Fuzzy interpretation of efficiency in data envelopment analysis and its application in a non-discretionary model

Data envelopment analysis (DEA) is a nonparametric model which evaluates the relative efficiencies of decision-making units (DMUs).These DMUs produce multiple outputs by using multiple inputs and the relative efficiency is evaluated using a ratio of total weighted output to total weighted input.In this paper an alternative interpretation of efficiency is first given. The interpretation is based on the fuzzy concept even though the inputs and outputs data are crisp numbers.With the interpretation, a new model for ranking DMUs in DEA is proposed and a new perspective of viewing other DEA models is now made possible.The model is then extended to incorporate situations whereby some inputs or outputs, in a fuzzy sense, are almost discretionary variables

Efficiency in the worst production situation using data envelopment analysis

Data envelopment analysis (DEA) measures relative efficiency among the decision making units (DMU) without considering noise in data.The least efficient DMU indicates that it is in the worst situation.In this paper, we measure efficiency of individual DMU whenever it losses the maximum output, and the efficiency of other DMUs is measured in the observed situation.This efficiency is the minimum efficiency of a DMU.The concept of stochastic data envelopment analysis (SDEA) is a DEA method which considers the noise in data which is proposed in this study.Using bounded Pareto distribution, we estimate the DEA efficiency from efficiency interval. Small value of shape parameter can estimate the efficiency more accurately using the Pareto distribution.Rank correlations were estimated between observed efficiencies and minimum efficiency as well as between observed and estimated efficiency.The correlations are indicating the effectiveness of this SDEA model

Inexact discretionary inputs in data envelopment analysis

In this chapter, the relationship between fuzzy concepts and the efficiency score in Data envelopment analysis (DEA) is dealt with.A new DEA model for handling crisp data using fuzzy concept is proposed.In addition, the relationship between possibility sets and the efficiency score in the traditional crisp CCR model is presented.The relationship provides an alternative perspective of viewing efficiency.With the usage of the appropriate fuzzy and possibility sets to represent certain characteristics of the input data, many DEA models involving input data with various characteristics could be studied.Furthermore, based upon the proposed models, two nondiscretionary models are introduced in which some inputs or outputs, in a fuzzy sense, are inexact discretionary variables.For this purpose, a two-stage algorithm will be presented to treat the DEA model in the presence of an inexact discretionary variable.With this relationship, a new perspective of viewing and exploring other DEA models is now made possible

Analyzing the solutions of DEA through information visualization and data mining techniques: SmartDEA framework

Data envelopment analysis (DEA) has proven to be a useful tool for assessing efficiency or productivity of organizations, which is of vital practical importance in managerial decision making. DEA provides a significant amount of information from which analysts and managers derive insights and guidelines to promote their existing performances. Regarding to this fact, effective and methodologic analysis and interpretation of DEA solutions are very critical. The main objective of this study is then to develop a general decision support system (DSS) framework to analyze the solutions of basic DEA models. The paper formally shows how the solutions of DEA models should be structured so that these solutions can be examined and interpreted by analysts through information visualization and data mining techniques effectively. An innovative and convenient DEA solver, SmartDEA, is designed and developed in accordance with the proposed analysis framework. The developed software provides a DEA solution which is consistent with the framework and is ready-to-analyze with data mining tools, through a table-based structure. The developed framework is tested and applied in a real world project for benchmarking the vendors of a leading Turkish automotive company. The results show the effectiveness and the efficacy of the proposed framework

The role of multiplier bounds in fuzzy data envelopment analysis

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.The non-Archimedean epsilon ε is commonly considered as a lower bound for the dual input weights and output weights in multiplier data envelopment analysis (DEA) models. The amount of ε can be effectively used to differentiate between strongly and weakly efficient decision making units (DMUs). The problem of weak dominance particularly occurs when the reference set is fully or partially defined in terms of fuzzy numbers. In this paper, we propose a new four-step fuzzy DEA method to re-shape weakly efficient frontiers along with revisiting the efficiency score of DMUs in terms of perturbing the weakly efficient frontier. This approach eliminates the non-zero slacks in fuzzy DEA while keeping the strongly efficient frontiers unaltered. In comparing our proposed algorithm to an existing method in the recent literature we show three important flaws in their approach that our method addresses. Finally, we present a numerical example in banking with a combination of crisp and fuzzy data to illustrate the efficacy and advantages of the proposed approach

