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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 contribution
posted on 2016-10-04, 13:30 authored by Victor PodinovskiVictor Podinovski, Tatiana Bouzdine-ChameevaSingle-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.
History
School
- Business and Economics
Department
- Business
Published in
European Journal of Operational ResearchVolume
257Issue
2Pages
412-419Citation
PODINOVSKI, 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.Publisher
© ElsevierVersion
- AM (Accepted Manuscript)
Publisher statement
This 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/Acceptance date
2016-09-06Publication date
2016-09-15Notes
This 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.ISSN
0377-2217Publisher version
Language
- en