Robust Data Envelopment Analysis Model Research Articles

Evaluation of bank efficiency by considering the uncertainty of nonperforming loans

Research of banking operations has recently attracted increasing interest among bank managers and scholars, especially research on the evaluation of bank efficiency. As a prominent factor, nonperforming loans are always considered when measuring bank efficiency. Actually, the complex structures and uncertainty of non-performing loans have been neglected in previous studies. In our study, a new robust two-stage DEA (data envelopment analysis) model is proposed to analyze bank efficiency while considering the structure and uncertainty of nonperforming loans. The proposed model was utilized to assess Chinese commercial banks’ performance. Results indicated traditional model may overestimate banks’ performances, which will mislead bank decision-makers seeking to implement improvement strategies. Moreover, the majority of banks performed better in producing deposits compared with earning profits. Lastly, gaps between small medium banks and state-owned banks are still larger when considering the structure and uncertainty of nonperforming loans. Specific recommendations are proposed for each type of bank.

Constructing a robust data envelopment analysis model to evaluate the profitability efficiency of banks with financial loss

ABSTRACT This paper introduces a robust data envelopment analysis (DEA) model to address the limitations of traditional models in handling nonpositive data and applies it to measure the profitability efficiency of banks, including those facing financial losses. The proposed model offers several advantages over current approaches. The model is designed to resist the influence of extreme values and effectively handle variables with positive values for some banks and nonpositive values for others, can be applied under various returns-to-scale conditions and does not require any prior knowledge, overcomes the lack of translation invariance, considers nonradial input or output slack, and uses benchmark targets with economic interpretation. Numerical examples are provided to illustrate its effectiveness, and the results are compared with those obtained from commonly used methods, highlighting its superior performance in handling nonpositive data. Finally, the proposed method is applied to measure the profitability efficiency of commercial banks, demonstrating its practicality in real-world scenarios.

Robust data envelopment analysis with variable budgeted uncertainty

Including uncertainty in data envelopment analysis (DEA) is vital to achieving stable and reliable performance evaluations for the field of operational research as business environments are becoming increasingly volatile and unpredictable. Robust DEA models with budgeted uncertainty have been drawing particular attention in the DEA literature for modelling uncertainties, aiming to obtain robust efficiency scores in a way that guarantees the feasibility of solutions. A concern with such robust DEA models – which has been largely ignored in the literature – is that incorporating high uncertainty levels might result in too conservative efficiency measures, possibly reducing the decision support value of such information. To address this concern, this paper tackles uncertainties by employing variable budgeted uncertainty, which is a generalisation of the budgeted uncertainty. We introduce a novel robust DEA model with variable budgeted uncertainty that is less conservative than extant robust DEA models. Furthermore, we suggest a solution for specifying the probabilistic bounds for constraint violations of the uncertain parameters in robust DEA models. A comparison of the introduced robust DEA model with existing robust DEA models based on a numerical example shows an average reduction in the price of robustness by approximately 20%. Finally, the usefulness and applicability of the suggested model are demonstrated by using a large-scale data set in the context of grocery retailing.

A novel robust data envelopment analysis with asymmetric uncertainty and an application to National Basketball Association

While data availability provides adequate support for decision-making, asymmetrically distributed uncertainty remains an inevitable factor in the decision-making process. Robust data envelopment analysis (RDEA) is one of the most popular methods to handle uncertainty in input and output data. However, previous RDEA studies assume that the uncertainty of the data is symmetrically distributed, which is often violated in practical applications, such as in sports and finance. This paper aims to relax that assumption and extend RDEA models to more general scenarios. To this end, this paper proposes a new RDEA method that can capture asymmetrically distributed uncertainties from historical data and can be easily solved. In addition, a comprehensive case study of player efficiency evaluation is conducted to illustrate the merits of the proposed method. The contributions can be concluded as follows. This study introduces a novel approach to considering asymmetrically distributed uncertainty sets in the RDEA domain, which has not been previously explored. The proposed model outperforms existing RDEA models, providing more reliable and complete ranking results. Additionally, we demonstrate a comprehensive data-driven application that showcases how to build uncertainty sets from historical data and utilize our RDEA model for efficiency evaluation. Furthermore, our model's flexibility allows decision-makers to adjust its conservativeness according to their preferences, offering more dependable results. By utilizing our proposed model, decision-makers can make better-informed decisions while also receiving guidance on how to enhance the reliability of their results.