Carbon efficiency evaluation:an analytical framework using fuzzy DEA

Data Envelopment Analysis (DEA) is a powerful analytical technique for measuring the relative efficiency of alternatives based on their inputs and outputs. The alternatives can be in the form of countries who attempt to enhance their productivity and environmental efficiencies concurrently. However, when desirable outputs such as productivity increases, undesirable outputs increase as well (e.g. carbon emissions), thus making the performance evaluation questionable. In addition, traditional environmental efficiency has been typically measured by crisp input and output (desirable and undesirable). However, the input and output data, such as CO2 emissions, in real-world evaluation problems are often imprecise or ambiguous. This paper proposes a DEA-based framework where the input and output data are characterized by symmetrical and asymmetrical fuzzy numbers. The proposed method allows the environmental evaluation to be assessed at different levels of certainty. The validity of the proposed model has been tested and its usefulness is illustrated using two numerical examples. An application of energy efficiency among 23 European Union (EU) member countries is further presented to show the applicability and efficacy of the proposed approach under asymmetric fuzzy numbers

Stakeholder perception on corporate reputation and management efficiency : Evidence from the Spanish Defence sector

The Spanish Ministry of Defence was the first to elaborate a Social Responsibility (SR) report stating that efficiency plays a leading role. The territorial organs to manage the image and trust in the armed forces, are given by the Spanish Defence Delegations (SDD), and all of them are certified with a seal of excellence. In this work, defence economics and analysis of efficiency line up with the concept of SR. The main aim is to analyse if SR policy has an effective influence and, as a consequence, a high degree of performance can be expected. To this end, given a set of discretionary variables, the efficiency of the 19 SDD during the 2015-2017 period is analysed by means of Data Envelopment Analysis technique. A bootstrap procedure is used to eliminate the bias of the estimates and obtain a robust ranking. The results show an unusual positive behavior in public sector

Application of Multi-Criteria Decision Making (MCDM) Approached on Teachers' Performance Evaluation and Appraisal

Education quality is the ultimate result of significant contribution by each stake holder in an education system. However, it is believed that faculty quality has direct bearing on improving and sustaining quality in education. Teacher’s performance evaluation is nothing but a Multi Criteria Decision Making Problem (MCDM). There are several quality attributes that influence the efficiency of a potential teacher while guiding his/her students towards a positive and value added academic outcome. However, the extent of significance of quality attributes may vary from individuals’ viewpoint. In other words, different attributes may have different weightage according to their priority of significance while evaluating quality/performance level of a teacher. But there is no clear-cut methodology for assigning this priority weightage for the attributes. Therefore, expert opinion is indeed required to estimate those attribute weightage values. In the present reporting, a methodology adapted from Multi-Criteria-Decision Making (MCDM) has been proposed in order to evaluate performance of a teacher. Grey relational analysis has been explored in order to prioritize quality attributes that are expected to influence performance level of a teacher. Based on COPRAS- method, numerical values (interval scores) on different attributes assigned for a group of teachers (multiplied by individual weightage) have been accumulated to compute an overall quality estimate indicating performance level of individual teachers. Application feasibility as well as efficiency of this method and guidelines in solving such a multi-attribute decision making problem has been described illustratively in this paper

Interval and fuzzy optimization. Applications to data envelopment analysis

Enhancing concern in the efficiency assessment of a set of peer entities termed Decision Making Units (DMUs) in many fields from industry to healthcare has led to the development of efficiency assessment models and tools. Data Envelopment Analysis (DEA) is one of the most important methodologies to measure efficiency assessment through the comparison of a group of DMUs. It permits the use of multiple inputs/outputs without any functional form. It is vastly applied to production theory in Economics and benchmarking in Operations Research. In conventional DEA models, the observed inputs and outputs possess precise and realvalued data. However, in the real world, some problems consider imprecise and integer data. For example, the number of defect-free lamps, the fleet size, the number of hospital beds or the number of staff can be represented in some cases as imprecise and integer data. This thesis considers several novel approaches for measuring the efficiency assessment of DMUs where the inputs and outputs are interval and fuzzy data. First, an axiomatic derivation of the fuzzy production possibility set is presented and a fuzzy enhanced Russell graph measure is formulated using a fuzzy arithmetic approach. The proposed approach uses polygonal fuzzy sets and LU-fuzzy partial orders and provides crisp efficiency measures (and associated efficiency ranking) as well as fuzzy efficient targets. The second approach is a new integer interval DEA, with the extension of the corresponding arithmetic and LU-partial orders to integer intervals. Also, a new fuzzy integer DEA approach for efficiency assessment is presented. The proposed approach considers a hybrid scenario involving trapezoidal fuzzy integer numbers and trapezoidal fuzzy numbers. Fuzzy integer arithmetic and partial orders are introduced. Then, using appropriate axioms, a fuzzy integer DEA technology can be derived. Finally, an inverse DEA based on the non-radial slacks-based model in the presence of uncertainty, employing both integer and continuous interval data is presented

DEA target setting using lexicographic and endogenous directional distance function approaches

Belarmino Adenso Díaz Fernández es el investigador principal del proyecto "Análisis y diseño de redes logísticas eficientes, robustas y sostenibles