On measuring the inefficiency with the inner-product norm in data envelopment analysis

A technique for assessing the sensitivity of efficiency classifications in Data Envelopment Analysis (DEA) is presented. It extends the technique proposed by Charnes et al. (A. Charnes, J.J. Rousseau, J.H. Semple, Journal of Productivity Analysis 7 (1996) 5–18). An organization's input–output vector serves as the center for a cell within which the organization's classification remains unchanged under perturbations of the data. The maximal radius among such cells can be interpreted as a stability measure of the classification. Our approach adopts the inner-product norm for the radius, while the previous work does the polyhedral norms. For an efficient organization, the maximal-radius problem is a convex program. On the other hand, for an inefficient organization, it is reduced to a nonconvex program whose feasible region is the complement of a convex polyhedral set. We show that the latter nonconvex problem can be transformed into a linear reverse convex program. Our formulations and algorithms are valid not only in the CCR model but in its variants.