A generalized robust data envelopment analysis model based on directional distance function

In the literature of data envelopment analysis, the directional distance function (DDF) model is commonly used to measure efficiency improvement, as it allows the decision-maker to choose an appropriate direction that permits input contraction and output expansion. However, choosing the right direction is challenging in empirical research. Additionally, efficiency measurement becomes problematic when input and output data are uncertain. To address these issues, we present an equivalent DDF model in multiplier form and use the robust optimization approach to construct a technology in order to develop a generalized robust-DDF measure of efficiency. Among the three commonly used predefined directions (input-oriented, output-oriented, and proportional) considered in this study, we define the robust direction as the one with the minimum price that decision-maker must pay to be immune to data uncertainty. To demonstrate the usefulness of our proposed robust direction measure, we apply it a real-life data on life insurance companies in India over eight years (2011–12–2018–19). Our results show that the proportional direction exhibits the lowest price of robustness and is therefore the most appropriate for measuring potential efficiency improvement. Additionally, the increasing efficiency trend in the life insurance industry confirms the evidence of increased work intensity due to competition resulting from insurance reforms, supporting the competition and X-efficiency hypothesis.

A robust DEA model under discrete scenarios for assessing bank branches

Conventional Data Envelopment Analysis (DEA) assesses the performance of Decision-Making Units (DMUs) by measuring only one type of efficiency using definite data. However, due to the vastness of some industries, such as banks, calculating only one type of efficiency cannot confirm DMUs as efficient or inefficient. Also, real-world cases are often faced with uncertain data, and conventional DEA lacks the power to consider these uncertainties in evaluation. In this paper, we develop a multi-objective DEA model to calculate three types of efficiencies, including profitability, operational, and transactional for bank branches when there are uncertain data. First, we apply a modified DEA model which is capable of calculating the common weight of all inputs and outputs by solving only one linear programming model. Then, we employ a robust approach to handle the uncertainty in data. The uncertainty in data is described with discrete scenarios. Discrete scenarios require a set of possible values for each parameter with uncertain nature. Finally, we apply a fuzzy programming method to convert the proposed multi-objective model into a single-objective one. Our main goal is to calculate three types of efficiencies for bank branches under four different scenarios. To validate the accuracy of the proposed model, a real case of 45 Agriculture bank branches located in West Azerbaijan in Iran is examined. The results show that the proposed model can produce accurate results under different scenarios. We also perform a comparative analysis on each efficiency aspect to specify the benchmark branches and also inefficient branches. Comparative analysis can help managers recognize where improvement should be prioritized.

A robust DEA model in the presence of uncertain integer-valued parameters

PurposeUncertainty in data, whether in real-valued or integer-valued data, may result in infeasible optimal solutions or unreliable efficiency scores and ranking of decision-making units. To handle the uncertainty in integer-valued factors in data envelopment analysis (DEA) models, this study aims to propose a robust DEA model which is applicable in the presence of such factors.Design/methodology/approachThis research focuses on the application of fuzzy interpretation of efficiency to a mixed-integer DEA (MIDEA) model. The robust optimization approach is used to address the uncertain integer-valued parameters in the proposed MIDEA model.FindingsIn this study, the authors proposed an MIDEA model without any equality constraint to avoid the arise problem by such constraints in the construction of the robust counterpart of the conventional MIDEA models. We have studied the characteristics and conditions for constructing the uncertainty set with uncertain integer-valued parameters and a robust MIDEA model is proposed under a combined box-polyhedral uncertainty set. The applicability of the developed models is shown in a case study of Malaysian public universities.Originality/valueThis study develops an MIDEA model equivalent to the conventional MIDEA model excluding any equality constraint which is crucial in robust approach to avoid restricted feasible region or infeasible solutions. This study proposes a robust DEA approach which is applicable in cases with uncertain integer-valued parameters, unlike previous studies in robust DEA field where uncertain parameters are generally assumed to be only real-valued.

