Efficient Facet Based Efficiency Index: A Variable Returns to Scale Specification

The appearance of strictly positive slack variables in DEA solutions causes well known computational and analytical problems studied by Olesen and Petersen (1996) and Green et al. (1996) under constant returns to scale. This paper discusses variable returns to scale and suggests the use of efficient facets (EFs) in the reference technology. It is found to give a lower bound of the efficiency scores. Most importantly, efficiency measured with respect to EFs—the EF based efficiency index—may decrease if additional variables are introduced but are disposed in production. Thus, units are penalized for disposal of incoming variables, and the EF based efficiency index captures the net efficiency of a unit. EF is found to be a useful tool also to search a suitable set of variables for efficiency measurement. Its use is demonstrated with Finnish university data and it is found to change the measured performance of the university sector quite significantly.