Efficiency measurement in data envelopment analysis in the presence of ordinal and interval data

Ebrahimi, Bohlool; Tavana, Madjid; Rahmani, Morteza; Santos‐Arteaga, Francisco J.

doi:10.1007/s00521-016-2826-2

Cited by 16 publications

(4 citation statements)

References 23 publications

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“…In the model, and are inputs and outputs of , respectivily, and and are the weights of inputs and the weights of outputs, respectivily. And then, Banker et al [35] presented the Banker, Charnes, and Cooper (BCC) model:…”

Section: Data Envelopment Analysismentioning

confidence: 99%

An Inverse BCC Model for Evaluating and Ordering Decision-Making Units under Fuzziness

Zavieh,

Niksefat,

Nasseri

2024

Fuzzy. Info. Tech.

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One of the most prevalent problems in linear programming as one of the convenient models in the field of operation research environment is Data Envelopment Analysis (DEA), which supports the efficiency of Decision-Making Units (DMUs). Usually, accurate data are common; however, in the real world, we are facing an inaccurate situation. In this paper, a new model for assessing DMUs in a fuzzy environment is presented; we consider the inverse DEA model with the variable return to scale with fuzzy numbers for fluctuating data. A case study is given to illustrate its performance. KEYWORDSfuzzy mathematical programming; fuzzy ordering; data envelopment analysis 1 Introduction D ata Envelopment Analysis (DEA) is a technique for deliberating the performance of Decision-Making Units (DMUs) with numerous inputs and outputs. Each DMU uses several inputs to generate several outputs. Moreover, the performance of DMUs is evaluated based on obtained inputs and outputs. DEA has been widely used in many fields of science. Pascoe et al. [1] used DEA to assess management alternatives in the presence of multiple objectives. Examples of the use of DEA to assess the financial effectiveness of insurance companies are presented in Ref. [2]. Nasseri and Khatir [3] organized a two-stage DEA model by taking into account undesirable output with fuzzy stochastic data. As one step forward, the Inverse of the DEA (IDEA) model has been recently introduced by Wei et al. [4] so that it tries to answer the question: If input (output) in a DMU is agitated, then how output (input) should be changed to keep the relative performance of the DMU? IDEA models have different applications in practical cases [5−7] . Furthermore, the IDEA model with a variable return to scale (Inverse Banker, Charnes, and Cooper model (IBCC)) is suggested by Lertworasirikul et al. [8] Next, Ghiyasi [9] proposed several problematic issues, and he challenged that the suggested Multi-Objective Linear Programming (MOLP) model by Lertworasirikul et al. [8] is not as effective as it was claimed.Fuzzy uncertainty, grey uncertainty, and rough uncertainty are intertwined facets of imprecision in

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Section: Data Envelopment Analysismentioning

confidence: 99%

An Inverse BCC Model for Evaluating and Ordering Decision-Making Units under Fuzziness

Zavieh,

Niksefat,

Nasseri

2024

Fuzzy. Info. Tech.

View full text Add to dashboard Cite

show abstract

“…Khalili-Damghani et al [23] evaluated the performance of a combined cycle power plant considering uncertainty modeled by interval data and undesirable output factors. Recently, Ebrahimi et al [7] reviewed the weaknesses of some of the existing DEA methods with interval or ordinal data. They showed that converting such type of data into exact data leads to a violation of DEA axioms.…”

Section: Literature Review Interval Dea Modelsmentioning

confidence: 99%

Integrated dynamic interval data envelopment analysis in the presence of integer and negative data

Bansal¹,

Mehra²

2022

JIMO

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The conventional data envelopment analysis (DEA) models presume that the values of input-output variables of the decision-making units (DMUs) are precisely known. However, some real-life situations can authoritatively mandate the data to vary in concrete fine-tuned ranges, which can include negative values and measures that are allowed to take integer values only. Our study proposes an integrated dynamic DEA model to accommodate interval-valued and integer-valued features that can take negative values. The proposed one-step model follows the directional distance function approach to determine the efficiency of DMUs over time in the presence of carryovers connecting the consecutive periods. We use the pessimistic and optimistic standpoints to evaluate the respective lower and upper bounds of the interval efficiency scores of the DMUs. We compare our proposed approach with a few relevant studies in the literature. We also validate our model on a synthetically generated dataset. Furthermore, we showcase the proposed procedure's applicability on a real dataset from 2014 to 2018 of airlines operating in India.

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“…Traditionally, many supplier evaluation models have been based on cardinal data, with less emphasis on ordinal data. However, emphasis has shifted to the simultaneous consideration of cardinal and ordinal data in the supplier selection process (Saen 2007;Ebrahimi et al 2018). The DEA base model is primarily designed to handle positive numbers (Pastor and Ruiz 2007), although in some cases negative numbers should be incorporated into the evaluation dataset (Izadikhah and Saen, 2016).…”

Section: Literature Reviewmentioning

confidence: 99%

Supplier selection: comparison of DEA models with additive and reciprocal data

Dobos

Vörösmarty

2020

Cent Eur J Oper Res

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Supplier evaluation is one of the most important fields of application for data envelopment analysis (DEA). Criteria may include negative data in both input and output factors. Data translation can solve this problem, but interpretation is not evident from the literature. Use of an additive model is one method of managing the problem of negative data. This paper addresses this issue in relation to the supplier ranking problem. It describes the development of a ranking with cross-efficiency that incorporates negative data into the additive model. The additive model we describe is compared with previously used DEA models in which data is replaced with reciprocal values when necessary. We present a supplier-evaluation-related example of this case. After the efficiency evaluation, a supplier ranking system is constructed. To do this, we use the cross-efficiencies obtained from the additive model. Aggregate efficiencies help display the suppliers in descending order of efficiency. Finally, the paper compares self-and peer-appraisal indicators for reciprocal and additive DEA models.

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Efficiency measurement in data envelopment analysis in the presence of ordinal and interval data

Cited by 16 publications

References 23 publications

An Inverse BCC Model for Evaluating and Ordering Decision-Making Units under Fuzziness

An Inverse BCC Model for Evaluating and Ordering Decision-Making Units under Fuzziness

Integrated dynamic interval data envelopment analysis in the presence of integer and negative data

Supplier selection: comparison of DEA models with additive and reciprocal data

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