Characterizing and finding full dimensional efficient facets in DEA: a variable returns to scale specification

Abstract

The full dimensional efficient facets (FDEFs) of a production possibility set (PPS) play a key role in data envelopment analysis (DEA). Finding the FDEFs has been the subject of intensive research over the past decade. The available algorithms for finding the FDEFs in the current DEA literature either require information about the position of all the extreme efficient decision-making units on the facets of the PPS or knowledge of all extreme optimal solutions of the multiplier form of the BCC model. In this article, we develop an algorithm that does not require such crucial information that may not be easily available. To this purpose, we first carefully analyse the structure of the FDEFs of PPS with BCC technology, using basic concepts of polyhedral set theory. We then utilize this information to devise an algorithm for finding the FDEFs, using mixed integer linear programming. We illustrate our algorithm using a set of real data.

Keywords:

• data envelopment analysis
• full dimensional efficient facet
• convex analysis

Correction

In the original version of this paper the name of author Israfil Roshdi was incomplete. This has been corrected in this final version.

Correction

In the original version of this paper the name of author Israfil Roshdi was incomplete. This has been corrected in this final version.

Acknowledgements

The authors thank the referees for their exceptionally insightful and constructive comments.

Notes

1 Note that there exist at least m+s extreme BCC-efficient DMUs on each SDH of T_v (see Theorem 3).

2 For more details about adjacent basic optimal solutions, see Bazaraa et al (2005).