Notes on Sensitivity and Stability of the Classifications of Returns to Scale in Data Envelopment Analysis

Abstract

As its title suggests, this note constitutes a critique of the paper by Seiford and Zhu (1999), "Sensitivity and Stability of the Classifications of Returns to Scale (RTS) in Data Envelopment Analysis". By means of counter examples, we discuss some problems related to results presented in that paper. JEL Classification: C44, C61, C67

Consistency of returns-to-scale characterizations of production frontiers with respect to model specification

“…It is worth noting that the focus of our paper is different from the question of stability of RTS characterizations first considered by Seiford and Zhu (1999) and further clarified by Jahanshahloo, Lofti and Zohrehbandian (2005) and Seiford and Zhu (2005). These studies consider the standard VRS model of Banker et al (1984) and explore the maximum proportional changes of the input and output vectors of the single DMU under the assessment that does not change its RTS type.…”

Notes on Sensitivity and Stability of the Classifications of Returns to Scale in Data Envelopment Analysis: A Comment

“…Finally, consider the example provided in Jahanshahloo, Lotfi and Zohrehbandian (2004). DMU 2 's RTS stability should be analyzed by Theorem 4, because model (3) is infeasible when DMU 2 is under consideration.…”

“…If model (9) is infeasible, then DMU 0 does not belong to T 0 and the RTS classification should be dealt with Theorem 10 (Seiford and Zhu, 1999, p. 65). Seiford and Zhu (1999) also indicate that Theorems 4 and 10 are true under the general situation discussed in section 4.As a result, the issue pointed out in Jahanshahloo, Lotfi and Zohrehbandian (2004) can be addressed directly by the these results in Seiford and Zhu (1999). We should add "model (3) is feasible" as a condition for Theorems 11 and 12 and "model (9) is feasible" for Theorems 16 and 17 in Seiford and Zhu (1999).…”

“…As a result, the issue pointed out in Jahanshahloo, Lotfi and Zohrehbandian (2004) can be addressed directly by the these results in Seiford and Zhu (1999). We should add "model (3) is feasible" as a condition for Theorems 11 and 12 and "model (9) is feasible" for Theorems 16 and 17 in Seiford and Zhu (1999).…”

“…As noted in Jahanshahloo, Lotfi and Zohrehbandian (2004), a number of Theorems (e.g., Theorems 11, 12, 16 and 17) in Seiford and Zhu (1999) may not be true for some decision making units (DMUs). They proposed a remedy for these Theorems.…”