Comment on some mathematical properties of a DEA model for the joint determination of efficiencies

Abstract

Molinero and Tsai (1997) proposed a data envelopment analysis (DEA) model to evaluate a production entity that is characterized by shared inputs and shared outputs. They claimed that their proposed model has a convex solution space, and thus a convex program. This conclusion, if it were correct, should be applicable potentially not only to the model given by the authors, but also arguably to all the researches concerning shared inputs and/or shared outputs in the literature. Because of its potential influence, we show that the conclusion is not correct and the significance of the incorrectness without reducing the interestingness of their work, as the establishment of Kuhn-Tucker condition is interesting by itself.

Keywords:

• shared input
• shared output
• DEA

Acknowledgements

The authors are grateful for the comments and suggestions of the two anonymous reviewers. This research is supported by National Natural Science Funds of China (No. 71301155, 71301037), National Natural Science Funds of China for Innovative Research Groups (No. 71121061) and the Fundamental Research Funds for the Central Universities (J2014hgbz0172).