Data-Driven Robust Data Envelopment Analysis for Evaluating the Carbon Emissions Efficiency of Provinces in China

To combat global warming, China proposed the “dual carbon” policy in 2020. In this context, it becomes crucial to improve carbon emissions efficiency. Currently, some scholars have utilized data envelopment analysis (DEA) to study carbon emissions efficiency. However, uncertainty about climate and government economic policy is ignored. This paper establishes a robust DEA model to reduce uncertainty and improve robustness. First, robust optimization theory is combined with DEA to establish the robust DEA model. Second, considering three uncertainty sets (box set, ellipsoid set, and polyhedron set), a robust DEA model for different situations is considered. Finally, to address the problem of over-conservatism in robust optimization, this paper applies the data-driven robust DEA model to further analyze the carbon emissions efficiency of China. The results of the data-driven robust DEA model suggest that the government should focus on coordinated regional development, promote the transformation and upgrading of the energy structure, innovate in green technology, and advocate for people to live a green and low-carbon lifestyle.

Data-Driven Robust DEA Models for Measuring Operational Efficiency of Endowment Insurance System of Different Provinces in China

China is facing an increasingly serious aging problem, which puts forward higher requirements for the smoothness of the endowment insurance system. Accurate evaluation of the efficiency of the system can help the government to find problems and improve the system. Some scholars have used data envelopment analysis (DEA) method to measure the efficiency of endowment insurance system. However, according to the literature, the impact of government policy adjustment and economic shocks on output of the data was ignored. In this study, a robust optimization method is applied to deal with uncertainty. Robust DEA models proposed in this paper are based on three kinds of uncertainty sets. A data-driven robust optimization method is also applied to resolve the over-conservative problem. Compared with the robust DEA method, based on analysis it is found that the data-driven robust DEA method is more flexible and reliable for efficiency estimating strategies. The results of data-driven robust DEA models illustrate that the government should increase its support for the endowment insurance system, especially for the underdeveloped regions.

Robust optimization and its duality in data envelopment analysis

Robust Data Envelopment Analysis (RDEA) is a DEA-based conservative approach used for modeling uncertainties in the input and output data of Decision-Making Units (DMUs) to guarantee stable and reliable performance evaluation. The RDEA models proposed in the literature apply robust optimization techniques to the linear and conventional DEA models which lead to the difficulty of obtaining a robust efficient DMU. To overcome this difficulty, this paper tackles uncertainty in DMUs from the original fractional DEA model. We propose a robust fractional DEA (RFDEA) model in both input and output orientation which enables us to overcome the deficiency of existing RDEA models. The linearized models of the fractional DEA are further used to establish duality relations from a pessimistic and optimistic view of the data. We show that the primal worst of the multiplier model is equivalent to the dual best of the envelopment model. Furthermore, we show that the robust efficiency in the input- and output-oriented DEA models are still equivalent in the new approach which is not the case in conventional RDEA models. We finally present a study of the largest airports in Europe to illustrate the efficacy of the proposed models. The proposed RDEA is found to provide an effective management evaluation strategy under uncertain environments.

Data envelopment analysis model with decision makers’ preferences: a robust credibility approach

Data envelopment analysis (DEA) is one of the widely used methods to measure the efficiency scores of decision making units (DMUs). Conventional DEA is unable to consider both uncertainty in data and decision makers’ (DMs) judgments in the evaluations. This study, to address the shortcomings of the conventional DEA, proposes a new best worst method (BWM)- robust credibility DEA (BWM-RCDEA) model to estimate the efficiency scores of DMUs considering DMs’ preferences and uncertain data, simultaneously. First, to handle uncertainty in input and output variables, fuzzy credibility model has been applied. Additionally, uncertainty in constructing fuzzy sets is modeled using robust optimization with fuzzy perturbation degree. In this paper, two new types of RCDEA models are proposed: RCDEA model with exact perturbation in fuzzy inputs and outputs and RCDEA model with fuzzy perturbation in fuzzy inputs and outputs. In addition, to deal with flexibility of weights and incorporating DMs’ judgement into the RCDEA model, a bi-objective BWM-RCDEA model is introduced. Finally, the proposed bi-objective model is solved using min–max approach. To illustrate the usefulness and capability of the proposed model, efficiency scores of 39 distribution companies in Iran is investigated and results are analyzed and discussed. Finally, based on the results, recommendations have been made for policy makers.

