Abstract: It is proved that,firstly, the input possibility set spanned by samples (DMUs in terms of DEA) can be divided into areas of increasing return to scale (IRS), constant return to scale (CRS) and decreasing return to scale (DRS); secondly, C-D production function is quasi-concave, and non-concave on the area of IRS. The concept of IRS frontier of a production possibility set is proposed. Based on the division of input possibility set and the position of the production function surface, BCC frontier and the IRS frontier, a method to estimate production function is proposed. According to the method, production function is divided into a non-concave segments on area of IRS and a concave segment on area of non-IRS, and the estimation is processed in following steps. First, dividing the input possibility set into IRS area and non-IRS area; second, forming IRS frontier on IRS area and BCC frontier on non-IRS area, respectively; third, estimating parameters of each segment with corresponding frontier by a linear programming model, respectively. The validity of the estimation method is verified through an instance.

Key words: data envelopment analysis (DEA), production function, return to scale, weak efficiency, production frontier