Computational Accuracy and Infinitesimals In Data Envelopment Analysis

Ali, Agha Iqbal; Seiford, Lawrence M.

doi:10.1080/03155986.1993.11732232

Cited by 69 publications

(50 citation statements)

References 6 publications

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“…Também é exibido um exemplo ilustrativo, no qual o valor apropriado deste elemento satisfaz um intervalo de segurança (0, *), dado pela expressão: *  {1/ Maxj [r y(r,j)]}. Os modelos de DEA escolhidos foram implementados na ferramenta de modelagem AIMMS (Advanced integrated multidimensional modeling software) que, segundo [26], tratase de um ambiente computacional de desenvolvimento abrangente em modelagem de programação matemática, no qual podem ser criadas plenamente aplicações funcionais, prontas para serem usadas por pessoas mais leigas ou usuários finais.…”

Section: 'Pseudo-eficiência' Nos Modelos Deaunclassified

Modelo Dea Não-Arquimediano Para a Avaliação Do Sistema De Transporte Público De Passageiros Em Macaé

Ignacio¹,

Sampaio²

2014

Anais Do XVII Simpósio De Pesquisa Operacional E Logística Da Marinha

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ResumoO presente artigo apresenta um método de avaliação do sistema de transporte público da cidade de Macaé, utilizando a ferramenta de análise de eficiência conhecida como DEA ou Análise Envoltória de Dados, que compara as eficiências do sistema de Macaé com os de outras cidades brasileiras. O modelo DEA aplicado é uma extensão do modelo DEA/BCC básico, que evita a ocorrência de DMU pseudo-eficientes, ou seja, um modelo DEA/BCC-Não Arquimediano que restringe os multiplicadores do modelo a um elemento infinitesimal maior do que zero. Também são apresentadas as sugestões de melhoria do sistema de transporte público de passageiros de Macaé. Palavras chaves:DEA, DE-Não arquimediano, Sistemas de transporte. Abstract This paper presents an evaluation method of the public transport system of the Macae city, using the analysis tool known as DEA (Data envelopment analysis) which compares the efficiencies of Macae system with those of other cities. The DEA model used is an extension of DEA / basic BCC, which prevents the occurrence of pseudo-efficients decision makers units (DMU), ie a DEA / BCC Non-Archimedean model that restricts the multipliers to a greater than zero infinitesimal element. Suggestions for improvement of the public transport of passengers of Macaé system are also presented.

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Section: 'Pseudo-eficiência' Nos Modelos Deaunclassified

Modelo Dea Não-Arquimediano Para a Avaliação Do Sistema De Transporte Público De Passageiros Em Macaé

Ignacio¹,

Sampaio²

2014

Anais Do XVII Simpósio De Pesquisa Operacional E Logística Da Marinha

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“…However, the two-stage optimization procedure is a robust computational methodology that relieves the researcher of the need to make discretionary assumptions about some of the underlying parameters in these latter two models. As Ali and Seiford (1993b) note, improper choices in the values of these parameters can lead to serious computational errors.…”

Section: Methodsmentioning

confidence: 99%

The Operational Impacts of Government Restructuring of the Airline Industry

Schrega¹

2010

J Transp Res Forum

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In July 2000, the Civil Aviation Administration of China (CAAC) called for the consolidation of the 10 state-owned air carriers into three groups, headed by Air China, China Eastern, and China Southern. A few months later in November 2000, the State Council of China mandated that this consolidation be accomplished by the third quarter of 2001. As part of this mandate, the CAAC yielded its management control of air carriers with its focus now being on safety and regulatory issues. Furthermore, the CAAC was required to divest itself of assets held in many of the state-owned airlines and its interests in more than 120 airports around China, except Beijing Capital Airport. Utilizing data from the International Civil Aviation Organization for 2003 and 2004, this study investigates the operational impacts of this industry restructuring. The relative operational efficiency of Air China, China Eastern, and China Southern is compared to a sample of Asian, European and United States flag carriers. Data envelopment analysis is utilized to derive efficiency scores for individual airlines. The operational efficiency model used in this study is derived from that utilized by Schefczyk (1993). The underlying structural drivers of efficiency are then investigated via a tobit analysis with implications for managerial policy discussed.

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“…As shown by Ali and Seiford (1993b), the single-stage solution approach has important theoretical and computational drawbacks. From a theoretical perspective, the constant ϵ has to be sufficiently small for the multiplier model to be feasible or, equivalently, for the envelopment model to have a finite optimum value.…”

Section: Introductionmentioning

confidence: 99%

“…Intuitively, the latter concern can be addressed (and the precision of the approximate solution improved) by taking ϵ as a very small value. However, specifying a very small ϵ leads to well-documented computational problems arising from finite numerical tolerance of optimization software (Ali and Seiford 1993b).…”

Section: Introductionmentioning

confidence: 99%

“…The most common question addressed in this strand of research concerns estimation of the assurance interval [0, ϵ * ], where ϵ * > 0 is the maximum value ϵ that keeps the multiplier models feasible (Ali and Seiford 1993b, Mehrabian et al 2000, Amin and Toloo 2004, Alirezaee 2005, MirHassani and Alirezaee 2005. Clearly, choosing an ϵ from the assurance region does not guarantee that the resulting single-stage optimal solution is a good approximation of the true radial efficiency of DMU o and the corresponding component slacks.…”

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confidence: 99%

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Solving DEA models in a single optimization stage: Can the non-Archimedean infinitesimal be replaced by a small finite epsilon?

Podinovski

Bouzdine‐Chameeva

2017

European Journal of Operational Research

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Single-stage DEA models aim to assess the input or output radial efficiency of a decision making unit and potential mix inefficiency in a single optimization stage. This is achieved by incorporating the sum of input and output slacks, multiplied by a small (theoretically nonArchimedean infinitesimal) value epsilon in the envelopment model or, equivalently, by using this value as the lower bound on the input and output weights in the dual multiplier model. When this approach is used, it is common practice to select a very small value for epsilon. This is based on the expectation that, for a sufficiently small epsilon, the radial efficiency and optimal slacks obtained by solving the single-stage model should be approximately equal to their true values obtained by the two separate optimization stages. However, as well-known, selecting a small epsilon may lead to significant computational inaccuracies. In this paper we prove that there exists a threshold value, referred to as the effective bound, such that, if epsilon is smaller than this bound, the solution to the single-stage program is not approximate but precise (exactly the same as in the two-stage approach), provided there are no computational errors.

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Computational Accuracy and Infinitesimals In Data Envelopment Analysis

Cited by 69 publications

References 6 publications

Modelo Dea Não-Arquimediano Para a Avaliação Do Sistema De Transporte Público De Passageiros Em Macaé

Modelo Dea Não-Arquimediano Para a Avaliação Do Sistema De Transporte Público De Passageiros Em Macaé

The Operational Impacts of Government Restructuring of the Airline Industry

Solving DEA models in a single optimization stage: Can the non-Archimedean infinitesimal be replaced by a small finite epsilon?

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