A robust credibility DEA model with fuzzy perturbation degree: An application to hospitals performance

Performance evaluation enables decision makers (DMs) to have a better view about the weaknesses and strengths of leading units to improve efficiencies as a crucial goal. Data envelopment analysis (DEA) is the most popular technique to measure performance efficiency of decision making units (DMUs). However, conventional DEA is unable to consider uncertainty of input and output data in the evaluations. In this study, in order to address uncertainty in data, a robust credibility DEA (RCDEA) model has been introduced. First, a fuzzy credibility approach is used to construct fuzzy data. Then, a robust optimization approach is applied to consider uncertainty in constructing fuzzy sets. Moreover, perturbation level is considered as exact and fuzzy values. To illustrate the capability of the proposed model, 28 hospitals are evaluated in northwestern region of Iran and results are analyzed. According to the results, as perturbation degree increases, DMUs get normalized lower efficiencies and vise-versa.

تحلیل پوششی داده‌ها در شرایط عدم قطعیت برای بهبود انرژی مصرفی باغات کیوی استان مازندران

Introduction: One of the principal requirements for sustainable agriculture is efficient energy use. Energy use in agriculture has been increasing in response to the growing global population, limited arable land and desire for higher living standards. It should be noted that agriculture contributes significantly to atmospheric GHG emissions, with 10-12% of the net global CO2 (carbon dioxide) emissions. The scientific community believes global warming will pose one of the major environmental challenges in the future, with the bulk of GHG originating from fossil fuel consumption. Kiwifruit is an economically important fruit crop in northern Iran, because the northern region of Iran is a suitable, natural habitat for kiwifruit cultivation. The high kiwifruit production in Iran has reached a point that Iran is now well-known on global markets and in recent years this fruit has contributed a large share to agricultural exports. More recently, Mazandaran horticulturists have been encouraged to produce more kiwifruit. Increased production leads to greater energy consumption by Iranian kiwifruit orchards due to the added application of inputs, such as fertilizers and fuel. Besides, where there is no clear energy consumption pattern in agricultural production, especially fruit orchards, a lot of energy dissipates in the fruit production cycle. Therefore, it seems necessary to provide a model for the energy consumption of kiwifruit orchards in Mazandaran Province to prevent excessive energy utilization. Energy analysis is one of the methods has been used to evaluate the status of agricultural production. In this regard, many researchers have used Data Envelopment Analysis (DEA) for optimization the energy consumption in agricultural productions. DEA is recognized as a methodology widely used to evaluate the relative efficiency of a set of decision-making units (DMUs) involved in a production process. Although DEA is a powerful tool to measure efficiency but the uncertainty in the applied data in this model is inevitable and there is need to use different models that be able to control this uncertainty. Materials and Methods: In this study, in order to determine the efficiency of kiwifruit orchards in Mazandaran province and in terms of uncertainty of input data, the Robust Data Envelopment Analysis model (RDEA) and Fuzzy Interval Data Envelopment Analysis model (FIDEA) were used. The method incorporates the degree of conservatism in the maximum probability bound for constraint violation. The required data were collected by distributing and completing a questionnaire and face-to-face interview using random sampling method in 1397-98. Results and Discussion: The results showed that the average technical efficiency of all kiwi fields in RDEA model at three levels of probability include: 10, 50 and 100% is equal to 0.93, 0.96 and 0.98%, respectively. The results of FIDEA model showed that if the level of parameter α (optimal use of production factors) increases, the average efficiency of kiwi fields will increase. The highest energy savings are related to chemical pesticides and the lowest amount of savings is related to the chemical fertilizers and electricity inputs, respectively. So, holding the training courses on the correct and optimal use of production inputs from an economic and managerial point of view and improving the level of knowledge of farmers and factors involved in kiwi production in Mazandaran province can improve the efficiency and save energy consumptions. Conclusion: Evaluating the performance of many activities by a traditional DEA approach requires precise input and output data. However, input and output data in real-world problems are often imprecise or vague. To deal with imprecise data, this study uses RDEA and FIDEA approaches as a way to quantify vague data in DEA models. It is shown that the approaches can be a useful tool in DEA models without introducing additional complexity into the problem. A case study of kiwifruit orchard units is presented to illustrate the reliability and flexibility of the models. As a result, efficiency decreases as the constraint violation probability increased. Additionally, the RDEA approach provides both a deterministic guarantee about the efficiency level of the model, as well as a probabilistic guarantee that is valid for all symmetric distributions.

