Efficiency evaluation in data envelopment analysis using strong defining hyperplanes a cross-efficiency framework

• Published in: OR Spectrum Vol. 43; no. 2; pp. 441 - 465
• Main Authors: Dellnitz, Andreas, Reucher, Elmar, Kleine, Andreas
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2021
• Subjects: Business and Management; Calculus of Variations and Optimal Control; Optimization; Operations Research/Decision Theory; Regular Article; Facet analysis; Strong defining hyperplanes; Cross-efficiency evaluation; Data envelopment analysis
• ISSN: 0171-6468; 1436-6304
• DOI: 10.1007/s00291-021-00623-2

Cross-efficiency analysis in DEA generally uses a two-stage procedure: first, optimize a DMU’s individual efficiency score; next, push the efficiencies of all DMUs in a desired direction. In order to reduce subjective judgement in the second step, we provide a cross-efficiency method using only strong defining hyperplanes of the underlying technology. We develop a new DEA-based algorithm, and prove its finiteness and correctness. To reduce the computational burden, we show how one can combine the procedure with a known beneath-and-beyond procedure. Numerical investigations—comprising real-world data—demonstrate the superiority of the new method.