Efficiency decomposition and frontier projection of two-stage network DEA under variable returns to scale

Lei Chen and Ying-Ming Wang

European Journal of Operational Research, 2025, vol. 322, issue 1, 157-170

Abstract: The efficiency decomposition and frontier projection of traditional two-stage network data envelopment analysis (DEA) model under variable returns to scale (VRS) are often not equivalent; which not only contradicts DEA theory, but also reduces the scientificity of the model. The main reason for this inequivalence is that there is a synergistic effect of variable scale return in two different stages. Therefore, this paper describes the production frontier of two-stage DEA under VRS for analyzing this synergistic effect, and then the efficiency evaluation pitfalls of two-stage DEA under VRS are identified. From the input orientation, output orientation, non-orientation perspectives, different two-stage network DEA models under VRS are respectively constructed to solve these evaluation pitfalls, and the equivalence relationships of their multiplier model and envelopment model are proved; and then the efficiency decomposition and frontier projection with equivalence relationship can be obtained to meet the different needs of decision-makers. Furthermore, variable intermediate element is discussed in the non-orientation model for achieving the Pareto optimality of two stages during the process of efficiency decomposition and frontier projection. By these models, the theoretical foundation of two-stage network DEA under VRS has been further improved. Finally, two examples are provided to illustrate the effectiveness of the new models.

Keywords: Data envelopment analysis; Two-stage network; Equivalence relationship; Efficiency decomposition; Frontier projection; Variable returns to scale (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:322:y:2025:i:1:p:157-170

DOI: 10.1016/j.ejor.2024.10.011

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