A geometrical approach for fuzzy DEA frontiers.

Interval DEA frontiers are here used in situation where one input or output is subject to uncertainty in its measurement and is presented as an interval data. We built an efficient frontier without any assumption about the probability distribution function of the imprecise variable. We take into account only the minimum and the maximum values of each imprecise variable. Two frontiers are constructed: the optimistic and the pessimistic ones. We use fuzszy relationships to introduce a new efficiency index based on a set of some Fuzzy T Norms. We will explore only the case where only on single variable presents a certain degree of uncertainty

Setting targets with interval data envelopment analysis models via wang method

Data envelopment analysis (DEA) is a mathematical programming for evaluating the relative efficiency of decision making units (DMUs). The first DEA model (CCR model) assumed for exact data, later some authors introduced the applications of DEA which the data was imprecise. In imprecise data envelopment analysis (IDEA) the data can be ordinal, interval and fuzzy. Data envelopment analysis also can be used for the future programming of organizations and the response of the different policies, which is related to the target setting and resource allocation. The existing target model that conveys performance based targets in line with the policy making scenarios was defined for exact data. In this paper we improved the model for imprecise data such as fuzzy, ordinal and interval data. To deal with imprecise data we first established an interval DEA model. We used one of the methods to convert fuzzy and ordinal data into the interval data. A numerical experiment is used to illustrate the application to our interval model

Confident-DEA: A Unified Approach For Efficiency Analysis With Cardinal, Bounded And Ordinal Data

This paper proposes an extension to the existing literature in DEA, the authors call Confident-DEA approach. The proposed new approach involves a bi-level convex optimization model, and hence NP-hard, to which a solution method is suggested. Confident-DEA constitutes a generalization of DEA for dealing with imprecise data and hence a potential method for forecasting efficiency. Imprecision in data is defined as two forms, one is bounded data and the second is cardinal data. Complementing the methodology proposed by Cooper et al (1999) which provides single valued efficiency measures, Confident-DEA provides a range of values for the efficiency measures, e.g. an efficiency confidence interval, reflecting the imprecision in data. For the case of bounded data, a theorem defining the bounds of the efficiency confidence interval is provided. For the general case of imprecise data, that is a mixture of ordinal and cardinal data, a Genetic-Algorithm-based meta-heuristic is used to determine the upper and lower bounds defining the efficiency confidence interval. To the best knowledge of the authors, this is the first work combining Genetic algorithms with DEA. In both cases of imprecision, a Monte-Carlo type simulation is used to determine the distribution of the efficiency measures, taking into account the distribution of the bounded imprecise data over their corresponding intervals. Most of previous DEA works dealing with imprecise data implicitly assumed a uniform distribution. Confident-DEA, on the other hand, allows for any type of distribution and hence expands the scope of the analysis. The bounded data used in the illustrative examples are assumed to have truncated normal distributions. However, the methodology suggested here allows for any other distribution for the data

Measuring efficiency of a hierarchical organization with fuzzy DEA method

The paper analyses how the data envelopment analysis (DEA) and fuzzy set theory can be used to measure and evaluate the efficiency of a hierarchical system with n decision making units and a coordinating unit. It is presented a model for determining the of activity levels of decision making units so as to achieve both fuzzy objectives of achieving global target levels of coordination unit on the inputs and outputs and individual target levels of decision making units, and then some methods to resolve fuzzy models are proposed.fuzzy DEA, policy making in multi-level organisations, efficiency analysis

Supplier Selection by the Pair of Nondiscretionary Factors-Imprecise Data Envelopment Analysis Models

Discretionary models for evaluating the efficiency of suppliers assume that all criteria are discretionary, that is, controlled by the management of each supplier and varied at its discretion. These models do not assume supplier selection in the conditions that some factors are nondiscretionary. The objective of this paper is to propose a new pair of nondiscretionary factors-imprecise data envelopment analysis (NF-IDEA) models for selecting the best suppliers in the presence of nondiscretionary factors and imprecise data. A numerical example demonstrates the application of the proposed method.Full Tex