Relationships between technical efficiency and subsidies for Czech farms: A two-stage robust approach

Subsidies for agriculture in the European Union have been a matter of debate for a long time. However, even after many years of debate, it remains unclear whether the subsidies have a positive or negative effect on farm efficiency. We propose a robust two-stage framework to study the subsidies-effect to farm technical efficiency while controlling farm heterogeneity. First, technical efficiency scores are computed using a modern robust data envelopment analysis model. Then, a quantile regression model is applied to explain the relationship between technical efficiency and the total subsidies and other commonly used explanatory variables. In the empirical part, we analyze a sample of Czech farms during the period from 2010 to 2015. It is revealed that the subsidies-effect is negative and varies based on the technical efficiency of the farm. Higher efficient farms face a less distorting effect than lower efficient farms.

Robustness of Farrell cost efficiency measurement under data perturbations: Evidence from a US manufacturing application

Measuring economic and cost efficiency receives ever-increasing attention of the executives and managers of small-and medium-sized enterprises (SMEs) to minimise total production costs. The conventional Farrell cost efficiency (CE) as a key determinant requires the precise information on inputs, outputs and input prices, while in praxis uncertainty is inherent and inevitable in data and its negligence conceivably results in a dire approximation for CE measures. This paper is concerned with Farrell CE in situations of both endogenous and exogenous uncertainty. The source of uncertainty allows us to define two different scenarios; (i) in situations of endogenous uncertainty in input and output data where the uncertainty is affected by the decision maker's decisions, and (ii) in situations of uncertain prices for inputs where the uncertainty is exogenously given. In the first scenario, the theory of robust optimisation is adopted to develop the robust data envelopment analysis (DEA) models with the aim of grappling uncertainties in input and output data when measuring technical and cost efficiencies. The second scenario aims to accommodate uncertainties on price information by developing a pair of robust DEA models based upon robust optimisation estimating the upper and lower bounds for CE measures. This unprecedented study helps us to provide a generalised framework for economic efficiency with uncertainties in which conventional properties of Farrell measures are fulfilled. In addition to comparing the developed approach in this paper with other existing approaches through a simple numerical example, the usefulness and applicability of the suggested framework are minutely studied in an empirical application in the context of allocation problems.

Measuring efficiency in the Chilean wine industry: a robust DEA approach

ABSTRACT The Chilean wine industry has been quite innovative in terms of winemaking and trading. Yet, to survive in this competitive industry, wine managers should be aware of the relevance of monitoring their performance. In this paper, we assess how the five wineries listed on the Santiago Stock Exchange of Chile are efficient while using their critical resources for making profits. Particularly, we apply data envelopment analysis (DEA) to benchmark and rank these wineries’ technical efficiency based on four inputs and one output. We use data gathered from consolidated financial statements that are prepared using estimates, judgements, and assumptions. To account for some level of ex-post adjustments in data, we evaluate these wineries’ relative efficiency using a robust DEA model, which deals with ambiguous, imprecise, and uncertain input-output parameters. We analyse several levels of variability suitable for this data source, and we evaluate how changing the conservatism level affects technical efficiency and the rankings of the wineries. We also conduct a comparison between the five Chilean wineries and nine others from the New World. As the main conclusion, we found that Chilean wineries keep their efficiency level when including international firms in the analysis.

Application of a robust data envelopment analysis model for performance evaluation of electricity distribution companies

