A unified approach to non-radial graph models in data envelopment analysis: common features, geometry, and duality

• Published in: European journal of operational research Vol. 289; no. 2; pp. 611 - 627
• Main Authors: Halická, Margaréta, Trnovská, Mária
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.03.2021
• Subjects: Data envelopment analysis; Non-radial models; Russell measure model; Slacks-based model; Weighted additive model; Non-radial models; Slacks-based model; Weighted additive model; Russell measure model; Data envelopment analysis
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2020.07.019

•A unified analysis of non-radial, non-proportional, non-oriented models is provided.•The analysis is performed via two equivalent general envelopment schemes.•Properties common to all models in the schemes are specified and proved.•A general non-radial multiplier model is formulated and its properties are established.•The results help to find the supporting hyperplane containing all multiple projections. In data envelopment analysis (DEA), non-radial graph models represent an important class characterized by the independent treatment of each input and output factor in the efficiency measurement. The extensive literature on this topic often analyses individual models in isolation, so much so that the same model may be known under different names due to alternative formulations of different authors. In this paper, a unified analysis of non-radial graph models is offered, viewing each of them via two equivalent schemes: the slack-variables scheme and the Russell-type scheme. Under these schemes, the properties common to the whole class are specified and justified. Along with the two envelopment form schemes, a general dual (multiplier) form is presented. Primal-dual relationships between the envelopment and multiplier non-radial models are analyzed in order to reveal new useful properties and insights.