CLASSIFICATION AND RANK OF DMUS WITH INTERVAL INPUTS AND OUTPUTS IN DATA ENVELOPMENT ANALYSIS

摘要

The original data envelopment analysis (DEA) model assumes that inputs and outputs data must be exact values. However, in the real word the data may be imprecise due to insufficient information or measure error and so on. For this reason, interval DEA is proposed. Andersen P and Petersen N C put forward a modified DEA (MDEA) in their paper called "A procedure for ranking efficient units in data envelopment analysis" in 1993 which can bring out more discriminative efficiency scores. This paper firstly extend the MDEA to an interval modified DEA (IMDEA) model. To get the upper bound of the efficiency score of the j_0 decision making unit (DMU_0), a DEA model with exact value is set up by adjusting the levels of interval inputs and outputs in favor of DMU_0 and aggressively against the other DMUs. On the contrary the model of getting lower bound of DMU_0 is also set up. As a result, efficiency score interval of each DMU is obtained. The efficiency score interval is more discriminative than the one got directly from general interval DEA. Based on this, all the DMUs are classified into three types: interval efficient, partly interval efficient and interval inefficient ones. The next, a new order relation between intervals which can express the DM's preference to the three types is brought forward. Consequently, a full and more convictive ranking is made on all the DMUs and more practical information is supplied for the decision maker. Finally an example is given.