Continuous models combining slacks-based measures of efficiency and super-efficiency
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866929549940359168 |
|---|---|
| author | Bolos, Vicente J. Benitez, Rafael Coll-Serrano, Vicente |
| author_facet | Bolos, Vicente J. Benitez, Rafael Coll-Serrano, Vicente |
| contents | In the framework of data envelopment analysis (DEA), Tone (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 (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 (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 (2013) and Chen et al. (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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_14303 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Continuous models combining slacks-based measures of efficiency and super-efficiency Bolos, Vicente J. Benitez, Rafael Coll-Serrano, Vicente Optimization and Control 90C08, 90C30, 90C47, 90C90 In the framework of data envelopment analysis (DEA), Tone (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 (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 (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 (2013) and Chen et al. (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. |
| title | Continuous models combining slacks-based measures of efficiency and super-efficiency |
| topic | Optimization and Control 90C08, 90C30, 90C47, 90C90 |
| url | https://arxiv.org/abs/2410.14303 |