PurposeThis study evaluates the efficiency and productivity change of 39 electricity distribution companies in Iran over the period 2005-2014. For purposes of electricity management and utilization of scarce resources, Iran’s 33 provinces have been classified into five regions by the Ministry of the Interior. Analyzing the efficiency of distribution companies across these regions yields significant understanding of these resources and helps policymakers to generate more informed decisions.Design/methodology/approachThe proposed method of this study develops nonparametric data envelopment analysis (DEA) with the consideration of geographic classification, size and type of company. At the first stage, a DEA model is used to estimate the relative technical efficiency and productivity change of these companies. At the second stage, distributions of efficiency improvements are examined based on geographic classification, size and type of the company type. A stability test is also conducted to verify the proposed model’s robustness.FindingsThe results demonstrate that the average technical efficiency of the companies increased during the years 2006-2009, but decreased during 2010-2014. The productivity measurement reveals that low efficiency change was the largest contributor to the small increase in productivity change rather than technology change. In addition, testing the hypothesis that the large and small companies have statistically the same efficiency scores revealed no statistical difference among them. Moreover, another test did not detect a difference among companies at the urban and provincial levels.Practical implicationsBy applying this approach, policymakers and practitioners in the power industry at the country and corporate level can effectively compare the efficiency and productivity changes among electricity distribution companies, and therefore generate more informed decisions.Originality/valueThe paper’s novel concept applies DEA to Iran’s electricity distribution companies and analyzes them by examining geographic classification, size and the type of the companies. In addition, a stability test is conducted and productivity changes are estimated.

A second-order cone programming based robust data envelopment analysis model for the new-energy vehicle industry

The validity of performance evaluation is determined by, and therefore greatly influenced by, the accuracy of data set. To address such imprecise and negative data problems widely spread in the real world, this paper proposes a second-order cone based robust data envelopment analysis (SOCPR-DEA) model, which is more robust to data variety. Further, this new computational tractable model is applied to analyze 13 new-energy vehicle (NEV) manufacturers from China. The findings support that the SOCPR-DEA model could well mitigate the deficiency caused by data variety, and the evidence from Chinese NEV industry shows that a focus strategy is more likely to enhance a firm’s efficiency especially at its emerging stage, and the efficiency is more sensitive with production cost than other factors such as research and development, sales income, earnings per share, and predicted income. In addition, this paper also gives some industrial implications and policy suggestions based on these interesting findings.

A New Robust Dynamic Data Envelopment Analysis Approach for Sustainable Supplier Evaluation

Supplier selection is one of the intricate decisions of managers in modern business era. There are different methods and techniques for supplier selection. Data envelopment analysis (DEA) is a popular decision-making method that can be used for this purpose. In this paper, a new dynamic DEA approach is proposed which is capable of evaluating the suppliers in consecutive periods based on their inputs, outputs, and the relationships between the periods classified as desirable relationships, undesirable relationships, and free relationships with positive and negative natures. To this aim various social, economic, and environmental criteria are taken into account. A new method for constructing an ideal decision-making unit (DMU) is proposed in this paper which differs from the existing ones in the literature according to its capability of considering periods with unit efficiencies which do not necessarily belong to a unique DMU. Furthermore, the new ideal DMU has the required ability to rank the suppliers with the same efficiency ratio. In the concerned problem, the supplier that has unit efficiency in each period is selected to construct an ideal supplier. Since it is possible to have more than one supplier with unit efficiency in each period, the ideal supplier can be made with different scenarios with a given probability. To deal with such uncertain condition, a new robust dynamic DEA model is elaborated based on a scenario-based robust optimization approach. Computational results indicate that the proposed robust optimization approach can evaluate and rank the suppliers with unit efficiencies which could not be ranked previously. Furthermore, the proposed ideal DMU can be appropriately used as a benchmark for other DMUs to adjust the probable improvement plans.

An integrated multi response Taguchi- neural network- robust data envelopment analysis model for CO2 laser cutting

Taguchi method is a common method for controlling quality in off-line mode. Initially, this method is introduced to optimize a quality characteristic. Since optimizing one aspect of quality may deteriorate other aspects, so, to overcome this shortage, multi response Taguchi (MRT) method is extended. In MRT method, due to the existence of some uncontrollable factors or impossibility of implementing all the experiments, just some of the experiments are implemented and other experiments are designed by neural network (NN) technique. It is clear that there is uncertainty in the results of NN which can lead to incorrect decision making. Hence, the robust optimization approach is used to handle uncertainty in NN results. In this paper, first, the experiments are designed by the Taguchi method, then some experiments are implemented and other experiments are estimated by a back-propagation neural network (BPNN) technique. Finally, the best combination of quality parameters is selected by using optimal robust data envelopment analysis (RDEA) model. To illustrate the capability of the proposed approach, the experiments are performed on a CO2 laser cutting machine in a manufacturing company in Iran.