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Visualizing Efficiency and Reference Relations in Data Envelopment Analysis with an Application to the Branches of a German Bank

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  • Marcus Porembski
  • Kristina Breitenstein
  • Paul Alpar

Abstract

The interest in Data Envelopment Analysis (DEA) as a method for analyzing the productivity of homogeneous Decision Making Units (DMUs) has significantly increased in recent years. One of the main goals of DEA is to measure for each DMU its production efficiency relative to the other DMUs under analysis. Apart from a relative efficiency score, DEA also provides reference DMUs for inefficient DMUs. An inefficient DMU has, in general, more than one reference DMU, and an efficient DMU may be a reference unit for a large number of inefficient DMUs. These reference and efficiency relations describe a net which connects efficient and inefficient DMUs. We visualize this net by applying Sammon’s mapping. Such a visualization provides a very compact representation of the respective reference and efficiency relations and it helps to identify for an inefficient DMU efficient DMUs respectively DMUs with a high efficiency score which have a similar structure and can therefore be used as models. Furthermore, it can also be applied to visualize potential outliers in a very efficient way. Copyright Springer Science+Business Media, Inc. 2005

Suggested Citation

  • Marcus Porembski & Kristina Breitenstein & Paul Alpar, 2005. "Visualizing Efficiency and Reference Relations in Data Envelopment Analysis with an Application to the Branches of a German Bank," Journal of Productivity Analysis, Springer, vol. 23(2), pages 203-221, May.
    • Handle: RePEc:kap:jproda:v:23:y:2005:i:2:p:203-221
    DOI: 10.1007/s11123-005-1328-5
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    References listed on IDEAS

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    2. Lívia Mariana Lopes de Souza Torres & Francisco S. Ramos, 2024. "Are Brazilian Higher Education Institutions Efficient in Their Graduate Activities? A Two-Stage Dynamic Data-Envelopment-Analysis Cooperative Approach," Mathematics, MDPI, vol. 12(6), pages 1-41, March.
    3. Kristiaan Kerstens & Bouye Ahmed Moulaye Hachem & Ignace Van de Woestyne & Niels Vestergaard, 2008. "Optimal Capacity Utilization and Reallocation in a German Bank Branch Network: Exploring Some Strategic Scenarios," Working Papers 2008-ECO-19, IESEG School of Management.
    4. Wheelock, David C. & Wilson, Paul W., 2008. "Non-parametric, unconditional quantile estimation for efficiency analysis with an application to Federal Reserve check processing operations," Journal of Econometrics, Elsevier, vol. 145(1-2), pages 209-225, July.
    5. Martin Bod′a & Emília Zimková, 2018. "Iso-analysis for knowing the sources of technical efficiency and performance," Operational Research, Springer, vol. 18(2), pages 421-449, July.
    6. Hashem Omrani & Farzane Adabi & Narges Adabi, 2017. "Designing an efficient supply chain network with uncertain data: a robust optimization—data envelopment analysis approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(7), pages 816-828, July.
    7. Léopold Simar & Paul W. Wilson, 2015. "Statistical Approaches for Non-parametric Frontier Models: A Guided Tour," International Statistical Review, International Statistical Institute, vol. 83(1), pages 77-110, April.
    8. Wilson, Paul W., 2018. "Dimension reduction in nonparametric models of production," European Journal of Operational Research, Elsevier, vol. 267(1), pages 349-367.
    9. Salomé Kahindo & Stéphane Blancard, 2022. "Reducing pesticide use through optimal reallocation at different spatial scales: The case of French arable farming," Agricultural Economics, International Association of Agricultural Economists, vol. 53(4), pages 648-666, July.
    10. Schotter, Andreas P.J. & Buchel, Olha & Vashchilko (Lukoianova), Tatiana, 2018. "Interactive visualization for research contextualization in international business," Journal of World Business, Elsevier, vol. 53(3), pages 356-372.
    11. Amir Moradi-Motlagh & Ali Emrouznejad, 2022. "The origins and development of statistical approaches in non-parametric frontier models: a survey of the first two decades of scholarly literature (1998–2020)," Annals of Operations Research, Springer, vol. 318(1), pages 713-741, November.
    12. Paradi, Joseph C. & Zhu, Haiyan, 2013. "A survey on bank branch efficiency and performance research with data envelopment analysis," Omega, Elsevier, vol. 41(1), pages 61-79.
    13. David C. Wheelock & Paul W. Wilson, 2009. "Robust, dynamic nonparametric benchmarking: the evolution of cost-productivity and efficiency among U.S. credit unions," Working Papers 2009-008, Federal Reserve Bank of St. Louis.
    14. Paradi, Joseph C. & Rouatt, Stephen & Zhu, Haiyan, 2011. "Two-stage evaluation of bank branch efficiency using data envelopment analysis," Omega, Elsevier, vol. 39(1), pages 99-109, January.

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