The overall efficiency of the dynamic DEA models

Zýková, Petra

doi:10.1007/s10100-021-00777-y

Cited by 7 publications

(5 citation statements)

References 19 publications

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“…The problem of ranking efficient DMUs continues to be an active issue that keeps generating new studies and methods within DEA (Jablonsky 2012;Zýková 2022). Since its inception in the papers of Pastor et al (1999) and Tone (2001), the SBM superefficiency model has proved to be an important tool for ranking efficient DMUs which has been widely used by DEA practitioners in the last years.…”

Section: Discussionmentioning

confidence: 99%

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

Bolós

Benítez

Coll-Serrano

2022

Cent Eur J Oper Res

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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.

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Section: Discussionmentioning

confidence: 99%

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

Bolós

Benítez

Coll-Serrano

2022

Cent Eur J Oper Res

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“…𝑟 𝑖(𝑥 𝑐𝑟𝑠 =1) = 𝑓(𝑥 𝑐𝑟𝑠 𝑖 ) 𝑥 𝑐𝑟𝑠 𝑖 (30) 𝜀 𝑖 (𝑥 𝑐𝑟𝑠 =𝑖) = 𝑟 𝑖(𝑥 𝑐𝑟𝑠 =1) . 𝑥 𝑐𝑟𝑠 𝑖 (31) where 𝑟 𝑖 is the return for each input unit. Equation (31) seems a simple approach, though it explains that for a given input 𝑥 𝑐𝑟𝑠 𝑖 there are 𝑥 𝑐𝑟𝑠 input units with the same output at 𝑥 𝑐𝑟𝑠 = 1, which is 𝑟 𝑖 .…”

Section: Evaluating Time In the Affinity Coefficient 2111 Foundationsmentioning

confidence: 99%

“…A usual criticism to typical economical approaches has been the lack of time embedded in the models, though DEA address this issue through dynamic models, as seen in Zýková (2022) and Tsutsui (2014 and2010). Moreover, another important constraint that is not commonly covered by literature is the finite number of resources, which is the novel critical input parameter.…”

Section: Introductionmentioning

confidence: 99%

The Synergic Entropy : a parametric volatility boosted by synergy among companies

Videira

2023

Preprint

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The theory equates the maximum output deviations (efficient frontier) caused by combined inputs with affinity-synergy in a system, which leads to a parametric volatility – a curve that is similar to data envelopment analysis. The input is a cumulative variable (e.g: merged assets) and the output is a flow variable (e.g.: merged incomes). Rather than being purely stochastic, volatility is estimated by a novel parameter for risk named synergy, which is constrained by critical input (scarce resources). The outputacceleration derived from the mergers among inputs, boosted by synergy, is the main foundation of the approach, which special case gives Shannon and Boltzmann-Gibbs entropies. Tests are done in the 11 USA Sectors over their quarterly financial statements, proving that synergy is significant for financial statements, whereas typical betas only present significance in stock market data. A practical application is a novel discount rate for valuation using synergy, whose results for each sector are stable and coherent with perceived risk. Systems that rely on causal relations between output and multiple inputs can be regressed under novel parameters, rather than reckoning exclusively in optimization procedures.

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“…A typical criticism of the mainstream approaches has been the lack of time embedded in the models, though DEA addresses this issue through dynamic models, as seen in Zýková (2022) and Tsutsui (2014 and2010). Moreover, another essential constraint not commonly covered by literature is the finite number of resources, which is the novel critical input parameter.…”

Section: Introductionmentioning

confidence: 99%

The Synergic Entropy. An efficient frontier output derived from merged input units boosted by synergy and constrained by critical input

Videira

2023

FMIR

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The theory equates the maximum output deviations (efficient frontier) caused by combined inputs with affinity-synergy in a system, which leads to a parametric volatility whose curve can be compared to data envelopment analysis (DEA). The input is a cumulative variable (e.g.: merged assets), and the output is a flow variable (e.g.: combined incomes). Rather than being purely stochastic, volatility is estimated by a novel parameter for risk named synergy, which is constrained by critical input (scarce resources). The output acceleration derived from the mergers among inputs, boosted by synergy, is the main foundation of the approach, which particular case gives Shannon and Boltzmann-Gibbs entropies. Tests are done in the 11 USA Sectors over their quarterly financial statements, proving that synergy is significant for financial statements, whereas typical betas only present significance in stock market data. A practical application is a novel discount rate for valuation using synergy, whose results for each sector are stable and coherent with perceived risk. Systems that rely on causal relations between output and multiple inputs can be regressed under novel parameters, rather than reckoning exclusively in optimization procedures.

show abstract

The overall efficiency of the dynamic DEA models

Cited by 7 publications

References 19 publications

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

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

The Synergic Entropy : a parametric volatility boosted by synergy among companies

The Synergic Entropy. An efficient frontier output derived from merged input units boosted by synergy and constrained by critical input

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