Classical Data Envelopment Analysis Research Articles

Stage stochastic incremental data envelopment analysis models and applications

Data envelopment analysis (DEA) is a mathematical programming method that can evaluate the relative efficiency of multiple inputs and multiple outputs of a decision-making unit (DMU). The classical DEA model assumes that inputs and outputs are determined. However, there are some applications where the inputs-outputs are stochastic. In practice, it is important to evaluate stage performance. It is essential to eliminate the effect of preceding stage inputs (outputs) on stage performance in order to accurately assess stage performance. In this paper, we propose stage stochastic incremental DEA models that integrate two different kinds of inputs and outputs. The first kind of model takes into account the assessment of stage efficiency when determinate incremental inputs and stochastic incremental outputs are applied at the beginning and end of the stage. The second kind of model uses stochastic incremental inputs-outputs to evaluate stage efficiency. To verify the efficacy of the suggested models, the first kind of model is applied to assess the stage financing efficiency of 15 energy-saving and environmental protection clean enterprises (ESEPCEs). The second kind of model is applied in assessing the stage investment efficiency of 15 ESEPCEs. The empirical results show that the proposed models not only eliminate the effect of prior performance but also more accurately assess stage efficiency in a stochastic environment.

A new intuitionistic fuzzy scheme of data envelopment analysis for evaluating rural comprehensive health service centers

In this study, the classical CCR-IO DEA model (an input-oriented form of the DEA model of Charnes, Cooper, and Rhodes [24] is extended to an intuitionistic fuzzy environment. For this aim, the trapezoidal intuitionistic fuzzy numbers are used to show the values of inputs and outputs. An intuitionistic fuzzy number is characterized by membership, non-membership, and hesitancy degrees. Therefore, such type of fuzzy numbers is more complete and contains more information to reflect a fuzzy type of uncertainty comparing to the conventional fuzzy values. In order to solve the proposed intuitionistic fuzzy CCR-IO model, for the first time a possibility-based approach is developed for the intuitionistic fuzzy DEA models. In this approach for the first time the ME measure of fuzzy events is extended to intuitionistic fuzzy DEA models, therefore, some new definitions and propositions are presented and clarified. This measure is more flexible and effective comparing to the other measures such as credibility, necessity, and possibility measures. A case study from the health care sector of Iran is considered to evaluate the proposed solution approach numerically. The case study is solved under different scenarios, a full sensitivity analysis is performed, and finally some useful managerial insights are presented. In addition, the results of the proposed intuitionistic CCR-IO model are compared to the classical models of the literature.

A double bootstrap data envelopment analysis model with stochastic reducible outputs and expandable inputs: An application to power plants

Clean production of electricity is not only cost-effective but also effective in reducing pollutants. Toward this end, the use of clean fuels is strongly recommended by environmentalists. Benchmarking techniques, especially data envelopment analysis, are an appropriate tool for measuring the relative efficiency of firms with environmental pollutants. In classic data envelopment analysis models, decision-makers are faced with production processes in which reducible inputs are used to produce expandable outputs. In this contribution, we consider production processes when the input and output data are given in stochastic form and some throughputs are reducible and some others are expandable. A stochastic directional distance function model is proposed to calculate the relative technical efficiency of firms. In order to evaluate firm-specific technical efficiency, we apply bootstrap DEA. We first calculate the technical efficiency scores of firms by classic DEA model. Then, the double bootstrap DEA model is applied to determine the impact of explanatory variables on firm efficiency. To demonstrate the applicability of the procedure, we present an empirical application wherein we employ power plants.

A cutting-edge data envelopment analysis model for measuring sustainable supplier performance like never before

One of the challenges for suppliers is to increase their market share due to the limited target market. In other words, in the supply chain, the demand for suppliers' products is limited. Therefore, suppliers produce a determined share of the required amount by producers. However, when it comes to the share in the amount of output among suppliers, the output of suppliers in this indicator is interdependent. In the classical data envelopment analysis (DEA) models, there are no models that assess the suppliers according to the dependence of at least one output on each other. In this paper, a model is presented that can assess sustainable suppliers in the presence of interdependent output among suppliers by using DEA models and their extension. It can also determine the total benchmarks of decision making units (DMUs) in such a way that satisfies the interdependent output constraint. In other words, benchmarks are not determined independently. Ultimately, an approach is presented to determine efficient projections for inefficient DMUs by considering the concept of interdependent output. To represent the applicability of our proposed model, a dataset for two consecutive years including 32 sustainable suppliers with consideration of interdependent output has been implemented using the model presented in this paper. The resulting sustainability has been compared with a classical model.

