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.

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.

scholarly journals A full investigation of the directional congestion in data envelopment analysis

2019 ◽  
Author(s):  
somayeh khezri ◽  
Akram Dehnokhalaji ◽  
Farhad Hosseinzadeh Lotfi
Keyword(s):  
Decision Making ◽  
Data Envelopment Analysis ◽  
Data Envelopment ◽  
Input Output ◽  
Input And Output ◽  
Dea Models ◽  
Systems Of Inequalities ◽  
Full Investigation ◽  
Decision Making Units ◽  
Inputs And Outputs

One of interesting subjects in Data Envelopment Analysis (DEA) is estimation of congestion of Decision Making Units (DMUs). Congestion is evidenced when decreases (increases) in some inputs re- sult in increases (decreases) in some outputs without worsening (im- proving) any other input/output. Most of the existing methods for measuring the congestion of DMUs utilize the traditional de nition of congestion and assume that inputs and outputs change with the same proportion. Therefore, the important question that arises is whether congestion will occur or not if the decision maker (DM) increases or de- creases the inputs dis-proportionally. This means that, the traditional de nition of congestion in DEA may be unable to measure the con- gestion of units with multiple inputs and outputs. This paper focuses on the directional congestion and proposes methods for recognizing the directional congestion using DEA models. To do this, we consider two di erent scenarios: (i) just the input direction is available. (ii) none of the input and output directions are available. For each scenario, we propose a method consists in systems of inequalities or linear pro- gramming problems for estimation of the directional congestion. The validity of the proposed methods are demonstrated utilizing two nu- merical examples.

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 An empirical application of data envelopment analysis in credit rating

2021 ◽  
Author(s):  
Mariya Demirova
Keyword(s):  
Data Envelopment Analysis ◽  
Credit Rating ◽  
Optimization Technique ◽  
Market Price ◽  
Principal Component ◽  
Data Envelopment ◽  
Financial Health ◽  
Stochastic Dea ◽  
Dea Models ◽  
Potential Tool

Data Envelopment Analysis (DEA) is a nonparametric optimization technique that evaluates the relative efficiency of decision-making units and is used in this thesis as an empirical estimator of credit rating. The purpose of this research is to combine different DEA models and technique and obtain the best model that captures different aspects of credit risk. Various models are evaluated by combining four Slack DEA models with Principal Component Analysis (PCA), Absolute Weights Restriction, and Stochastic DEA. We found that Goal Vector Approach Stochastic PCA (SGV+PCA), applied to a sample consisting of five sectors, is the best model. SGV+PCA DEA model obtains a high correlation with Standard & Poor’s (S&P) credit rating and with Market Price; it also classified twelve bankrupted companies within the 17% of the less efficient companies in the sample, suggesting that the model is a good financial health estimator and is a potential tool for credit rating analysis.

Performance measurement in data envelopment analysis without slacks: an application to electricity distribution companies

2018 ◽  
Vol 52 (4-5) ◽  
pp. 1069-1085
Author(s):  
Azam Pourhabib ◽  
Sohrab Kordrostami ◽  
Alireza Amirteimoori ◽  
Reza Kazemi Matin
Keyword(s):  
Data Envelopment Analysis ◽  
Performance Measurement ◽  
Reference Points ◽  
Data Envelopment ◽  
Efficiency Evaluation ◽  
Electricity Distribution ◽  
Input Output ◽  
Target Setting ◽  
Dea Models ◽  
Weights Restrictions

In performance measurement of the firms using tools such as data envelopment analysis (DEA) models, weak efficient units are almost appeared as reference points in the models. To avoid zero weights or equivalently non-zero slacks in DEA assessment, weights restrictions are used frequently. In DEA literature, two-stage procedures are developed to deal with non-zero slacks based on restricting input/output weights in multiplier formulating the CCR DEA model. In this paper, a single-stage approach for efficiency evaluation is developed to ensure zero slacks in target setting and avoid weights dissimilarity. A real case on electricity distribution companies in Iran has been given to demonstrate the applicability of the proposed approach.

A Unified Mathematical Model for Stochastic Data Envelopment Analysis

2021 ◽  
Vol 12 (1) ◽  
pp. 127-141
Author(s):  
Basma E. El-Demerdash ◽  
Assem A. Tharwat ◽  
Ihab A. A. El-Khodary
Keyword(s):  
Data Envelopment Analysis ◽  
Organizational Performance ◽  
Real Life ◽  
Efficiency Measurement ◽  
Data Envelopment ◽  
Stochastic Dea ◽  
Chance Constrained Approach ◽  
Dea Efficiency ◽  
Stochastic Data ◽  
And Performance

