Integer interval DEA: An axiomatic derivation of the technology and an additive, slacks-based model

Arana‐Jiménez, Manuel; Sánchez-Gil, M. Carmen; Younesi, Atefeh; Lozano, Sebastián

doi:10.1016/j.fss.2020.12.011

Cited by 15 publications

(10 citation statements)

References 41 publications

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“…Zhou et al ( 2019 ) constructed a dynamic three-stage network DEA model considering decision-makers’ optimistic and pessimistic attitudes to evaluate the sustainable supply chain (SSC). Arana-Jiménez et al ( 2021 ) developed a two-stage SBM model to assess the efficiency when the data were integer and interval values. Based on the BCC model and simple Russell model, Poordavoodi et al ( 2020 ) combined the interval DEA model with interval entropy weight to evaluate the efficiency of Web services.…”

Section: Literature Reviewmentioning

confidence: 99%

Exploring the effect of COVID-19 on airline environmental efficiency through an interval epsilon-based measure model

Huang

Cui

2021

Environ Sci Pollut Res

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Section: Literature Reviewmentioning

confidence: 99%

Exploring the effect of COVID-19 on airline environmental efficiency through an interval epsilon-based measure model

Huang

Cui

2021

Environ Sci Pollut Res

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“…(2019), Jahani Sayyad Noveiri and Kordrostami (2020), Jahani Sayyad Noveiri et al . (2022) and Arana-Jiménez et al . (2021).…”

Section: Introductionmentioning

confidence: 96%

“…Therefore, models are needed that do not create optimal points beyond the production possibility set by rounding the number up or down if integer data is used or not lead to a weak and inefficient operating point (Lozano and Villa, 2006). Therefore, DEA models have been proposed to solve these problems, some of which are Lozano and Villa (2006), Kuosmanen and Kazemi Matin (2009), Du et al (2012), Chen et al (2012), Kordrostami et al (2018), Fathi Ajirlo et al (2019), Jahani Sayyad Noveiri and Kordrostami (2020), Jahani Sayyad Noveiri et al (2022 and Arana-Jim enez et al (2021). In the previous studies related to OSS, this type of data was not taken into consideration, and the main goal of this study is to calculate scales in the presence of integer data and undesirable outputs.…”

Section: Introductionmentioning

confidence: 99%

Average-profit efficiency and optimal scale sizes with integer data and undesirable outputs

Omshi

Kordrostami

Amirteimoori

et al. 2023

JES

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PurposeData envelopment analysis (DEA) is a significant method for measuring the relative efficiency of decision making units (DMUs) that use the least inputs, produce the most desirable outputs and emit the least undesirable outputs in order to maximize their profits. In DEA, detecting an optimal scale size (OSS) is also vital and could be more applicable in economic activities when there are integer and undesirable measures. The purpose of this research is to measure average-profit efficiency (APE) and OSSs with integer data and undesirable outputs.Design/methodology/approachThis study presents an alternative concept of APE using the concepts of most productive scale size (MPSS), profit efficiency and scales, containing desirable and undesirable outputs along with integer and non-integer measures. In fact, the OSS minimizes APE as the optimal scale, which is the ratio of the profit efficiency to the radial average output. Considering the prices of the inputs and desirable outputs, as well as the lack of any specific weight for the undesirable outputs, a two-step model for the numerical calculation of OSS is presented. In addition, the proposed approach is applied to a real data set of Iranian gas companies while there are integer measures and undesirable outputs.FindingsThe results show the introduced approach is beneficial to estimate OSSs from the aspect of maximizing profits of firms with undesirable outputs and integer values.Originality/valueEstimating OSSs is the significant issue for managers, but its investigation in the presence of integer measures and undesirable outputs is presently under-considered.

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“…This paper considers inputs and outputs with continuous interval-valued data as a way of modelling mathematical uncertainty. The most similar DEA approach is that proposed by Arana-Jimenez et al [28]. That work considers a hybrid scenario in which, in addition to integer interval data, some inputs or outputs are given as continuous intervals, but no super-efficiency model is proposed to rank or discriminate the efficient DMUs.…”

Section: Introductionmentioning

confidence: 99%

“…That work considers a hybrid scenario in which, in addition to integer interval data, some inputs or outputs are given as continuous intervals, but no super-efficiency model is proposed to rank or discriminate the efficient DMUs. In the present work, we focus on the continuous interval variables, with an enhanced formulation of the model given in [28] and a super-efficiency model. Thus, while [28] uses two phases for the slacks-based model under an additive and non-oriented approach, in the present work a one-phase interval Slack-based model is proposed.…”

Section: Introductionmentioning

confidence: 99%

A Novel Slacks-Based Interval DEA Model and Application

Arana-Jiménez,

Lozano-Ramírez,

Sánchez-Gil

et al. 2024

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This paper proposes a novel slacks-based interval DEA approach that computes interval targets, slacks, and crisp inefficiency scores. It uses interval arithmetic and requires solving a mixed-integer linear program. The corresponding super-efficiency formulation to discriminate among the efficient units is also presented. We also provide a case study of its application to sustainable tourism in the Mediterranean region, assessing the sustainable tourism efficiency of twelve Mediterranean regions to validate the proposed approach. The inputs and outputs cover the three sustainability dimensions and include GHG emissions as an undesirable output. Three regions were found to be inefficient, and the corresponding inputs and output improvements were computed. A total rank of the regions was also obtained using the super-efficiency model.

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Integer interval DEA: An axiomatic derivation of the technology and an additive, slacks-based model

Cited by 15 publications

References 41 publications

Exploring the effect of COVID-19 on airline environmental efficiency through an interval epsilon-based measure model

Exploring the effect of COVID-19 on airline environmental efficiency through an interval epsilon-based measure model

Average-profit efficiency and optimal scale sizes with integer data and undesirable outputs

A Novel Slacks-Based Interval DEA Model and Application

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