Theory of integer-valued data envelopment analysis under alternative returns to scale axioms

Matin, Reza Kazemi; Kuosmanen, Timo

doi:10.1016/j.omega.2008.11.002

Cited by 58 publications

(27 citation statements)

References 9 publications

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“…Using basic DEA models for different types of returns to scale and feasibility checks of inequality set for each point produced by the algorithm can easily show that the result is the same as that of the MILP model presented by Kazemi Matin and Kuosmanen (). See Theorem for more detail.…”

Section: Some Characteristics Of the Algorithmmentioning

confidence: 78%

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An enumeration algorithm for integer-valued data envelopment analysis

Alirezaee¹,

Sani²

2011

Intl. Trans. in Op. Res.

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Data envelopment analysis (DEA) models assume real-valued inputs and outputs, but on many occasions, some inputs and/or outputs can only take integer values. In these cases, using DEA models can result in misleading efficiency assessments and inaccurate performance targets. In this paper, we propose an enumeration algorithm for computing efficiency scores and performance targets of decision-making units with integer value inputs/outputs. In the presented algorithm, we do not use any of the mixed integer linear programming (MILP) models that are used in previous studies. We show that the result of our algorithm and that of the MILP model presented in this context is the same. We also generalize our algorithm for different types of returns to scale as well as for the hybrid setting with real-valued data.

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Section: Some Characteristics Of the Algorithmmentioning

confidence: 78%

“…Then, they proposed a modification of the classic Farrell input efficiency measure and derived a MILP formulation for computing it. Kazemi Matin and Kuosmanen () extended and generalized Kuosmanen and Kazemi Matin's axiomatic foundation for the IDEA to the variable, non‐decreasing and non‐increasing returns to scale environments.…”

Section: Introductionmentioning

confidence: 99%

An enumeration algorithm for integer-valued data envelopment analysis

Alirezaee¹,

Sani²

2011

Intl. Trans. in Op. Res.

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“…Kuosmanen and Kazemi Matin () developed a new axiomatic foundation for integer‐valued DEA models, proposed a modification of the classic Farrel input efficiency measure, and derived an MILP formulation—the integer DEA “IDEA” model —for computing it. Kazemi Matin and Kuosmanen () generalized the IDEA model in different types of return‐to‐scales. On the other hand, Alirezaee and Rafiee Sani () proposed a numeration algorithm (NA) that computed efficiency scores and performance targets for integer‐valued DEA without solving any integer‐programming problems.…”

Section: Introductionmentioning

confidence: 99%

Trade‐offs in integer data envelopment analysis

Alirezaee

Sani

2016

Int Trans Operational Res

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If production trade-offs-which represent simultaneously feasible exchanges in the inputs and outputs of decision-making units (DMUs)-are added to an integer production possibility set (IPPS), a new IPPS is produced; conventional axioms of production do not generate a new IPPS, however. This paper develops the axiomatic foundation for data envelopment analysis (DEA) for integer-value inputs and outputs in the presence of production trade-offs by introducing a new axiom of "natural trade-offs." First, a mixed-integer linear programming formula called an integer DEA trade-off (IDEA-TO) is presented for computing efficiency scores and reference points. The numeration algorithm (NA) method presented in this concept is improved, and an improved numeration algorithm (INA) method for solving integer DEA (IDEA) models is developed. Finally, comparison between the two methods and a generalized INA method for solving the IDEA-TO model are presented.

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“…An integrated method to performance evaluation using DEA and fuzzy preference relations has been proposed by Wu (). Kuosmanen and Matin (); Kazemi Matin and Kuosmanen () proposed an axiomatic foundation to improve the integer‐valued DEA model of Lozano and Villa (). They proposed a modification of the classic input efficiency measure and derived a mixed integer linear programming DEA formulation for computing this measure of efficiency.…”

Section: Introductionmentioning

confidence: 99%

Data envelopment analysis with discrete‐valued inputs and outputs

Amirteimoori

Kordrostami

2013

Expert Systems

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The conventional data envelopment analysis (DEA) measures the relative efficiencies of a set of decision making units, which has real‐valued inputs and outputs. In many real occasions, there are cases in which some inputs and/or outputs must only take some particularised real or integer values. These values are referred to as discrete data. The need to deal with discrete‐valued data in DEA naturally occurs when we use real‐valued or integer‐valued DEA, but the reduced inputs and outputs of an inefficient decision making unit are restricted to some particular real or integer values. In this case, axioms such as unbounded ray, convexity and free disposability as discussed in the conventional DEA are violated. In this paper, an alternative extension of DEA in the case of discrete‐valued data has been faced. An axiomatic foundation is proposed to define the new production possibility set. In order to exemplify the method, a case of 25 Iranian gas companies' activities are illustrated.

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Theory of integer-valued data envelopment analysis under alternative returns to scale axioms

Cited by 58 publications

References 9 publications

An enumeration algorithm for integer-valued data envelopment analysis

An enumeration algorithm for integer-valued data envelopment analysis

Trade‐offs in integer data envelopment analysis

Data envelopment analysis with discrete‐valued inputs and outputs

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