Multi-choice conic goal programming model-based network data envelopment analysis

In multi-stage processes, classical Data Envelopment Analysis (DEA) acts like a black box and measures the efficiency of decision-making units (DMUs) without considering the internal structure of the system. Unlike classical DEA, recent studies have shown that the overall system efficiency scores are more meaningful if researched using the Network DEA (NDEA) methodology. NDEA performs simultaneous efficiency evaluations of sub-processes and the entire system. Recently, the composition method integrated with multi-objective programming (MOP) has been preferred by many authors to alleviate the drawbacks of earlier methods such as decomposition, slack-based measure (SBM) and the system-centric approach. This study proposes a novel approach incorporating Multi-Choice Conic Goal Programming into the NDEA (MCCGP-NDEA). It provides a more accurate representation of the Pareto front by revealing potential Pareto optimal solutions which are overlooked by the composition methods. Due to its ability to modify stage weights based on the decision makers' (DMs) preferences, it is likely to gather more samples from the Pareto surface. Computational results on available benchmark problems confirm that the proposed MCCGP-NDEA is a viable alternative to existing methods.

A simulation-based DEA approach for multiple criterion decision-making problems with uncertain mixed-criteria values

In ex-ante decision scenarios, predicting criterion values accurately is difficult for decision makers (DMs). Inconsiderable work is normally required for measuring criteria by uncertain random values or ordinal values. However, in the classical data envelopment analysis (DEA) model, criterion values are the constants that limit the application of the classical DEA model in ex-ante decision scenarios. This paper presents a simulation-based DEA approach, which captures random and ordinal criterion values by a simple and direct simulation-based approach. The approach includes three steps. In the first step, Monte Carlo simulation methods are used to convert uncertain random values or ordinal values into cardinal data. In the second step, we use traditional DEA methods to compute the efficiency score of decision-making units (DMUs). In the third step, we ranked all DMUs by calculating the DEA-efficient acceptability of each DMU in multiple simulations and then selected the optimal DMU. The proposed approach is illustrated by experimental examples and a case study of a municipal wastewater treatment system.

A firm-specific Malmquist productivity index model for stochastic data envelopment analysis: an application to commercial banks

In the data envelopment analysis (DEA) literature, productivity change captured by the Malmquist productivity index, especially in terms of a deterministic environment and stochastic variability in inputs and outputs, has been somewhat ignored. Therefore, this study developed a firm-specific, DEA-based Malmquist index model to examine the efficiency and productivity change of banks in a stochastic environment. First, in order to estimate bank-specific efficiency, we employed a two-stage double bootstrap DEA procedure. Specifically, in the first stage, the technical efficiency scores of banks were calculated by the classic DEA model, while in the second stage, the double bootstrap DEA model was applied to determine the effect of the contextual variables on bank efficiency. Second, we applied a two-stage procedure for measuring productivity change in which the first stage included the estimation of stochastic technical efficiency and the second stage included the regression of the estimated efficiency scores on a set of explanatory variables that influence relative performance. Finally, an empirical investigation of the Iranian banking sector, consisting of 120 bank-year observations of 15 banks from 2014 to 2021, was performed to measure their efficiency and productivity change. Based on the findings, the explanatory variables (i.e., the nonperforming loan ratio and the number of branches) indicated an inverse relationship with stochastic technical efficiency and productivity change. The implication of the findings is that, in order to improve the efficiency and productivity of banks, it is important to optimize these factors.

Efficiency analysis in two‐stage data envelopment analysis with shared resources and undesirable outputs: an application in the banking sector

AbstractIn classic and traditional data envelopment analysis (DEA) models, the production process is considered as single stage process and the internal structures have been ignored. In many real‐world occasions, however, the processes have two‐ or multi‐stage structures with or without shared resources. Two‐stage DEA models deal with the calculation of the technical efficiency of a system, taking into consideration its internal structures. In this contribution, we consider a two‐stage production process in which both stages are fed by shared resources, and there are undesirable products from the second stage. In the model we will propose, an optimal split on shared resources is given. To demonstrate the applicability of the proposed approach, data on 40 bank branches in seven years 2014–2020 is presented. In our real application in the banking sector, we find out that the most important sources of inefficiency of bank branches are related to interest revenue and overdue debt (undesirable output). Moreover, we saw that almost all branches were inefficient in the second stage (sale and service section) in all the seven years of evaluation.

