Zusammenfassung
Die Data Envelopment Analyse (DEA) ist ein Ansatz, um die Auswirkung von Größen mit mehrfachen Eingängen und Ausgängen festzustellen. Es wird gezeigt, daß die Wirksamkeitsberechnungen stabil sind bei beliebigen Störungen, die in der konvexen Hülle der Eingangsund Ausgangsdaten liegen. Ferner wird nachgewiesen, daß die zugehörigen resringierten Lagrangefunktionen stetig sind. Zum Beweis dieser Aussagen werden Punkt-Mengen-Abbildungen herangezogen sowie ein spezieller Stabilitätsbereich der Input-Optimierung.
Abstract
Efficiency evaluations in data envelopment analysis are shown to be stable for arbitrary perturbations in the convex hulls of input and output data. Also, the corresponding restricted Lagrange multiplier functions are shown to be continuous. The results are proved using point-to-set mappings and a particular region of stability from input optimization.
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Research partly supported by National Science Foundation Grants, Office of Naval Research Grant, and by the Natural Sciences and Engineering Council of Canada.
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Charnes, A., Zlobec, S. Stability of efficiency evaluations in data envelopment analysis. ZOR - Methods and Models of Operations Research 33, 167–179 (1989). https://doi.org/10.1007/BF01423647
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DOI: https://doi.org/10.1007/BF01423647