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Column generation with free replicability in DEA

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  • Ehrgott, Matthias
  • Tind, Jørgen

Abstract

The evaluation of efficiency scores in data envelopment analysis is based on the construction of artificial decision making units subject to some assumptions, usually requiring convexity of the production possibility set. This demands divisibility in input and output, which is not always possible. The so-called free replicability model, proposed by Henry Tulkens, permits input and output to enter in only discrete amounts. The model is of a mixed integer programming type, for which the number of variables, here corresponding to the decision making units, may be critical in order to reach an optimal solution. We suggest to use column generation techniques to include only those decision making units that may contribute to the creation of an optimal solution.

Suggested Citation

  • Ehrgott, Matthias & Tind, Jørgen, 2009. "Column generation with free replicability in DEA," Omega, Elsevier, vol. 37(5), pages 943-950, October.
    • Handle: RePEc:eee:jomega:v:37:y:2009:i:5:p:943-950
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    References listed on IDEAS

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    2. Podinovski, Victor V. & Kuosmanen, Timo, 2011. "Modelling weak disposability in data envelopment analysis under relaxed convexity assumptions," European Journal of Operational Research, Elsevier, vol. 211(3), pages 577-585, June.
    3. Li, Xiangyong & Aneja, Y.P. & Huo, Jiazhen, 2012. "A robust branch-and-cut approach for the minimum-energy symmetric network connectivity problem," Omega, Elsevier, vol. 40(2), pages 210-217, April.
    4. Walter Briec & Kristiaan Kerstens & Ignace Van de Woestyne, 2022. "Nonconvexity in Production and Cost Functions: An Exploratory and Selective Review," Springer Books, in: Subhash C. Ray & Robert G. Chambers & Subal C. Kumbhakar (ed.), Handbook of Production Economics, chapter 18, pages 721-754, Springer.
    5. Li, Xiangyong & Aneja, Y.P. & Huo, Jiazhen, 2012. "Using branch-and-price approach to solve the directed network design problem with relays," Omega, Elsevier, vol. 40(5), pages 672-679.
    6. Barnabé Walheer, 2020. "Output, input, and undesirable output interconnections in data envelopment analysis: convexity and returns-to-scale," Annals of Operations Research, Springer, vol. 284(1), pages 447-467, January.
    7. Kuosmanen, Timo & Kazemi Matin, Reza, 2011. "Duality of weakly disposable technology," Omega, Elsevier, vol. 39(5), pages 504-512, October.

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