Abstract
To deal with the undesirable factors in Data Envelopment Analysis (DEA), a non-linear DEA model was previously developed
for a paper production system, where the desirable outputs are increased and the undesirable outputs are decreased for efficiency
improvement. To convert the proposed non-linear model into a linear one, a linear approximation to the non-linear constraint is
used and an approximate efficiency score is obtained. In this paper, we propose a new method to solve the non-linear
programming problem and calculate the efficiency scores accurately, in which a second-order cone programming (SOCP) is
defined and applied to transfer the non-linear programming model into a linear one. We applied the proposed model to measure
the environmental performance of 30 paper mills along the Huai River in China. It was found that the efficiency scores obtained
by our model is obvious different with the ones by approximate models.