Randomizing Efficiency Scores in DEA Using Beta Distribution

2014 ◽  
Vol 1 (4) ◽  
pp. 1-15
Author(s):  
Parakramaweera Sunil Dharmapala
Keyword(s):  
Beta Distribution ◽  
Data Envelopment ◽  
Imprecise Data ◽  
Output Data ◽  
Uniform Sampling ◽  
The Past ◽  
Stochastic Dea ◽  
Dea Models ◽  
Assurance Regions ◽  
Fuzzy Dea

Data Envelopment Analysis (DEA) has come under criticism that it is capable of handling only the deterministic input/output data, and therefore, efficiency scores reported by DEA may not be realistic when the data contain random error. Several researchers in the past have addressed this issue by proposing Stochastic DEA models. Some others, citing imprecise data, have proposed Fuzzy DEA models. This paper proposes a method to randomize efficiency scores in DEA by treating each score as an ‘order statistic' that follows a Beta distribution, and it uses Thompson et al.'s (1996) DEA model appended with Assurance Regions (AR) randomized by our “uniform sampling”. In an application to a set of banks, the work demonstrates the randomization and derives some statistical results.

Randomizing DEA Efficiency Scores with Beta Distribution

2014 ◽  
pp. 1977-1985
Author(s):  
P. Sunil Dharmapala
Keyword(s):  
Data Envelopment Analysis ◽  
Order Statistic ◽  
Beta Distribution ◽  
Data Envelopment ◽  
Random Errors ◽  
Input Output ◽  
Stochastic Dea ◽  
Dea Models ◽  
Dea Efficiency ◽  
Statistical Results

A criticism leveled against Data Envelopment Analysis (DEA) is that it is incapable of handling input/output data contaminated with random errors, and therefore, efficiency scores reported by DEA do not reflect reality. Several researchers have addressed this issue by incorporating statistical noise into DEA modeling, thus giving birth to Stochastic DEA. In this chapter, utilizing well known DEA models, we propose a method to randomize efficiency scores by treating each score as an order statistic of an underlying Beta distribution. In an application to a set of banks, we demonstrate how to do this randomization and derive some statistical results.

A New Method for Solving Dual DEA Problems with Fuzzy Stochastic Data

2019 ◽  
Vol 18 (01) ◽  
pp. 147-170 ◽  
Author(s):  
Ali Ebrahimnejad ◽  
Madjid Tavana ◽  
Seyed Hadi Nasseri ◽  
Omid Gholami
Keyword(s):  
Real Life ◽  
Equivalent Model ◽  
Random Input ◽  
Output Data ◽  
Programming Technique ◽  
Dea Model ◽  
Deterministic Equivalent ◽  
Input And Output ◽  
Stochastic Dea ◽  
Dea Models

Data envelopment analysis (DEA) is a widely used mathematical programming technique for measuring the relative efficiency of decision-making units which consume multiple inputs to produce multiple outputs. Although precise input and output data are fundamentally used in classical DEA models, real-life problems often involve uncertainties characterized by fuzzy and/or random input and output data. We present a new input-oriented dual DEA model with fuzzy and random input and output data and propose a deterministic equivalent model with linear constraints to solve the model. The main contributions of this paper are fourfold: (1) we extend the concept of a normal distribution for fuzzy stochastic variables and propose a DEA model for problems characterized by fuzzy stochastic variables; (2) we transform the proposed DEA model with fuzzy stochastic variables into a deterministic equivalent linear form; (3) the proposed model which is linear and always feasible can overcome the nonlinearity and infeasibility in the existing fuzzy stochastic DEA models; (4) we present a case study in the banking industry to exhibit the applicability of the proposed method and feasibility of the obtained solutions.

scholarly journals Forecasting the Confidence Interval of Efficiency in Fuzzy DEA

