Refined bounds for the non-Archimedean ϵ in DEA. (June 2023)

• Record Type: Journal Article
• Authors: Sadeghi, Jafar; Begen, Mehmet A.; Ødegaard, Fredrik
• Is Part Of: Computers & operations research. Volume 154(2023)
• Publication Date: 2023-06
• Subjects: Non-Archimedean -- Data envelopment analysis -- Pareto–Koopmans efficiency measures -- Epsilon efficiency measures; Operations research -- Periodicals; Electronic digital computers -- Periodicals; 004.05
• DOI: 10.1016/j.cor.2023.106163
• Languages: English
• ISSNs: 0305-0548

Abstract

Abstract: Motivated by measuring the Pareto–Koopmans efficiency of public service units, we present refined bounds for the crucial non-Archimedean infinitesimal, aka epsilon. In non-parametric efficiency modeling, epsilon plays a key role as a multiplication factor to the sum of input and output slacks in the objective function. However, selecting an appropriate value for epsilon is non-trivial. It has to be sufficiently small to guarantee the envelopment model is bounded (or multiplier model to be feasible), yet large enough to provide managerial insight and not cause computational problems. Furthermore, the appropriate value is context dependent on the input and output metrics, and sensitive to assumptions regarding constant or variable returns-to-scale. Finally, different epsilon values may lead to drastically different ordering of the relative efficiency measures. To guarantee consistent relative order of the evaluated units we provide two refined bounds. The first, positive efficiency measures, serves as a precursor to ensure the obtained Pareto–Koopmans efficiency measures are positive and well-defined. The second and main contribution, robust efficiency measures, ensures the relative efficiency measures are provably consistent. We illustrate our bounds and their implications from an evaluation study of twelve public healthcare centers. Highlights: Two refined bounds for the non-Archimedean infinitesimal in DEA models. Bounds to ensure consistent relative rank order among DMU. Consideration of input- and output-oriented efficiency measurement models. Empirical analysis of public health care centers.