Application Of Data Envelopment Analysis In Multi-Stage Exchange Production System

Data Envelopment Analysis (DEA) is a mathematical programming method of evaluating the relative efficiency of a series of decision making unit (DMU) with multi-input and multi-output. This method can evaluate the performance difference, namely relative efficiency, of DMUs just through the real input and output, without the function between input and output or the weight assumption. Classical DEA model is generally used in a single stage production system, or a multi-stage production system which is treated as a black-box system without the internal mechanism, equal to a single stage one. But it's not suitable for many real production systems obviously.There are many multi-stage production systems with exchange of substance with outside during the process. How to evaluate the efficiency of a production system and then improve the efficiency scientifically, which is really a valuable problem. In order to evaluate the performance of this system, we use DEA method to set up mathematic models from three different points of view, which include the single stage model, multi-stage black-box model which ignore the internal mechanism and multi-stage total model which include the internal mechanism according to the fact. We define the different DEA efficiency of DMU and prove the existence theorem and dimension irrelevance theorem of efficient DMU, and so on. At last we analyze the relationship among the efficiency of different models. And we get conclusion that if there is an efficient DMU in the total model, then there must be an efficient one in the black-box model.