A single-stage optimization procedure for data envelopment analysis

In data envelopment analysis, a conventional procedure for testing efficiency of decision making units (DMUs) consists of two stages, each requiring solution of a linear program. The first stage identifies the input or output radial efficiency of a DMU, and the second stage maximizes the sum of component input and output slacks. A traditional alternative is the single-stage approximation of the two-stage procedure in which the objective functions of the first and second stages are combined, with the latter multiplied by a small positive constant epsilon. A known drawback of such approach is that very small values of epsilon may cause computational inaccuracies and large values do not allow a good approximation. In this paper, we develop a new single-stage linear programming approach that does not require the specification of a small constant epsilon and is completely equivalent to the conventional two-stage solution procedure. It produces exactly the same sets of primal and dual optimal solutions as the two separate stages of the two-stage approach. The new single-stage procedure is applicable to any convex polyhedral technology.