Performance analysis of listed companies in the UAE-using DEA Malmquist index approach

Data Envelopment Analysis (DEA) is becoming an increasingly popular tool for assessing the relative performance of industries and companies. By applying DEA theory to the non-financial sector, the relative efficiency of 27 listed corporations in the United Arab Emirates (UAE) has been analyzed in this paper. The focus of the study has been on the impact of the financial crisis and the recovery thereafter. Further, the productivity change was decomposed into technical efficiency change and technological change by using the non-para- metric Malmquist Productivity Index (MPI) over the period from 2007 to 2014. Based on Malmquist analysis, we find that the most efficient industries during the post-crisis period were food and beverages, telecommunication and pharmaceuticals. In contrast, the sectors that were adversely affected by the crisis were services, real estate, construction and cements. The break-up of the TFP indicated that the efficiency indices in the top performing industries were driven by technological improvements or frontier effects. The top-per- forming companies in the UAE during the 2007-14 period demonstrated innovation-led growth, aided by the use of better technology, investments in capital equipment, and adoption of new production processes

Super-efficiency and stability intervals in additive DEA

This is a PDF file of an unedited manuscript that has been accepted for publication in Journal of the Operational Research Society. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. The final version will be available at: http://dx.doi.org/10.1057/jors.2012.1

Pronóstico del intervalo de confianza en la eficiencia de las unidades de toma de decisiones en el análisis envolvente de datos

Data Envelopment Analysis (DEA) is a well-known method for calculating the efficiency of Decision-Making Units (DMUs) based on their inputs and outputs. When the data is known and in the form of an interval in a given time period, this method can calculate the efficiency interval. Unfortunately, DEA is not capable of forecasting and estimating the efficiency confidence interval of the units in the future. This article, proposes a efficiency forecasting algorithm along with 95% confidence interval to generate interval data set for the next time period. What’s more, the manager’s opinion inserts and plays its role in the proposed forecasting model. Equipped with forecasted data set and with respect to data set from previous periods, the efficiency for the future period can be forecasted. This is done by proposing a proposed model and solving it by the confidence interval method. The proposed method is then implemented on the data of an automotive industry and, it is compared with the Monte Carlo simulation methods and the interval model. Using the results, it is shown that the proposed method works better to forecast the efficiency confidence interval. Finally, the efficiency and confidence interval of 95% is calculated for the upcoming period using the proposed model.El análisis envolvente de datos (DEA) es un método bien conocido para calcular la eficiencia de las unidades de toma de decisiones (DMU) en función de sus entradas y salidas. Cuando los datos son conocidos y en forma de intervalo en un período de tiempo dado, este método puede calcular el intervalo de eficiencia. Desafortunadamente, la DEA no es capaz de pronosticar y estimar el intervalo de confianza de eficiencia de las unidades en el futuro. Este artículo propone un algoritmo de pronóstico de eficiencia junto con un intervalo de confianza del 95% para generar un conjunto de datos de intervalo para el próximo período de tiempo. Además, la opinión del gerente se inserta y desempeña su papel en el modelo de pronóstico propuesto. Equipado con un conjunto de datos pronosticado y con respecto al conjunto de datos de períodos anteriores, se puede pronosticar la eficiencia para el período futuro. Esto se hace proponiendo un modelo propuesto y resolviéndolo mediante el método del intervalo de confianza. A continuación, el método propuesto se implementa sobre los datos de una industria automotriz y se compara con los métodos de simulación de Monte Carlo y el modelo de intervalo. Usando los resultados, se muestra que el método propuesto funciona mejor para pronosticar el intervalo de confianza de eficiencia. Finalmente, se calcula la eficiencia y el intervalo de confianza del 95% para el próximo período utilizando el modelo propuesto