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On measuring the inefficiency with the inner-product norm in data envelopment analysis. (English) Zbl 0981.90056

Summary: A technique for assessing the sensitivity of efficiency classifications in data envelopment analysis is presented. It extends the technique proposed by A. Charnes, J. J. Rousseau, and J. H. Semple, [J. Productivity Analysis 7, 5-18 (1996)]. An organization’s input-output vector serves as the center for a cell within which the organization’s classification remains unchanged under perturbations of the data. The maximal radius among such cells can be interpreted as a stability measure of the classification. Our approach adopts the inner-product norm for the radius, while the previous work does the polyhedral norms. For an efficient organization, the maximal-radius problem is a convex program. On the other hand, for an inefficient organization, it is reduced to a nonconvex program whose feasible region is the complement of a convex polyhedral set. We show that the latter nonconvex problem can be transformed into a linear reverse convex program. Our formulations and algorithms are valid not only in the CCR model but in its variants.

MSC:

90C29 Multi-objective and goal programming
90C30 Nonlinear programming
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