Discrete and Integer Valued Inputs and Outputs in Data Envelopment Analysis

Kuosmanen, Timo; Keshvari, Abolfazl; Matin, Reza Kazemi

doi:10.1007/978-1-4899-7553-9_4

Cited by 10 publications

(4 citation statements)

References 50 publications

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“…To consider integer-valued outputs; i.e. y I (k) ∈ Z |I | + , we apply the approach proposed by Kuosmanen and Kazemi Matin (2009) and Kuosmanen et al (2015). iii.…”

Section: Proposed Methodologymentioning

confidence: 99%

RETRACTED ARTICLE: Evaluating sustainably resilient supply chains: a stochastic double frontier analytic model considering Netzero

et al. 2022

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In era of reglobalization, sustainably resilient supply chains (SCs) are imperative in corporations to improve performance and meet stockholders’ expectations. However, sustainably resilient SCs could not be effective if are not assessed by using advanced frameworks, systems, and models. As such, developing a novel network data envelopment model (DEA) to appraise sustainably resilient SCs is our purpose in this article. To do so, we present a new double-frontier methodology to provide optimistic and pessimistic efficiency measures in network structures. Moreover, ideas of outputs weak disposability, chance-constrained programming, and discrete dominance are incorporated in a unified framework of modelling efficient and inefficient production technologies. The new network DEA model also can address dissimilar types of data, including undesirable and integer-valued and ratio outputs, stochastic intermediate products, and integer-valued inputs in a unified framework. Furthermore, an aggregated Farrell type efficiency measure is developed which allows to provide the complete ranking of units so that each decision-making unit (DMU) has its own rank in both overall and divisional point of view. We show the unique features of our developed model using a real case study in paint industry to evaluate the efficiency and reducing carbon dioxide (CO2) emissions. The results show that how well the proposed models can evaluate the sustainability and resilience of supply chains in the presence of uncertainty and with dissimilar types of data.

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“…To consider integer-valued outputs; i.e. y I (k) ∈ Z |I | + , we apply the approach proposed by Kuosmanen and Kazemi Matin (2009) and Kuosmanen et al (2015). iii.…”

Section: Proposed Methodologymentioning

confidence: 99%

RETRACTED ARTICLE: Evaluating sustainably resilient supply chains: a stochastic double frontier analytic model considering Netzero

et al. 2022

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“…Therefore, they proposed an MIDEA model based on Kourosh and Arash method (Khezrimotlagh et al , 2014) to overcome the shortcomings of the previous studies on integer-valued data in DEA models. Kuosmanen et al (2015) argued that the work of Khezrimotlagh et al (2013) has led to confusion by discrediting the contributions of Kuosmanen and Matin’s (2009) model and disregarding the importance of their proposed axiomatic foundation and mathematical formulations.…”

Section: Literature Reviewmentioning

confidence: 99%

A robust DEA model in the presence of uncertain integer-valued parameters

Zehi

Khurizan

2023

JM2

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Purpose Uncertainty in data, whether in real-valued or integer-valued data, may result in infeasible optimal solutions or unreliable efficiency scores and ranking of decision-making units. To handle the uncertainty in integer-valued factors in data envelopment analysis (DEA) models, this study aims to propose a robust DEA model which is applicable in the presence of such factors. Design/methodology/approach This research focuses on the application of fuzzy interpretation of efficiency to a mixed-integer DEA (MIDEA) model. The robust optimization approach is used to address the uncertain integer-valued parameters in the proposed MIDEA model. Findings In this study, the authors proposed an MIDEA model without any equality constraint to avoid the arise problem by such constraints in the construction of the robust counterpart of the conventional MIDEA models. We have studied the characteristics and conditions for constructing the uncertainty set with uncertain integer-valued parameters and a robust MIDEA model is proposed under a combined box-polyhedral uncertainty set. The applicability of the developed models is shown in a case study of Malaysian public universities. Originality/value This study develops an MIDEA model equivalent to the conventional MIDEA model excluding any equality constraint which is crucial in robust approach to avoid restricted feasible region or infeasible solutions. This study proposes a robust DEA approach which is applicable in cases with uncertain integer-valued parameters, unlike previous studies in robust DEA field where uncertain parameters are generally assumed to be only real-valued.

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“…However, it may not be true in some cases where there are bounded and/or discrete data, such as Likert scales. And a few research focuses on modeling bounded and/or discrete data (Cooper et al , 2011; Zhu, 2003; Kuosmanen and Kazemi Matin, 2009; Kuosmanen et al , 2015; Cook et al , 1993, 1996). It shows that neglecting the variable type of data may obtain wrong results (Chen et al , 2017b).…”

Section: Literature Reviewmentioning

confidence: 99%

Bounded and discrete data in data envelopment analysis with assurance regions

Zhang

Feng

Yang

et al. 2020

JM2

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Purpose The purpose of this paper is to evaluate design performance of 51 gear shaping machines by using data envelopment analysis (DEA). Design/methodology/approach Existing studies extend traditional DEA by handling bounded and discrete data based on envelopment models. However, value judgment is usually neglected and fail to be incorporated in these envelopment models. In many cases, there is a need for prior preferences. Using existing DEA approaches as a backdrop, the current paper presents a methodology for incorporating assurance region (AR) restrictions into DEA with bounded and discrete data, i.e. the assurance region bounded discrete (AR-BD) DEA model. Then, the AR-BD DEA model is combined with a context-dependent DEA to obtain an efficiency stratification. Findings The authors examine different AR restrictions and calculate efficiency scores of five scenarios of AR restrictions by using the proposed AR-BD DEA model. It shows that AR restrictions have a great impact on the efficiency scores. The authors also identify nine efficient frontiers in total. For each decision-making unit, it could set benchmarks and improve its performance based on each higher efficient frontier. Originality/value This paper first evaluates efficiency of gear shaping machines by considering different (bounded and discrete) variable types of data and including AR restrictions. The AR-BD DEA model and context-dependent AR-BD DEA model proposed in this paper further enrich the DEA theory. The findings in this paper certainly provide useful information for both producers and consumers to make smart decisions.

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Discrete and Integer Valued Inputs and Outputs in Data Envelopment Analysis

Cited by 10 publications

References 50 publications

RETRACTED ARTICLE: Evaluating sustainably resilient supply chains: a stochastic double frontier analytic model considering Netzero

RETRACTED ARTICLE: Evaluating sustainably resilient supply chains: a stochastic double frontier analytic model considering Netzero

A robust DEA model in the presence of uncertain integer-valued parameters

Bounded and discrete data in data envelopment analysis with assurance regions

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