Efficiency Evaluation on Two-Stage Production Using DEA

Two-stage production process is a fundamental production form in industry. The efficiency measurement that only considers the initial inputs and final outputs is generally inadequate since it is not inclusive and ignores the inner structure of it. In this paper, we propose a two-stage DEA model while the inner structure is incorporated for efficiency evaluation under variable returns to scale. The relationship between system efficient and sub-process efficient is discussed. We prove that if sub-process S1 is efficient and sub-process S2 weakly efficient, then the system is weakly efficient. However, the converse may not hold. Numerical examples are provided for illustration purpose.