Efficiency-measuring DEA model for production system with k independent subsystems

Data Envelopment Analysis (DEA) is a mathematical programming approach to assess relative efficiencies with a group of decision making units (DMUs) such as production systems. There have been some useful models for their successful applications in many fields. In this paper, we first point out the defect of the first DEA model CCR (Charnes, Cooper and Rhodes, 1978) in measuring the efficiencies of the production system with k independent subsystems and propose a new model YMK (Yang, Ma and Koike) by improving CCR model. Some properties and the relationship between CCR and YMK models are also discussed. It is concluded that the overall efficiency (YMK) of each DMU has a great deal to do with the efficiencies of its subsystems under CCR model. In fact, the overall efficiency value (YMK) of each DMU is equal to the maximum among the efficiency values of all its subsystems under CCR model. The examples given demonstrate the effectiveness of YMK model in measuring efficiencies of the production system with k independent subsystems.