2021 ◽  
Vol 31 (1) ◽  
Author(s):  
Azarnoosh Kafi ◽  
Behrouz Daneshian ◽  
Mohsen Rostamy-Malkhalifeh
Keyword(s):  
Confidence Interval ◽  
Geometric Mean ◽  
Decision Makers ◽  
Data Sets ◽  
Data Envelopment ◽  
Future Time ◽  
Dea Models ◽  
Time Periods ◽  
Fuzzy Dea ◽  
Decision Making Units

Data Envelopment Analysis (DEA) is a well-known method that based on inputs and outputs calculates the efficiency of decision-making units (DMUs). Comparing the efficiency and ranking of DMUs in different time periods lets the decision makers to prevent any loss in the productivity of units and improve the production planning. Despite the merits of DEA models, they are not able to forecast the efficiency of future time periods with known input/output records of the DMUs. With this end in view, this study aims at proposing a forecasting algorithm with a 95% confidence interval to generate fuzzy data sets for future time periods. Moreover, managers’ opinions are inserted in the proposed forecasting model. Equipped with the forecasted data sets and with respect to the data sets from previous periods, this model can rightly forecast the efficiency of the future time periods. The proposed procedure also employs the simple geometric mean to discriminate between efficient units. Examples from a real case including 20 automobile firms show the applicability of the proposed algorithm.

scholarly journals Modified Fuzzy Data Envelopment Analysis Models

2020 ◽  
Vol 3 (3b) ◽  
pp. 208-221
Author(s):  
IJ DIKE
Keyword(s):  
Data Envelopment Analysis ◽  
Lower Bound ◽  
Uncertain Data ◽  
Interval Data ◽  
Data Envelopment ◽  
Or Efficiency ◽  
Input And Output ◽  
Dea Models ◽  
Relative Productivity ◽  
Fuzzy Dea

This paper examines the use of data envelopment analysis (DEA) in the conduct of efficiency measurement involving fuzzy (interval) input-output values. Data envelopment analysis is a linear programming method for comparing the relative productivity (or efficiency) of multiple service units. Standard DEA models assume crisp data for both the input and output values. In practice however, input and output values may be uncertain, vague, imprecise or incomplete. A new pair of fuzzy DEA models is presented which differs from existing fuzzy DEA models handling uncertain data. In this approach, upper bound interval data are used exclusively to obtain the upper frontier values while lower bound interval data are used exclusively to obtain the lower frontier values. The outcome, when compared with the outcome of existing approach, based on the same set of data, shows a swap in the upper and lower frontier values with exactly the same number of efficient decision making units (DMUs). This new approach therefore clears the ambiguity occasioned by the mixture of upper and lower bound values in the determination of the upper and lower frontier efficiency scores respectively.

scholarly journals A FUZZY DATA ENVELOPMENT ANALYSIS FOR CLUSTERING OPERATING UNITS WITH IMPRECISE DATA

2013 ◽  
Vol 21 (01) ◽  
pp. 29-54 ◽  
Author(s):  
SABER SAATI ◽  
ADEL HATAMI-MARBINI ◽  
MADJID TAVANA ◽  
PER J. AGRELL
Keyword(s):  
Data Envelopment Analysis ◽  
Parametric Method ◽  
Data Envelopment ◽  
Output Data ◽  
Fuzzy Environment ◽  
Input And Output ◽  
Fuzzy Data Envelopment Analysis ◽  
Human Decision ◽  
Fuzzy Dea ◽  
Operating Units

Data envelopment analysis (DEA) is a non-parametric method for measuring the efficiency of peer operating units that employ multiple inputs to produce multiple outputs. Several DEA methods have been proposed for clustering operating units. However, to the best of our knowledge, the existing methods in the literature do not simultaneously consider the priority between the clusters (classes) and the priority between the operating units in each cluster. Moreover, while crisp input and output data are indispensable in traditional DEA, real-world production processes may involve imprecise or ambiguous input and output data. Fuzzy set theory has been widely used to formalize and represent the impreciseness and ambiguity inherent in human decision-making. In this paper, we propose a new fuzzy DEA method for clustering operating units in a fuzzy environment by considering the priority between the clusters and the priority between the operating units in each cluster simultaneously. A numerical example and a case study for the Jet Ski purchasing decision by the Florida Border Patrol are presented to illustrate the efficacy and the applicability of the proposed method.

