A note on robustness of the efficient decision making units in data envelopment analysis

Sensitivity analysis of extreme efficient DMUs was studied by Zhu using the modified Charnes–Cooper–Rhodes model. Upward proportional variations of inputs and downward proportional variations of outputs were considered. The procedure suggested by Zhu is a new approach to sensitivity analysis and can result in sufficient and necessary conditions on the changes which do not alter the efficiency of DMUs. However, in certain instances the results presented by Zhu do not hold. The aim of this note is to point out shortcomings which can be met following procedure proposed by Zhu. This includes inefficiency of so-called projected points, domination of obtained hyperplane, case of simultaneous changes of inputs and outputs, and case of infeasibility even if all data are greater than 0.