On the Estimation of Directional Returns to Scale via DEA models
  Data envelopment analysis (DEA) is one of the most commonly used methods to estimate the returns to scale (RTS) of the public sector (e.g., research institutions). Existing studies are all based on the traditional definition of RTS in economics and assume that multiple inputs and outputs change in the same proportion, which is the starting point to determine the qualitative and quantitative features of RTS of decision making units (DMUs). However, for more complex products, such as the scientific research in institutes, changes of various types of inputs or outputs are often not in proportion. Therefore, the existing definition of RTS in the framework of DEA method may not meet the need to estimate the RTS of research institutions with multiple inputs and outputs. This paper proposes a definition of directional RTS in the DEA framework and estimates the directional RTS of research institutions using DEA models. Further in-depth analysis is conducted for an illustrative example of 16 basic research institutes in Chinese Academy of Sciences (CAS) in 2010. 
Guoliang Yang, Wenbin Liu, Wanfang Shen and Xiaoxuan Li
math.OC