European agricultural sector: The tortuous path across efficiency, sustainability and environmental risk

This research aims at investigating the relationship between efficiency, sustainability, and environmental risk in the European agricultural sector. On the one hand, we assess whether efficiency and sustainability are complementary or competing targets; on the other, we explore to what extent environmental risk exposure can represent a motivation or a threat to promoting sustainability in the sector. To do so, we construct three composite indicators, based on frontier techniques. In particular, we implement classical Data Envelopment Analysis (DEA) to estimate agricultural efficiency, a DEA model for undesirable output for the sustainable efficiency, and a Benefit of the Doubt model to assess environmental risk. The analysis highlights three main results: first, that efficiency and sustainability are not competing aims, at least for the analysed territories; second, countries that are exposed to environmental risk are less agricultural efficient; third, more sustainable countries are likely to be the most exposed to environmental risk, indicating that direct exposure to environmental risks might be a strong motivation engine to encourage sustainability. The study adds to previous literature debate by providing evidence about the agricultural sector’s vulnerability and of the difficulties of combining efficiency, sustainability, and environmental goals.

Benchmarking performance through efficiency analysis trees: Improvement strategies for colombian higher education institutions

We introduce benchmarking analysis based on state-of-the-art machine learning techniques applied to the measurement of efficiency to assess the performance of Higher Education Institutions (HEIs). We rely on Efficiency Analysis Trees (EAT) and its Convexified frontier counterpart (CEAT) to assess the efficiency of 144 private HEIs in Colombia and compare the results with those achieved with classical Data Envelopment Analysis (DEA). Both EAT and CEAT show a higher discriminatory power than DEA when determining efficiency scores. Our results identify the different splits of the production frontier, corresponding to each node of the efficiency tree, which groups HEIs according to specific management models. By identifying relevant peers for inefficient observations at the node level, we show which strategic guidelines can be adopted to improve the performance of each HEI. This process encourages mutual learning and suggests potential changes within each node leading to efficiency improvements.

Sustainable approach towards alternatives for the use of iron ore tailings in the construction sector using Data Envelopment Analysis methodology.

Iron ore tailings (IOTs) need to be properly managed to mitigate the environmental, social, and economic impacts of mining activities. To cope with this issue, we use data envelopment analysis (DEA) to evaluate alternatives for using IOT in the construction sector. The classical and weight restriction output-oriented DEA models were used in this analysis. The results show that the ranking of alternatives depends on the aspect being evaluated. Concrete block is the most environmentally friendly alternative when analysing both models. For both social and economic aspects, ceramics produced better results in the classical model, whereas Portland cement showed better outcomes in the weight restriction model. In this sense, the results suggest great potential for the use of IOT in the construction sector, enabling the reduction of risks and social and environmental impacts of tailings dams.

A novel model for merger analysis and target setting: A CSW-Inverse DEA approach

The inverse data envelopment analysis (DEA) is an advanced complementary method for efficiency analysis using the classical DEA approach. One of the inverse DEA (InvDEA) method applications is the mergers and acquisitions problem. It can be used for analyzing any under evaluation mergers and acquisitions. The current article is the first attempt to propose a novel inverse structure for the DEA model using the multiplier forms. This eventuates the possibility of incorporating decision maker preferences within the merger analysis.Moreover, compared with the existing models in the literature, the proposed novel models are capable of analyzing multiple merger scenarios simultaneously in a single method based on the common set of weights (CSW) rather than a series of models for studying multiple scenarios of mergers and acquisitions. Practically, this property enables decision-makers to consider and analyze multiple mergers and find possible potentials at the same time. The applicability of the proposed model is investigated by using a real-world dataset in banking.

Evaluating the Efficiencies of Logistics Centers with Fuzzy Logic: The Case of Turkey

The primary actor in today’s economic life, forming the backbone of the production-consumption cycle, is the distribution activities. Logistics centers (LCs) are organized areas where these activities are carried out together. Therefore, the efficiency and effectiveness of distribution activities are crucial for sustainability. This study incorporates fuzzy logic theory into the framework of data envelopment analysis (DEA) to measure the efficiency of LCs. Classical DEA assumes input and output data are precisely measured, making the efficiency scores unreliable and inconsistent when data precision is not always possible. The adoption of fuzzy logic is primarily to overcome possible uncertainties, errors, and ambiguities in data acquisition, preventing incorrect results. Hence, an approach assumes the data lie within specific intervals, was adopted to calculate the efficiencies of LCs based on α-cut levels. Officially obtained data on nine input and one output variable from twelve LCs operating in Turkey were used to calculate efficiency scores. As a result of the study, Köseköy/Izmit, Halkali/Istanbul, and Yenice/Mersin LCs were found to be fully efficient considering both lower and upper bound efficiencies. Moreover, the efficiency calculations using Fuzzy-DEA allowed for a more precise evaluation of LCs with high data sensitivity.

