Document Type : Original Article


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/


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. 


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