Continuous models combining slacks-based measures of efficiency and super-efficiency

Vicente J. Bolós (), Rafael Benítez () and Vicente Coll-Serrano
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Vicente J. Bolós: Universidad de Valencia
Rafael Benítez: Universidad de Valencia

Central European Journal of Operations Research, 2023, vol. 31, issue 2, No 1, 363-391

Abstract: Abstract In the framework of data envelopment analysis (DEA), Tone (Eur J Oper Res 130(3):498–509, 2001) introduced the slacks-based measure (SBM) of efficiency, which is a nonradial model that incorporates all the slacks of the evaluated decision-making units (DMUs) into their efficiency scores, unlike classical radial efficiency models. Next, Tone (Eur J Oper Res 143(1):32–41, 2002) developed the SBM super-efficiency model in order to differentiate and rank efficient DMUs, whose SBM efficiency scores are always 1. However, as pointed out by Chen (Eur J Oper Res 226(2):258–267, 2013), some interpretation problems arise when the so-called super-efficiency projections are weakly efficient, leading to an overestimation of the SBM super-efficiency score. Moreover, this overestimation is closely related to discontinuity issues when implementing SBM super-efficiency in conjunction with SBM efficiency. Chen (Eur J Oper Res 226(2):258–267, 2013) and Chen et al. (Ann Oper Res 278(1):101–121, 2019) treated these problems, but they did not arrive to a fully satisfactory solution. In this paper, we review these papers and propose a new complementary score, called composite SBM, that actually fixes the discontinuity problems by counteracting the overestimation of the SBM super-efficiency score. Moreover, we extend the composite SBM model to different orientations and variable returns to scale, and propose additive versions. Finally, we give examples and state some open problems.

Keywords: Data envelopment analysis; Super-efficiency; Super-inefficiency; Nonlinear programming; 90C08; 90C30; 90C47; 90C90 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10100-022-00813-5

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