Efficiency measurement is one aspect of organizational performance that managers are usually interested in determining. Data envelopment analysis (DEA) is a powerful quantitative tool that provides a means to obtain useful information about the efficiency and performance of organizations and all sorts of functionally similar, relatively autonomous operating units. DEA models are either with a constant rate of return (CRS) or variable return to scale (VRS). Furthermore, the models could be input-oriented or output-oriented. In many real-life applications, observations are usually random in nature; as a result, DEA efficiency measurement may be sensitive to such variations. The purpose of this study was to develop a unified stochastic DEA model that handles different natures of variables independently (random and deterministic) and can be adapted to model both input/output-oriented problems, whether it is CRS or VRS. The chance-constrained approach was adopted to handle the stochastic variables that exist in the model. The developed model is implemented through an illustrative example.

scholarly journals An empirical application of data envelopment analysis in credit rating

2021 ◽  
Author(s):  
Mariya Demirova
Keyword(s):  
Data Envelopment Analysis ◽  
Credit Rating ◽  
Optimization Technique ◽  
Market Price ◽  
Principal Component ◽  
Data Envelopment ◽  
Financial Health ◽  
Stochastic Dea ◽  
Dea Models ◽  
Potential Tool

Data Envelopment Analysis (DEA) is a nonparametric optimization technique that evaluates the relative efficiency of decision-making units and is used in this thesis as an empirical estimator of credit rating. The purpose of this research is to combine different DEA models and technique and obtain the best model that captures different aspects of credit risk. Various models are evaluated by combining four Slack DEA models with Principal Component Analysis (PCA), Absolute Weights Restriction, and Stochastic DEA. We found that Goal Vector Approach Stochastic PCA (SGV+PCA), applied to a sample consisting of five sectors, is the best model. SGV+PCA DEA model obtains a high correlation with Standard & Poor’s (S&P) credit rating and with Market Price; it also classified twelve bankrupted companies within the 17% of the less efficient companies in the sample, suggesting that the model is a good financial health estimator and is a potential tool for credit rating analysis.

Measuring Performance of a Three-Stage Network Structure Using Data Envelopment Analysis and Nash Bargaining Game: A Supply Chain Application

2018 ◽  
Vol 17 (05) ◽  
pp. 1429-1467 ◽  
Author(s):  
Mohammad Amirkhan ◽  
Hosein Didehkhani ◽  
Kaveh Khalili-Damghani ◽  
Ashkan Hafezalkotob
Keyword(s):  
Supply Chain ◽  
Data Envelopment Analysis ◽  
Nash Bargaining ◽  
Data Envelopment ◽  
Second Stage ◽  
Proposed Model ◽  
Nash Bargaining Game ◽  
Dea Models ◽  
Overall Efficiency

The issue of efficiency analysis of network and multi-stage systems, as one of the most interesting fields in data envelopment analysis (DEA), has attracted much attention in recent years. A pure serial three-stage (PSTS) process is a specific kind of network in which all the outputs of the first stage are used as the only inputs in the second stage and in addition, all the outputs of the second stage are applied as the only inputs in the third stage. In this paper, a new three-stage DEA model is developed using the concept of three-player Nash bargaining game for PSTS processes. In this model, all of the stages cooperate together to improve the overall efficiency of main decision-making unit (DMU). In contrast to the centralized DEA models, the proposed model of this study provides a unique and fair decomposition of the overall efficiency among all three stages and eliminates probable confusion of centralized models for decomposing the overall efficiency score. Some theoretical aspects of proposed model, including convexity and compactness of feasible region, are discussed. Since the proposed bargaining model is a nonlinear mathematical programming, a heuristic linearization approach is also provided. A numerical example and a real-life case study in supply chain are provided to check the efficacy and applicability of the proposed model. The results of proposed model on both numerical example and real case study are compared with those of existing centralized DEA models in the literature. The comparison reveals the efficacy and suitability of proposed model while the pitfalls of centralized DEA model are also resolved. A comprehensive sensitivity analysis is also conducted on the breakdown point associated with each stage.

scholarly journals Large discreet resource allocation: a hybrid approach based on dea efficiency measurement

2008 ◽  
Vol 28 (3) ◽  
pp. 597-608 ◽  
Author(s):  
Eliane Gonçalves Gomes ◽  
João Carlos Correia Baptista Soares de Mello ◽  
Lidia Angulo Meza
Keyword(s):  
Resource Allocation ◽  
Hybrid Approach ◽  
Data Envelopment ◽  
Efficiency Measures ◽  
Starting Point ◽  
Computational Work ◽  
Research Problems ◽  
Dea Models ◽  
Dea Efficiency ◽  
Zero Sum

Resource allocation is one of the traditional Operations Research problems. In this paper we propose a hybrid model for resource allocation that uses Data Envelopment Analysis efficiency measures. We use Zero Sum Gains DEA models as the starting point to decrease the computational work for the step-bystep algorithm to allocate integer resources in a DEA context. Our approach is illustrated by a numerical example.

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