Measuring the performances of decision-making units using interval efficiencies

Wang, Ying‐Ming; Yang, Jian-Bo

doi:10.1016/j.cam.2005.12.025

Cited by 61 publications

(51 citation statements)

References 5 publications

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“…Considering the minimum problem in model (6), the lower bound of interval efficiency of DMU 0 under evaluation, the lower bound model of model (6) can be transformed into that shown below when its denominator is fixed to one:…”

Section: Interval Efficiency Consisted Of the Optimistic And Pessimismentioning

confidence: 99%

“…This paper will evaluate the efficiencies of DMUs within the range of an interval so that the best and the worst relative efficiencies can be measured within a unified DEA model. Wang et al [6] have discussed this problem. A virtual anti-ideal DMU (ADMU) was introduced in [6], whose performance is definitely the worst among all the DMUs and the best relative efficiency can be used as the constraint on the lower bound efficiencies of DMUs; a new DEA model is developed, whose upper bound of constraint is one and lower bound of that is the best relative efficiency of the virtual ADMU.…”

Section: Introductionmentioning

confidence: 98%

“…Wang et al [6] have discussed this problem. A virtual anti-ideal DMU (ADMU) was introduced in [6], whose performance is definitely the worst among all the DMUs and the best relative efficiency can be used as the constraint on the lower bound efficiencies of DMUs; a new DEA model is developed, whose upper bound of constraint is one and lower bound of that is the best relative efficiency of the virtual ADMU. However, different conclusions may be obtained when efficiency is measured in different manner.…”

Section: Introductionmentioning

confidence: 98%

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Evaluating the performances of decision-making units based on interval efficiencies

Wang

2008

Journal of Computational and Applied Mathematics

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Efficiency could be not only the ratio of weighted sum of outputs to that of inputs but also that of weighted sum of inputs to that of outputs. When the previous efficiency measures the best relative efficiency within the range of no more than one, the decision-making units (DMUs) who get the optimum value of one perform best among all the DMUs. If the previous efficiency is measured within the range of no less than one, the DMUs who get the optimum value of one perform worst among all the DMUs. When the later efficiency is measured within the range of no more than one, the DMUs who get the optimum value of one perform worst among all the DMUs. If the later efficiency is measured within the range of no less than one, the DMUs who get the optimum value of one perform best among all the DMUs. This paper mainly studies an interval DEA model with later efficiency, in which efficiency is measured within the range of an interval, whose upper bound is set to one and the lower bound is determined by introducing a virtual ideal DMU, whose performance is definitely superior to any DMUs. The efficiencies, obtained from interval DEA model, turn out to be all intervals and are referred to as interval efficiencies, which combine the best and the worst relative efficiency in a reasonable manner to give an overall assessment of performances for all DMUs. Assessor's preference information on input and output weights is also incorporated into interval DEA model reasonably and conveniently. Through an example, some differences are found from the ranking results obtained from interval DEA model and bounded DEA model using the Hurwicz criterion approach to rank the interval efficiencies.

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Section: Interval Efficiency Consisted Of the Optimistic And Pessimismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 98%

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Evaluating the performances of decision-making units based on interval efficiencies

Wang

2008

Journal of Computational and Applied Mathematics

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“…Wang and Yang [4] proposed a pair of bounded DEA models for measurement of the overall performance of each DMU. The bounded DEA models make the most out of input and output information and measure the optimistic and pessimistic efficiencies for each DMU.…”

Section: Introductionmentioning

confidence: 99%

The interval efficiency based on the optimistic and pessimistic points of view

Azizi

2011

Applied Mathematical Modelling

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a b s t r a c tData envelopment analysis (DEA) is a data-oriented approach for evaluating the performances of a set of peer entities called decision-making units (DMUs), whose performance is determined based on multiple measures. The traditional DEA, which is based on the concept of efficiency frontier (output frontier), determines the best efficiency score that can be assigned to each DMU. Based on these scores, DMUs are classified into DEA-efficient (optimistic efficient) or DEA-non-efficient (optimistic non-efficient) units, and the DEA-efficient DMUs determine the efficiency frontier. There is a comparable approach which uses the concept of inefficiency frontier (input frontier) for determining the worst relative efficiency score that can be assigned to each DMU. DMUs on the inefficiency frontier are specified as DEA-inefficient or pessimistic inefficient, and those that do not lie on the inefficient frontier, are declared to be DEA-non-inefficient or pessimistic non-inefficient. In this paper, we argue that both relative efficiencies should be considered simultaneously, and any approach that considers only one of them will be biased. For measuring the overall performance of the DMUs, we propose to integrate both efficiencies in the form of an interval, and we call the proposed DEA models for efficiency measurement the bounded DEA models. In this way, the efficiency interval provides the decision maker with all the possible values of efficiency, which reflect various perspectives. A numerical example is presented to illustrate the application of the proposed DEA models.

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“…Entani and Tanaka [6] proposed the interval DEA model to obtain an efficiency interval consisting of evaluations from both the optimistic and pessimistic viewpoints. Wang and Yang [7] proposed a pair of bounded DEA models to measure the overall performances of a group of decision-making units (DMUs), which were characterized by interval efficiencies. To overcome the problem of these models incapable of determining an efficiency interval for any DMU when there is a zero value for each output, Azizi and Wang [8] proposed a pair of improved bounded DEA models to overcome the drawback.…”

Section: Introductionmentioning

confidence: 99%

Efficiency Bounds for Two-Stage Production Systems

Shi

2018

Mathematical Problems in Engineering

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Traditional data envelopment analysis (DEA) models find the most desirable weights for each decision-making unit (DMU) in order to estimate the highest efficiency score as possible. These efficiency scores are then used for ranking the DMUs. The main drawback is that the efficiency scores based on weights obtained from the standard DEA models ignore other feasible weights; this is due to the fact that DEA may have multiple solutions for each DMU. To overcome this problem, Salo and Punkka (2011) deemed each DMU as a "Black Box" and developed models to obtain the efficiency bounds for each DMU over sets of all its feasible weights. In many real world applications, there are DMUs that have a two-stage production system. In this paper, we extend the Salo and Punkka's (2011) model to a more common and practical case considering the two-stage production structure. The proposed approach calculates each DMU's efficiency bounds for the overall system as well as efficiency bounds for each subsystem/substage. An application for nonlife insurance companies has been discussed to illustrate the applicability of the proposed approach and show the usefulness of this method.

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Measuring the performances of decision-making units using interval efficiencies

Cited by 61 publications

References 5 publications

Evaluating the performances of decision-making units based on interval efficiencies

Evaluating the performances of decision-making units based on interval efficiencies

The interval efficiency based on the optimistic and pessimistic points of view

Efficiency Bounds for Two-Stage Production Systems

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