Finding strong defining hyperplanes of PPS using multiplier form

Jahanshahloo, G. R.; Shirzadi, Ahmad; Mirdehghan, S. M.

doi:10.1016/j.ejor.2008.01.053

Cited by 21 publications

(8 citation statements)

References 10 publications

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“…If the optimal solution of (4) is unique, then the corresponding supporting hyperplane is a defining hyperplane and if (4) has alternative optimal solutions, then there are uncountable supporting hyperplanes on the PPS at the projection of DMU on the efficient frontier in which a finite number of them are defining hyperplanes. Jahanshahloo et al [23] show that, in evaluating an efficient DMU, each extreme optimal solution of (4) such that ( * , * ) > 0 identifies an efficient defining hyperplane of the PPS.…”

Section: Definitionmentioning

confidence: 99%

Finding the Most Preferred Decision-Making Unit in Data Envelopment Analysis

Mohammadi

Mirdehghan

Jahanshahloo

2016

Advances in Operations Research

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Data envelopment analysis (DEA) evaluates the efficiency of the transformation of a decision-making unit’s (DMU’s) inputs into its outputs. Finding the benchmarks of a DMU is one of the important purposes of DEA. The benchmarks of a DMU in DEA are obtained by solving some linear programming models. Currently, the obtained benchmarks are just found by using the information of the data of inputs and outputs without considering the decision-maker’s preferences. If the preferences of the decision-maker are available, it is very important to obtain the most preferred DMU as a benchmark of the under-assessment DMU. In this regard, we present an algorithm to find the most preferred DMU based on the utility function of decision-maker’s preferences by exploring some properties on that. The proposed method is constructed based on the projection of the gradient of the utility function on the production possibility set’s frontier.

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Section: Definitionmentioning

confidence: 99%

Finding the Most Preferred Decision-Making Unit in Data Envelopment Analysis

Mohammadi

Mirdehghan

Jahanshahloo

2016

Advances in Operations Research

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“…In this method we also cannot determine the variation range of inputs and outputs and stability region of additional DMU. However, in our method, since n earlier DMUs evaluated by multiplier form and the classification of efficient and inefficient DMUs specified, we can easily find all defining hyperplanes of T v with applying the proposed algorithm in Jahanshahloo et al (2009). On the other hand, using optimal solutions of the multiplier form when n DMUs are evaluated, we can determine the stability region of additional DMU which satisfies the special conditions for the rest of DMUs (For example, the efficiency score of a specific inefficient unit must be preserved or some competitor efficient units need to be inefficient in the presence of additional DMU).…”

Section: Proposed Methodsmentioning

confidence: 99%

“…Regardless of the additional DMU, we first find all efficient DMUs (with model (2)) and defining hyperplanes of T v (for a review see Jahanshahloo et al 2005cJahanshahloo et al , 2007Jahanshahloo et al , 2009) which we are interested in. It has been assumed that the redundant hyperplanes, which have no effect on the PPS, are omitted.…”

Section: Proposed Methodsmentioning

confidence: 99%

Finding stability regions for preserving efficiency classification of variable returns to scale technology in data envelopment analysis

Zamani

Borzouei

2016

J Ind Eng Int

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This paper addresses issue of sensitivity of efficiency classification of variable returns to scale (VRS) technology for enhancing the credibility of data envelopment analysis (DEA) results in practical applications when an additional decision making unit (DMU) needs to be added to the set being considered. It also develops a structured approach to assisting practitioners in making an appropriate selection of variation range for inputs and outputs of additional DMU so that this DMU be efficient and the efficiency classification of VRS technology remains unchanged. This stability region is simply specified by the concept of defining hyperplanes of production possibility set of VRS technology and the corresponding halfspaces. Furthermore, this study determines a stability region for the additional DMU within which, in addition to efficiency classification, the efficiency score of a specific inefficient DMU is preserved and also using a simulation method, a region in which some specific efficient DMUs become inefficient is provided.

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“…The characterisations of the PPS in DEA is found by specifying all defining hyperplanes of the PPS which construct the frontier of the PPS. Jahanshahloo et al (2009) have shown that the hyperplane which corresponds to an extreme optimal solution of the multiplier form whose components corresponding to inputs and outputs are non-zero is an efficient defining hyperplane of the PPS. Fukuyama and Sekitani (2012) decomposed the efficient frontier in to a new class of maximal efficient faces, and they have found a method to identify all maximal efficient faces.…”

Section: Introductionmentioning

confidence: 99%

Characterisations of the production possibility set in data envelopment analysis: an MOLP approach

Mirdehghan

Heydari

2018

IJMOR

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The production possibility set in data envelopment analysis is a polyhedron and it is defined by the intersection of a finite number of half spaces which are constructed by their corresponding defining hyperplanes. Because of the importance of the characterisations of the production possibility sets in data envelopment analysis, we suggest two multi objective linear programming problems and then we identify some characterisations of the production possibility set by investigation of the relations among the suggested multi objective linear programming models and the input oriented envelopment and multiplier BCC models. In this paper, we use weighted sum and epsilon-constraint scalarisation methods to present some mathematical properties for finding some relations among the efficient solutions of the proposed multi objective linear programming models and the characteristics of the production possibility set and data envelopment analysis models.

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Finding strong defining hyperplanes of PPS using multiplier form

Cited by 21 publications

References 10 publications

Finding the Most Preferred Decision-Making Unit in Data Envelopment Analysis

Finding the Most Preferred Decision-Making Unit in Data Envelopment Analysis

Finding stability regions for preserving efficiency classification of variable returns to scale technology in data envelopment analysis

Characterisations of the production possibility set in data envelopment analysis: an MOLP approach

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