A note on imposing strong complementary slackness conditions in DEA

A new DEA model has been introduced recently combining the primal and the dual models in order to impose strong complementary slackness conditions. It was claimed that a reference set that contains the maximum number of efficient units can then be determined. The model is very interesting as a theoretical idea. However, not only does the computational burden increase significantly, but it seems also that the basic matrices may be inherently ill-conditioned, leading to erroneous results. Numerical experiments have been carried out on two real datasets of medium size with 163 and 920 units. These experiments, using well known reliable software, show pervasive existence of ill-conditioned matrices leading to obviously wrong estimates of efficiency scores, and units declared as efficient reference units while actually being inefficient.