Using the Outer Approximation Algorithm For Generating All Efficient Extreme Points of DEA

Abstract

In this paper, we propose a multiple objective linear programing (MOLP) problem, whose feasible region is same of the production possibility set of the data envelopment analysis (DEA) with variable return to scale (VRS).We show that efficient points of the MOLP in outcome space are corresponding to efficient units of DEA and vice versa. We use the outer approximation algorithm for generating all extreme efficient points in the outcome set of the MOLP problem, then, we obtain the extreme efficient units of the VRS DEA. Because it works in the outcome set rather than in the decision set of the MOLP problem, the outer approximation algorithm has several advantages over decision set-based algorithms. It is also relatively easy to implement. We also consider some extensions.