IMPRECISE DEA — ENVELOPMENT AND MULTIPLIER MODEL APPROACHES

2007 ◽  
Vol 24 (02) ◽  
pp. 279-291 ◽  
Author(s):  
YAO CHEN
Keyword(s):  
Ordinal Data ◽  
Linear Program ◽  
Data Envelopment ◽  
Imprecise Data ◽  
Dea Model ◽  
Exact Data ◽  
Dea Models ◽  
Standard Linear ◽  
Bounded Data ◽  
Scale Transformations

When multiple outputs and multiple inputs are imprecise data such as bounded data, ordinal data or ratio bound data, the standard linear data envelopment analysis (DEA) model becomes a nonlinear and is called imprecise DEA (IDEA) which can either be converted into a linear program by scale transformations and variable alternations, or solved using the standard DEA model by converting imprecise data into a set of exact data. The current paper investigates the working mechanism of IDEA and shows alternative ways to convert ordinal data into a set of exact data. It is shown that (i) the original IDEA — multiplier IDEA (MIDEA) which is developed from the multiplier DEA model presents the best efficiency scenario, and (ii) the primal IDEA (PIDEA) which is developed from the primal DEA model presents the worst efficiency scenario. The nonlinear PIDEA can also be easily executed by the standard linear DEA models based upon a set of derived exact data whereas it cannot be converted into a linear program via scale transformations and variable alternations.

Fuzzy stochastic Data Envelopment Analysis with application to NATO enlargement problem

2019 ◽  
Vol 53 (2) ◽  
pp. 705-721 ◽  
Author(s):  
Ali Ebrahimnejad ◽  
Seyed Hadi Nasseri ◽  
Omid Gholami
Keyword(s):  
Data Envelopment Analysis ◽  
Data Envelopment ◽  
Threshold Values ◽  
Discrimination Power ◽  
Dea Model ◽  
Nato Enlargement ◽  
Proposed Model ◽  
Stochastic Dea ◽  
Dea Models ◽  
Stochastic Data

Data Envelopment Analysis (DEA) is a widely used technique for measuring the relative efficiencies of Decision Making Units (DMUs) with multiple deterministic inputs and multiple outputs. However, in real-world problems, the observed values of the input and output data are often vague or random. Indeed, Decision Makers (DMs) may encounter a hybrid uncertain environment where fuzziness and randomness coexist in a problem. Hence, we formulate a new DEA model to deal with fuzzy stochastic DEA models. The contributions of the present study are fivefold: (1) We formulate a deterministic linear model according to the probability–possibility approach for solving input-oriented fuzzy stochastic DEA model, (2) In contrast to the existing approach, which is infeasible for some threshold values; the proposed approach is feasible for all threshold values, (3) We apply the cross-efficiency technique to increase the discrimination power of the proposed fuzzy stochastic DEA model and to rank the efficient DMUs, (4) We solve two numerical examples to illustrate the proposed approach and to describe the effects of threshold values on the efficiency results, and (5) We present a pilot study for the NATO enlargement problem to demonstrate the applicability of the proposed model.

scholarly journals Fuzzy Data envelopment Analysis with SBM using α-level Fuzzy Approach

2019 ◽  
pp. 481-501
Author(s):  
Qaiser Farooq Dar ◽  
Ahn Young Hyo ◽  
Gulbadian Farooq Dar ◽  
Shariq Ahmad Bhat ◽  
Arif Muhammad Tali ◽  
...  
Keyword(s):  
Data Envelopment Analysis ◽  
Data Envelopment ◽  
Fuzzy Data ◽  
Fuzzy Approach ◽  
Discrimination Power ◽  
Sbm Model ◽  
Fuzzy Data Envelopment Analysis ◽  
Dea Models ◽  
Α Level ◽  
Fuzzy Dea

