A variation of two-stage SBM with leader-follower structure: an application to Chinese commercial banks^*

^*Please note this paper has been re-typeset by Taylor & Francis from the manuscript originally provided to the previous publisher.

Abstract

The two-stage slack-based measure (SBM) model has many applications in the real world. Due to the limitations of the SBM model on which it is based, the two-stage SBM model unfortunately gives unrealistically low efficiencies and rather far projections (Tone in Eur J Oper Res 197(1):243–252, 2010) for inefficient decision- making unit. Based on the novel idea in Tone (2010), this paper proposes a variation of the two-stage SBM model by incorporating a leader–follower structure and applies the proposed approach to Chinese commercial banks. The results show that our proposed approach can increase efficiencies of inefficient banks and halve the projection distance of some inefficient banks.

Keywords:

• Data envelopment analysis (DEA)
• slack-based measure (SBM)
• two stages
• close projections

Acknowledgements

Authors would like to thank the Editor and anonymous reviewers. Their comments are valuable for us to improve the quality of this article. This research was supported by the National Natural Science Foundation of China (Nos. 71271196 and 71671172), the Youth Innovation Promotion Association of Chinese Academy of Sciences (CX2040160004) and Science Funds for Creative Research Groups of University of Science and Technology of China (WK2040160008).

Notes

^* Please note this paper has been re-typeset by Taylor & Francis from the manuscript originally provided to the previous publisher.

1. In real-world, practical applications of DEA, the number of DMUs is greater than the number of inputs or outputs, which means in formula (4a) the number of k variables is greater than the number of equations. This implies that in most instances, model (4) is solvable.

2. The Maximal Friends set is often less than the number of inputs (or outputs if the second stage is the leader stage) in many numerical examples, and in such cases the linear equation system is unsolvable.