Dual structures for the additive DEA model

Robert G. Chambers

European Journal of Operational Research, 2023, vol. 307, issue 2, 984-989

Abstract: We show that the weighted additive DEA score (WA) for the additive DEA model is simultaneously the (dual) support function for a translation of the DEA technology and the gauge of the dual polar set of the translated technology. Those results are used: to show that WA and the indicator function for the translated technology form a dual conjugate pair; to show that WA and the translated technology’s gauge function form a dual polar pair; to develop a simple but exact link between WA and the profit function for the DEA technology; to show that WA and the directional distance function form a dual polar pair; and to develop an exact decomposition of profit inefficiency that extends the Cooper, Pastor, Aparicio, and Borras (2011) and Aparicio et al. (2016) decomposition.

Keywords: Data envelopment analysis; Weighted additive DEA; Duality; Support functions; Gauge functions; Profit inefficiency decomposition (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:307:y:2023:i:2:p:984-989

DOI: 10.1016/j.ejor.2022.10.026

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