The applications of fuzzy analysis in data-oriented techniques are the challenging aspect in the field of applied operational research. The use of fuzzy set theoretic measure is explored here in the context of data envelopment analysis (DEA) where we are utilizing the fuzzy α-level approach in the three types of efficiency models. Namely, BCC models, SBM model and supper efficiency model in DEA. It was observed from the result that the fuzzy SBM model has good discrimination power over fuzzy BCC. On the other side, both the models fuzzy BCC and fuzzy SBM are not able to make the genuine ranking which is acceptable for all. So this weakness is overcome with the help of fuzzy super SBM model and all three models are applied to illustrate the types of decisions and solutions that are achievable when the data are vague and prior information is in imprecise. In this paper, we are considering that our inputs and outputs are not known with absolute precision in DEA and here, we using Fuzzy-DEA models based on an α-level fuzzy approach to assessing fuzzy data.

Generalized Fuzzy Sample DEA Model and its Application in the Evaluation of Projects

2011 ◽  
Vol 63-64 ◽  
pp. 407-411
Author(s):  
Ren Mu ◽  
Zhan Xin Ma ◽  
Wei Cui ◽  
Yun Morigen Wu
Keyword(s):  
Decision Making ◽  
Data Envelopment Analysis ◽  
Data Envelopment Analysis Model ◽  
Data Envelopment ◽  
Input Output ◽  
Output Data ◽  
Dea Model ◽  
Decision Making Unit ◽  
Fuzzy Input ◽  
Fuzzy Dea

Evaluating the performance of activities or organizations by traditional data envelopment analysis model requires crisp input/output data. However, in real-world problems inputs and outputs are often with some fuzziness. To evaluate DMU with fuzzy input/output data, researchers provided fuzzy data envelopment analysis (FDEA) model and proposed related evaluating method. But up to now, we still cannot evaluate a fuzzy sample decision making unit (SDMU) for FDEA model. So this paper proposes a generalized fuzzy DEA model which can evaluate a sample decision making unit and a numerical experiment is used to illustrate this model.

Double Frontier Two-Stage Fuzzy Data Envelopment Analysis

2020 ◽  
Vol 28 (01) ◽  
pp. 117-152 ◽  
Author(s):  
Alireza Amirteimoori ◽  
Hossein Azizi ◽  
Sohrab Kordrostami
Keyword(s):  
Decision Making ◽  
Data Envelopment Analysis ◽  
Efficiency Analysis ◽  
Programming Approach ◽  
Data Envelopment ◽  
Fuzzy Data ◽  
Insurance Company ◽  
Two Stage ◽  
Dea Models ◽  
Fuzzy Dea

Data envelopment analysis (DEA) is a mathematical programming approach with widespread applications in productivity and efficiency analysis. Compared with traditional DEA models, two-stage DEA models show the performance of each process and make available more information for decision making. In an article by Kao and Liu, models were proposed for combining a two-stage process to achieve overall fuzzy efficiency measures. Their method follows the simple geometric average approach and uses the product of two efficiencies. The present article applies a different angle for efficiency analysis in the two-stage fuzzy DEA. We suggest that the overall efficiency score of a decision-making unit (DMU) is defined as total weight of stage efficiencies, not as the simple product of their efficiency. Moreover, the proposed fuzzy DEA models are different from the model by Kao and Liu for fuzzy data in that our models are linear without the need for additional changes in variables and use the same set of constraints to measure the efficiency of DMUs with fuzzy input and output data. While the models by Kao and Liu are a nonlinear optimization problem that need additional changes in variables, and use different sets of constraints to measure fuzzy efficiencies. Additionally, our proposed approach evaluates the performance of DMUs from both optimistic and pessimistic viewpoints. Finally, using the proposed approach, the Taiwanese non-life insurance company problem will be investigated.

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