Stability of efficiency evaluations in data envelopment analysis

ZusammenfassungDie 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.AbstractEfficiency 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.

[1]  Sanjo Zlobec,et al.  Input optimization: I. Optimal realizations of mathematical models , 1985, Math. Program..

[2]  Sanjo Zlobec,et al.  On the continuity of a Lagrangian multiplier function in input optimization , 1986, Math. Program..

[3]  W. Hogan.  Point-to-Set Maps in Mathematical Programming , 1973 .

[4]  D. Klatte.  A sufficient condition for lower semicontinuity of solution sets of systems of convex inequalities , 1984 .

[5]  Abraham Charnes,et al.  Measuring the efficiency of decision making units , 1978 .

[6]  Sanjo Zlobec.  Survey of input optimization 1 , 1987 .

[7]  A. Lewin,et al.  Determining organizational effectiveness: another look, and an agenda for research , 1986 .

[8]  Abraham Charnes,et al.  Sensitivity and stability analysis in dea , 1984, Ann. Oper. Res..

[9]  Sanjo Zlobec.  Two characterizations of Pareto minima in convex multicriteria optimization , 1984 .

[10]  Rajiv D. Banker,et al.  Efficiency Analysis for Exogenously Fixed Inputs and Outputs , 1986, Oper. Res..

[11]  Diethard Klatte,et al.  On Procedures for Analysing Parametric Optimization Problems , 1982 .

[12]  A. Charnes,et al.  Management Models and Industrial Applications of Linear Programming , 1961 .

[13]  Abraham Charnes,et al.  Necessary and Sufficient Conditions for a Pareto Optimum in Convex Programming , 1977 .

[14]  Sanjo Zlobec,et al.  On a necessary condition for stability in perturbed linear and convex programming , 1987, Z. Oper. Research.

[15]  Boaz Golany,et al.  Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions , 1985 .

[16]  Aharon Ben-Tal,et al.  Optimality in nonlinear programming: A feasible directions approach , 1981 .