DEA on Relaxed Convexity Assumptions

In a recent paper, Petersen (Petersen, N. C. 1990. Data envelopment analysis on a relaxed set of assumptions. Management Sci. 36 305--314.) proposed to relax the convexity assumptions invoked in traditional Data Envelopment Analysis (DEA). Unfortunately, the new approach is not consistent with the relaxed assumptions. Also, the efficiency evaluations in input and output spaces are based on different technologies assumptions. The aim of this paper is to clarify which assumptions are actually involved and to develop modifications such that the input and output based measures are consistent. In effect, a family of DEA methods based on relaxed convexity assumptions is identified.