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Solving DEA models in a single optimization stage: Can the non-Archimedean infinitesimal be replaced by a small finite epsilon?
journal contributionposted on 2016-10-04, 13:30 authored by Victor PodinovskiVictor Podinovski, Tatiana Bouzdine-Chameeva
Single-stage DEA models aim to assess the input or output radial efficiency of a decision making unit and potential mix inefficiency in a single optimization stage. This is achieved by incorporating the sum of input and output slacks, multiplied by a small (theoretically non-Archimedean infinitesimal) value epsilon in the envelopment model or, equivalently, by using this value as the lower bound on the input and output weights in the dual multiplier model. When this approach is used, it is common practice to select a very small value for epsilon. This is based on the expectation that, for a sufficiently small epsilon, the radial efficiency and optimal slacks obtained by solving the single-stage model should be approximately equal to their true values obtained by the two separate optimization stages. However, as well-known, selecting a small epsilon may lead to significant computational inaccuracies. In this paper we prove that there exists a threshold value, referred to as the effective bound, such that, if epsilon is smaller than this bound, the solution to the single-stage program is not approximate but precise (exactly the same as in the two-stage approach), provided there are no computational errors.
- Business and Economics
Published inEuropean Journal of Operational Research
CitationPODINOVSKI, V.V. and BOUZDINE-CHAMEEVA, T., 2016. Solving DEA models in a single optimization stage: Can the non-Archimedean infinitesimal be replaced by a small finite epsilon? European Journal of Operational Research, 257(2), pp 412–419.
- AM (Accepted Manuscript)
Publisher statementThis work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/
NotesThis paper was published in the journal European Journal of Operational Research and the definitive published version is available at https://doi.org/10.1016/j.ejor.2016.09.022.