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A single-stage optimization procedure for data envelopment analysis

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  • Papaioannou, Grammatoula
  • Podinovski, Victor V.

Abstract

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.

Suggested Citation

  • Papaioannou, Grammatoula & Podinovski, Victor V., 2024. "A single-stage optimization procedure for data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 313(3), pages 1119-1128.
    • Handle: RePEc:eee:ejores:v:313:y:2024:i:3:p:1119-1128
    DOI: 10.1016/j.ejor.2023.09.036
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