Stochastic DEA Models: Estimating Production Frontiers with Composed Error Models

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.

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

International Journal of Information Technology & Decision Making ◽

10.1142/s0219622018500396 ◽

2019 ◽

Vol 18 (01) ◽

pp. 147-170 ◽

Cited By ~ 4

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.

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Fuzzy stochastic Data Envelopment Analysis with application to NATO enlargement problem

RAIRO - Operations Research ◽

10.1051/ro/2018075 ◽

2019 ◽

Vol 53 (2) ◽

pp. 705-721 ◽

Cited By ~ 4

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.

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Transformations in stochastic DEA models

Journal of Econometrics ◽

10.1016/0304-4076(90)90050-4 ◽

1990 ◽

Vol 46 (1-2) ◽

pp. 109-123 ◽

Cited By ~ 39

Author(s):

Jati K. Sengupta

Keyword(s):

Stochastic Dea ◽

Dea Models

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Randomizing DEA Efficiency Scores with Beta Distribution

Encyclopedia of Business Analytics and Optimization ◽

10.4018/978-1-4666-5202-6.ch178 ◽

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.

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Dynamic performance assessment of a supply chain process

Business Process Management Journal ◽

10.1108/bpmj-09-2014-0086 ◽

2015 ◽

Vol 21 (4) ◽

pp. 743-770 ◽

Cited By ~ 9

Author(s):

Anup Kumar ◽

Kampan Mukherjee ◽

Amit Adlakha

Keyword(s):

Decision Making ◽

Supply Chain ◽

Dynamic Environment ◽

Chain Process ◽

Content Type ◽

Supply Chain Efficiency ◽

Stochastic Dea ◽

Wide Range ◽

Dea Models ◽

Lagged Effects

Purpose – A variety of tools are available to measure supply chain efficiency, but there are a few methods available for assessing efficiency in dynamic environments. The purpose of this paper is to illustrate the use of data envelopment analysis (DEA) with the help vector auto regression in measuring internal supply chain performance in dynamic environment. Design/methodology/approach – Two DEA models were developed – the static DEA that is traditional DEA methodology and the dynamic DEA. The models are further enhanced with scenario analysis to derive more meaningful business insights for managers in making benchmarking and resource planning decisions. Findings – The results demonstrate that lagged effects can lead to changes in efficiency scores, rankings, and efficiency classification. So, using static DEA models in dynamic environment can be potentially misleading. Using impulse response analysis it has been seen that shocks given to marketing strategy in MR affects more at each of the decision-making unit’s (DMU’s) compared to other variables, further the authors could also investigate the dependent variables (output) shocks to input variables. Social implications – Methodology can be applied to a wide range of evaluation problems in place of conventional DEA models. Results show that lagged effects can lead to substantial discrepancies in evaluation results. Biased evaluation results would easily lead to erroneous decision and policy making for the firm. Therefore the authors should always take a broader perspective in evaluating longitudinal performance by incorporating the effects into evaluation and decision-making processes. Future work of this study could look into the possibility of modeling in a stochastic supply chain environment. In addition, it will also be interesting to look into evaluating the stochastic DEA model in multiple time periods in order to examine whether there is any technological influence on the supply chain efficiency. Originality/value – The contribution of this study provides useful insights into the use of DDEA as a modeling tool to aid managerial decision making in assessing supply chain efficiency in dynamic environment.

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A comparison between stochastic DEA and fuzzy DEA approaches: revisiting efficiency in Angolan banks

RAIRO - Operations Research ◽

10.1051/ro/2016065 ◽

2018 ◽

Vol 52 (1) ◽

pp. 285-303 ◽

Cited By ~ 6

Author(s):

P. Wanke ◽

C.P. Barros ◽

A. Emrouznejad

Keyword(s):

Performance Analysis ◽

Management Practices ◽

Banking Industry ◽

Vital Part ◽

Stochastic Dea ◽

Dea Models ◽

Managerial Implications ◽

Fuzzy Dea ◽

Inputs And Outputs

Performance analysis has become a vital part of the management practices in the banking industry. There are numerous applications using DEA models to estimate efficiency in banking, and most of them assume that inputs and outputs are known with absolute precision. Here, we compare Stochastic-DEA and Fuzzy-DEA models to assess, respectively, how the underlying randomness and fuzziness impact efficiency levels. The proposed models have been demonstrated using an application in Angolan banks. Findings reveal that conclusions with respect to the ranking of DMUs may vary substantially depending upon the type of the model chosen, although efficiency scores are similar to some extent when compared within the ambits of Stochastic-DEA and Fuzzy-DEA models. Additionally, modeling choices on fuzziness, rather than on randomness, appears to be the most critical source for variations in efficiency rankings. Managerial implications for Angolan banks are also explored.

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An empirical application of data envelopment analysis in credit rating

10.32920/ryerson.14660505.v1 ◽

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.

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An empirical application of data envelopment analysis in credit rating

10.32920/ryerson.14660505 ◽

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.

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Efficiency analysis of dairy farms in the Northern Great Plain region using deterministic and stochastic DEA models

Applied Studies in Agribusiness and Commerce ◽

10.19041/apstract/2012/5/19 ◽

2012 ◽

Vol 6 (5) ◽

pp. 113-122

Author(s):

Tímea Gál

Keyword(s):

Animal Health ◽

Dairy Farms ◽

Great Plain ◽

Northern Great Plain ◽

Stochastic Dea ◽

Plain Region ◽

Health Products ◽

Dea Models ◽

Cattle Breeders ◽

Inputs And Outputs

Running any dairy enterprise is a risky activity: the profitability of the enterprise is affected by the price fluctuation of feed and animal health products from inputs, as well as by the fluctuation of end-product prices. Under these circumstances, it is essential for the cattle breeders, in order to survive, to harness the reserves in management as effectively as possible. In this research the efficiency and risk of 32 sample dairy farms were analysed in the Northern Great Plain Region from the Farm Accountancy Data Network (FADN) by applying classical Data Envelopment Analysis (DEA) and stochastic DEA models. The choice of this method is justified by the fact that there was not such an available reliable database by which production functions could have been defined, and DEA makes possible to manage simultaneously some inputs and outputs, i.e. complex decision problems. By using DEA, the sources that cause shortfall on inefficient farms can be identified, analysed and quantified, so corporate decision support can be reinforced successfully. A disadvantage of the classical DEA model is that the stochastic factors of farming cannot be treated either on the side of inputs or outputs; therefore, their results can be adopted with reservations, especially in agricultural models. This may have been because we could not discover that many agricultural applications. Considering the price of inputs and outputs as probability variables, 5000 simulation runs have been done in this research. As a result, it can be stated that at which intervals of the input and output factors can become competitive and the fluctuation of these factors can cause what level of risk at each farm.

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