A unique equilibrium efficient frontier with fixed-sum outputs in data envelopment analysis

Abstract

Based on the equilibrium efficient frontier data envelopment analysis (EEFDEA) approach, Fang (J Oper Res Soc 67:412–420, 2015a) developed an equivalent linear programming model to improve and strengthen the EEFDEA approach. Furthermore, Fang (2015a) indicated that his secondary goal approach can achieve a unique equilibrium efficient frontier. However, through a simple counterexample we demonstrate that Fang’s secondary goal approach cannot always achieve uniqueness of the equilibrium efficient frontier. In this paper, we propose an algorithm based on the secondary goal approach to address the problem. The proposed algorithm is proven mathematically to be an effective approach to guaranteeing the uniqueness of the equilibrium efficient frontier.

Keywords:

• data envelopment analysis
• unique equilibrium efficient frontier
• fixed-sum outputs
• secondary goal approach

Acknowledgements

The research is supported by National Natural Science Funds of China (Nos. 71222106, 71571173), Research Fund for the Doctoral Program of Higher Education of China (No. 20133402110028), Foundation for the Author of National Excellent Doctoral Dissertation of P. R. China (No. 201279), and Top-Notch Young Talents Program of China. Qingyuan Zhu thanks the support of the State Scholarship Fund by the Office of China Scholarship Council (No. 201606340054).

Notes

1 Note that model (33 ) in this paper is slightly different from model (44 ) in Fang (2015a). To be specific, we changed the expression in the first constraint to since Fang (2015a) had a little mistake in his model.

2 Note that here we also revise the expression in the fourth constraint of model (66 ) in Fang (2015a) to .