Further discussion on linear production functions and DEA

Abstract

The purpose of the current paper is to clarify the misunderstanding in using the constant returns to scale (CRS) model in data envelopment analysis (DEA) to estimate returns to scale (RTS) classification. By illustrating the following two different assumptions: (a) all decision making units (DMUs) are assumed to be compared to a CRS frontier in the CCR model, i.e., all DMUs are assumed to be capable of operating under CRS and (b) all DMUs exhibit CRS, several incorrect points about RTS estimation raised by Chang, K.P. and Guh, Y.Y. (1991) (European Journal of Operational Research 52, 215–223) and Chang. K.P. (1997) (European Journal of Operational Research 97, 597–599) are examined. It is shown that the assumption (a) does not mean that the RTS classification cannot be estimated. The CRS frontier assumption cannot change the RTS nature of each DMU. Since the CCR model mixes a technical efficiency and a scale efficiency, it is possible and meaningful to use the CCR results to determine the RTS classification. Finally, the infeasibility of Chang and Guh's (1991) treatment of non-archimedean infinitesimal is discussed.