Abstract: The existing environmental efficiency evaluation DEA models have not considered the issue that different decision making units (DMUs) may impose different  preferences on different outputs (desirable and undesirable outputs), e.g., different DMUs may value GDP (desirable output), waste water discharge and waste gas emissions differently.  This paper aims at addressing this problem. We present a DEA model incorporating desirable outputs and undesirable outputs, which can increase desirable outputs and decrease undesirable outputs simultaneously. To restrict DMUs' different  preferences on outputs, we then extend the model by incorporating multiple sets AR constraints based on  Context-Dependent Assurance Regions DEA approach (CAR-DEA) in recent DEA literature. An application of 30  regions in China with real data set is used to illustrate the proposed approach.

Key words: data envelopment analysis, undesirable outputs, assurance region, CAR-DEA