Characterizing and finding full dimensional efficient facets in DEA: a variable returns to scale specification

Davtalab-Olyaie, Mostafa; Roshdi, Israfil; Jahanshahloo, G. R.; Asgharian, Masoud

doi:10.1057/jors.2013.97

Cited by 23 publications

(7 citation statements)

References 23 publications

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“…For comparison, we also list the time taken to solve one LP per DMU to identify the efficient DMUs. Comparing the runtime of Algorithm 1 with the standard DEA approach gives an indication of its performance for computing the efficient frontier of

T_{Λ}

because the initial step for existing algorithms (Davtalab‐Olyaie et al, ; Olesen & Petersen, ) consists of solving DEA LP models to identify extreme efficient DMUs. All computations were carried out on a PC with Intel (R) Core(TM) i3 processor with 4 GB RAM and 1GHz speed under a Windows 8 64 bit operating system.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Jahanshahloo, Lotfi, Rezai, and Balf () offer an enumerative method that first finds all efficient DMUs then identifies those that share the same facet, and finally constructs that facet. Davtalab‐Olyaie, Roshdi, Jahanshahloo, and Asgharian () first identify the extreme efficient DMUs and then perform a procedure that requires the repeated solution of mixed integer programmes to identify the efficient facets. Jahanshahloo, Lotfi, and Akbarian () propose an algorithm that finds weakly efficient facets of the technology set.…”

Section: Introductionmentioning

confidence: 99%

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A multiobjective optimization approach to compute the efficient frontier in data envelopment analysis

Ehrgott

Hasannasab

Raith

2019

Multi Criteria Decision Anal

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Data envelopment analysis is a linear programming‐based operations research technique for performance measurement of decision‐making units. In this paper, we investigate data envelopment analysis from a multiobjective point of view to compute both the efficient extreme points and the efficient facets of the technology set simultaneously. We introduce a dual multiobjective linear programming formulation of data envelopment analysis in terms of input and output prices and propose a procedure based on objective space algorithms for multiobjective linear programmes to compute the efficient frontier. We show that using our algorithm, the efficient extreme points and facets of the technology set can be computed without solving any optimization problems. We conduct computational experiments to demonstrate that the algorithm can compute the efficient frontier within seconds to a few minutes of computation time for real‐world data envelopment analysis instances. For large‐scale artificial data sets, our algorithm is faster than computing the efficiency scores of all decision‐making units via linear programming.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A multiobjective optimization approach to compute the efficient frontier in data envelopment analysis

Ehrgott

Hasannasab

Raith

2019

Multi Criteria Decision Anal

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“…Maximal efficient faces are usually called facets. 3 There exists a body of literature dealing with the identification of the facets of the DEA efficient frontier (see Olesen and Petersen (1996, Fukuyama and Sekitani (2012), Jahanshahloo et al (2007) and Davtalab-Olyaie et al (2014)).…”

Section: Introductionmentioning

confidence: 99%

Cross-benchmarking for performance evaluation: Looking across best practices of different peer groups using DEA

Ramon

Ruiz

Sirvent

2020

Omega

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In benchmarking, organizations look outward to examine others' performance in their industry or sector. Often, they can learn from the best practices of some of them and improve. In order to develop this idea within the framework of Data Envelopment Analysis (DEA), this paper extends the common benchmarking framework proposed in Ruiz and Sirvent (2016) to an approach based on the benchmarking of decision making units (DMUs) against several reference sets. We refer to this approach as cross-benchmarking. First, we design a procedure aimed at making a selection of reference sets (as defined in DEA), which establish the common framework for the benchmarking. Next, benchmarking models are formulated which allow us to set the closest targets relative to the reference sets selected. The availability of a wider spectrum of targets may offer managers the possibility of choosing among alternative ways for improvements, taking into account what can be learned from the best practices of different peer groups. Thus, cross-benchmarking is a flexible tool that can support a process of future planning while considering different managerial implications.

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“…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. Wei et al (2007) and Davtalab-Olyaie et al(2014 proposed some approaches to identify all full dimensional efficient and weak efficient facets of the PPS. Also, Jahanshahloo et al (2008) and Mehdiloozad et al (2015) proposed methods to find the reference sets of DMUs which can identify some characterisations of the PPS.…”

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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Characterizing and finding full dimensional efficient facets in DEA: a variable returns to scale specification

Cited by 23 publications

References 23 publications

A multiobjective optimization approach to compute the efficient frontier in data envelopment analysis

A multiobjective optimization approach to compute the efficient frontier in data envelopment analysis

Cross-benchmarking for performance evaluation: Looking across best practices of different peer groups using DEA

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

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