A note on “A discussion of testing DMUs' returns to scale” by Zhu and Shen European Journal of Operational Research 81 (1995) 590–596
✍ Scribed by Kuo-Ping Chang
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 167 KB
- Volume
- 97
- Category
- Article
- ISSN
- 0377-2217
No coin nor oath required. For personal study only.
✦ Synopsis
Chang and Guh (1991)
have shown that Charnes, Cooper and Rhodes' (CCR) (1978) data envelopment analysis (DEA) method cannot be used to test for decision-making-units' (DMUs) returns to scale, and Banker, Chames and Cooper's (BCC) (1984) method for determining DMUs' returns to scale can fail in some cases. Zhu and Shen (1995) claim that in our paper (Chang and Guh, 1991), it is the linear dependency among efficient DMUs and not the linear production frontier implied by the CCR method causing Banker's (1984) most productive scale size (mpss) concept not to work. Zhu and Shen misread our paper. Although we have used an example having linear dependency among efficient DMUs to show that Banker's Corollary 1 (for determining DMUs' returns to scale) can fail, it does not mean that without linear dependency, the corollary can work. The main point in our paper is that because the CCR method implicitly assumes constant-returns-toscale linear production technologies (i.e., all DMUs are assumed under constant returns to scale), it will be meaningless to talk about determining DMUs' returns to scale by that method. Also, since all the points on the constant-returns-to-scale frontier are mpss, it is not meaningful to find which is mpss. In this short note, I will give a proof for our point, and show that Zhu and Shen's other claims are not only misleading but unfounded.