Measuring an efficiency aggregation of medical diagnostic laboratories: A window NDEA approach

The efficiency evaluation of laboratories, as one of the most significant areas of healthcare, plays a key role in the quality of laboratory management. The classic data envelopment analysis (DEA) models have overlooked intermediate products, internal interactions and dealt with analyzing the network within the “Black Box” mode. This results in the loss of important information, and at times, a considerable modification occurs in efficiency results. This article evaluated the efficiency of some selected medical diagnostic laboratories in the city of Tehran according to the network data envelopment analysis (NDEA) approach. We considered a four-stage structure with additional inputs and undesirable outputs. We obtain the labs’ performance over a period of 6 months in 2022 by the NDEA window analysis process. To this aim, a four-stage structure model of three chief medical diagnostic laboratory processes as the pre-test, the test, and the post-test is designed. We considered sustainability criteria (economic, social, and environmental) to appraise the performance of laboratories, thus helping to improve the social, economic, and environmental problems of medical diagnostic laboratories. By using the Delphi viewpoint, the criteria for efficiency evaluation are achieved. The results showed that laboratory unit No. 22 maintained the highest average overall efficiency, since the high accuracy of this unit’s laboratory results had led to many physicians recommending this unit to their patients. We found that the only laboratory unit No. 20 had a decreasing trend, as it is located in an area that abounds with administrative and educational centers. At the beginning of the exam period, then the summer holidays, and finally the wave of end-of-summer trips, a decline occurs in efficiency over the period of six months.

Environmental efficiency evaluation of China's power system considering factor's spatial dependence: A dynamic spatial network DEA approach

Evaluating and improving the environmental efficiency of the power system is the key to achieving sustainable development. However, the classic DEA approach is susceptible to producing biased results due to its inability to address spatial dependence across factors. Considering the spatial dependence of inputs and outputs, this paper proposes a dynamic spatial network DEA model with slacks-based measure (SNSBM) to examine the environmental efficiency of China's power systems, with a focus on the undesirable outputs of CO2, NOx, and SO2. The investigation incorporates the Moran's I test to account for the spatial interactions of patent counts, coal consumption, CO2 emissions, and renewable power generation. Compared to the classic network DEA, the SNSBM results reveal distinct spatial characteristics and a heightened level of differentiation, which highlights the importance of eliminating spatial dependence. From a dynamic perspective, environmental efficiency shows a visible surge in transmission and distribution divisions after 2015, confirming the success of China's market-oriented reform. In addition, CO2 is the largest contributor to the environmental inefficiency of the power systems, followed by NOx and SO2. This study highlights the importance of spatial dependence and provides many insightful policy recommendations for improving the environmental efficiency of China's power systems.

Global correlation coordination model for ranking decision-making units based on cross-efficiency game

DEA cross-efficiency evaluation method can rank decision making units (DMUs) more reasonably than the classical DEA model, but the existing cross-efficiency evaluation methods still have many deficiencies. The most evident drawback is that the potential multiple solutions of the optimal weights lead to the non-uniqueness of the cross-efficiency value. Moreover, the traditional cross-efficiency ranking methods neglect the interaction between DMUs. It is a common scenario that the decision-making unit will incline to give high evaluation scores to those in same coalition, and relatively low evaluation scores to those with different coalitions on the contrary in the process of cross-efficiency evaluation. Aiming at solving the above problems, this study proposes a cross-efficiency game model considering correlation coordination degree among DMUs. The generalized Shapley value of cross-efficiency game is defined, and its desirable properties are proved in detail. Finally, a global correlation coordination (GCC) model is developed for ranking decision-making units comprehensively. The comparative example and practical application on R&D efficiency evaluation are provided to illustrate the rationality and feasibility of the GCC model.

