Hence, the question of pseudo-inefficiency is raised. This paper investigates Ratio-based Data Envelopment Analysis (DEA-R) models to detect pseudo-inefficiency in multi-period systems.
Methodology: The proposed algorithm consists of three steps. The average period efficiencies are calculated as the first step and the overall efficiency is evaluated as a block box. For the last step, a ratio of two quantities is estimated. If this ratio is close to unity, these two quantities have no significant difference. Otherwise, the estimate claims pseudo-inefficiency
Findings: A comparison is made between Kao and Liu [8] and the proposed algorithm to measure the efficiency of 22 Taiwanese commercial banks from 2009-2011. The results demonstrate the proposed method's practicality and superiority compared with the existing multi-period models.
Originality/Value: In the literature, pseudo-inefficiency has been detected by applying periodic weights. This paper proposes a three-step algorithm to investigate pseudo-inefficiency.
Keywords
- Farrell, M. J. (1957). The measurement of productive efficiency. Journal of the royal statistical society: series a (general), 120(3), 253-281. https://doi.org/10.2307/2343100
- Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European journal of operational research, 2(6), 429-444. https://doi.org/10.1016/0377-2217(78)90138-8
- Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management science, 30(9), 1078-1092.
- Fare, R., & Grosskopf, S. (1996). Intertemporal production frontiers: with dynamic DEA. Springer Dordrecht. Intertemporal Production Frontiers: With Dynamic DEA | SpringerLink
- Kao, C. (2014). Network data envelopment analysis: a review. European journal of operational research, 239(1), 1-16. https://doi.org/10.1016/j.ejor.2014.02.039
- Tone, K., & Tsutsui, M. (2014). Dynamic DEA with network structure: a slacks-based measure approach. Omega, 42(1), 124-131. https://doi.org/10.1016/j.omega.2013.04.002
- Mariz, F. B. A. R., Almeida, M. , & Aloise, D. (2017). A review of dynamic data envelopment analysis: state of the art and applications. International transaction in operation research, 25(2), 469-505.
- Kao, C., & Liu, S. T. (2014). Multi-period efficiency measurement in data envelopment analysis: the case of taiwanese commercial banks. Omega, 47, 90-98. https://doi.org/10.1016/j.omega.2013.09.001
- Jablonsky, J., Marek, L., & Berka, P. (2018). Multi-period data envelopment analysis models and resource allocation: a case study. Journal of physics: conference series(Vol. 1026, No. 1, p. 012002). IOP Publishing. DOI: 1088/1742-6596/1026/1/012002
- Bansal, P., & Mehra, A. (2018). Multi‑period additive efficiency measurement in data envelopment analysis with non‑positive and undesirable data. Operational research society of India, 55, 642-661. https://doi.org/10.1007/s12597-018-0343-z
- Tavana, M., Khalili-Damghani, K., Arteaga, F. J. S., & Hosseini, A. (2019). A fuzzy multi-objective multi-period network DEA model for efficiency measurement in oil refineries. Computers and industrial engineering, 135, 143-155.
- Xu, Y. W., Zhang, H. J., Cheng, K., Zhang, Z. X., & Chen, Y. T. (2021). Efficiency measurement in multi-period network DEA model with feedback. Expert systems with applications, 175, 114815. https://doi.org/10.1016/j.eswa.2021.114815
- Despić, O., Despić, M., & 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, 28(1-2), 33-44.
- Wei, C. K., Chen, L. C., Li, R. K., & Tsai, C. H. (2011). Using the DEA-R model in the hospital industry to study the pseudo-inefficiency problem. Expert systems with applications, 38(3), 2172-2176.
- Wei, C. K., Chen, L. C., Li, R. K., & Tsai, C. H. (2011). A study of developing an input-oriented ratio-based comparative efficiency model. Expert systems with applications, 38(3), 2473-2477.
- Mozaffari, M. R., Gerami, J., & Jablonsky, J. (2014). Relationship between DEA models without explicit inputs and DEA-R models. Central european journal of operations research, 22, 1-12.
- Mozaffari, M. R., Kamyab, P., Jablonsky, J., & Gerami, J. (2014). Cost and revenue efficiency in DEA-R models. Computers & industrial engineering, 78, 188-194. https://doi.org/10.1016/j.cie.2014.10.001
- Gerami, J., Mozaffari, M. R., & Wanke, P. F. (2020). A multi-criteria ratio-based approach for two-stage data envelopment analysis. Expert systems with applications, 158, 113508. https://doi.org/10.1016/j.eswa.2020.113508
- Mozaffari, M. R., Gerami, J., Wanke, P. F., Kamyab, P., & Peyvas, M. (2022). Ratio-based data envelopment analysis: an interactive approach to identify benchmark. Results in control and optimization, 6, 100081. https://doi.org/10.1016/j.rico.2021.100081
- Mozaffari, M. R., Dadkhah, F., Jablonsky, J., & Wanke, P. F. (2020). Finding efficient surfaces in DEA-R models. Applied mathematics and computation, 386, 125497. https://doi.org/10.1016/j.amc.2020.125497
)