Stability regions for maintaining efficiency in data envelopment analysis

This paper develops a procedure for performing a sensitivity analysis of the efficient decision making units (DMUs) within the Charnes et al. (CCR) [European Journal of Operational Research 2 (1978) 429–444] model of data envelopment analysis (DEA). The procedure yields an exact `input stability region' and `output stability region' within which the efficiency of a specific efficient DMU remains unchanged. Such stability regions are simply characterized by optimal solutions of modified CCR models which are easily computed. In contrast to existing sufficient conditions for the preservation of efficiency under changes in inputs or outputs, the paper provides both necessary and sufficient conditions for an efficient DMU to remain efficient. The procedure is illustrated by numerical examples. Somewhat surprisingly, for real world data sets, for most of the efficient DMUs, the amount of some individual input can be infinitely increased when keeping other inputs and all outputs constant. This indicates that these efficient DMUs are located at extreme positions.