A new multiple criteria data envelopment analysis with variable return to scale: Applying bi-dimensional representation and super-efficiency analysis

It is known that, in general, in practical real-world problems, when the number of Decision- Making Units (DMUs) is not large enough compared to the total number of input and output parameters, the traditional DEA models with Constant Return to Scale – CRS and with Variable Return to Scale – VRS have a weak power of discrimination, producing solutions that identify many DMUs as being efficient, in addition to obtaining unrealistic weight distributions. In this context, it is recommended to work with Multiple Criteria Data Envelopment Analysis - MCDEA models. So far, all MCDEA models available in the literature adopt CRS approach. This paper proposes a New Multiple Criteria Data Envelopment Analysis (NMCDEA) – VRS model, as well as performs a super-efficiency analysis for this model. Furthermore, through bi- dimensional graphic representations, a geometric demonstration is provided, showing that, in fact, the proposed model is a good representation of situations in which it is interesting to consider a VRS behavior. The results obtained through the optimization of instances available in the literature, for real instances, as well as the sensitivity analysis carried out, indicated that the NMCDEA-VRS has a much greater power of discrimination compared to the classic DEA–VRS model.

Measurement of Process-Performances of Turkish Airports Using Network Data Envelopment Analysis

The air transportation industry is continuously broadening by adding new airports operating with huge investments. Hence, increasing efficiency and productivity in this industry is becoming critical. At the same time, efficiency calculations are also an important tool used to identify weaknesses and contribute to the improvement of the performance of enterprises. Nevertheless, Classic DEA models are commonly insufficient to determine the efficiency of a system due to ignorance of its internal structure and the treatment of the system as a black box. Therefore, if a production system can be divided into subprocesses by using network DEA model, the results will be more plausible and satisfying. Within this scope, this paper aims to evaluate the efficiencies of 39 out of 56 airports in Türkiye from 2015 to 2019. The results indicate that less-populated airports managed by private entrepreneurs are more efficient than others. Moreover, another characteristic of these efficient airports is that they are both domestically and internationally preferred for leisure trips.

The Harmonious Relationship between Energy Utilization Efficiency and Industrial Structure Development under Carbon Emission Constraints: Measurement, Quantification, and Identification

Addressing the challenge of attaining a harmonious balance between energy utilization efficiency and the level of industrial structure development is crucial for promoting regional sustainable development. Aiming at the goal of carbon neutrality, a three-stage method to analyze the relationship between energy utilization and industrial structure development is proposed. The multidimensional input–output index system was augmented with a carbon emission constraint. Additionally, two classical data envelopment analysis models were integrated to establish a dynamic measurement model for energy utilization efficiency, ensuring comparability among all decision-making units. From two perspectives of industrial structure, rational degree and advanced degree, the industrial structure development index was proposed to quantitatively characterize the level of regional industrial structure development. Drawing upon the Tapio decoupling theory, an elaborate model for identifying harmonious relationships was constructed to refine the recognition of the harmonious state between energy utilization efficiency and industrial structural development. A city-scale case study was conducted in Heilongjiang Province, a typical energy province in Northern China. The results revealed that: (a) energy utilization efficiency in various cities has exhibited a consistent upward trend, with the average efficiency rising from 0.54 in 2010 to 0.88 in 2020. Core cities like Daqing and Harbin stand out in energy utilization, and the disparity in energy utilization levels between different cities is progressively diminishing; (b) the overall level of industrial structural development has shown a weak downward trend. Harbin has the best industrial structure development level, with a quantitative index higher than 0.8. For some cities with relatively backward industrial structures, it is necessary to clarify new industrial development positioning and promote deep optimization of industrial structures; and (c) the harmonious relationship between energy utilization efficiency and industrial structural development demonstrates stage characteristics, indicating an overall negative decoupling relationship with limited dynamic coordination. These distinct findings will assist in identifying potential solutions for achieving high-quality development in traditional industrial cities under carbon emission constraints.

A non-parametric synthesize measure for corporate governance: empirical evidence from Indian banks

The purpose of the present study is to craft a corporate governance index for Indian banks by eliminating the subjectivity in assigning weights. The present framework includes six corporate governance dimensions, which include the attributes related to the board committee, audit committee, risk management committee, remuneration committee and transparency of the banks. The study considers measuring the index value for corporate governance framework via a novel extension of the classical data envelopment analysis technique known as the benefit of doubt analysis, as this approach assigns the weights objectively to the different dimensions of corporate governance and thereafter provides a synthesised score to be termed as the corporate governance index. Further, the present study attempts to know any variation in the index score when the whole sample is divided into sub-sample for two different groups in terms of duality and non-duality of CEO leadership board and other is based on the large and small size of banks. The analysis reveals that non-duality boards and small-size banks are more adaptable to the governacne norms. The analysis further documented that in an emerging economy effective implementation of governance norms is not only beneficial in protecting the interest of the shareholders but also contributes to the business performance. Thus, based on the novel analysis the study provides few policy implications in terms of identifying the key areas for an effective corporate governance framework.