Conventional Data Envelopment Analysis Models Research Articles

Applications of data envelopment analysis in acute care hospitals: a systematic literature review, 1984-2022.

This study reviews scholarly publications on data envelopment analysis (DEA) studies on acute care hospital (ACH) efficiency published between 1984 and 2022 in scholarly peer-reviewed journals.We employ systematic literature review (SLR) method to identify and analyze pertinent past research using predetermined steps. The SLR offers a comprehensive resource that meticulously analyzes DEA methodology for practitioners and researchers focusing on ACH efficiency measurement. The articles reviewed in the SLR are analyzed and synthesized based on the nature of the DEA modelling process and the key findings from the DEA models. The key findings from the DEA models are presented under the following sections: effects of different ownership structures; impacts of specific healthcare reforms or other policy interventions; international and multi-state comparisons; effects of changes in competitive environment; impacts of new technology implementations; effects of hospital location; impacts of quality management interventions; impact of COVID-19 on hospital performance; impact of teaching status, and impact of merger. Furthermore, the nature of DEA modelling process focuses on use of sensitivity analysis; choice of inputs and outputs; comparison with Stochastic Frontier Analysis; use of congestion analysis; use of bootstrapping; imposition of weight restrictions; use of DEA window analysis; and exogenous factors. The findings demonstrate that, despite several innovative DEA extensions and hospital applications, over half of the research used the conventional DEA models. The findings also show that the most often used inputs in the DEA models were labor-oriented inputs and hospital beds, whereas the most frequently used outputs were outpatient visits, followed by surgeries, admissions, and inpatient days. Further research on the impact of healthcare reforms and health information technology (HIT) on hospital performance is required, given the number of reforms being implemented in many countries and the role HIT plays in enhancing care quality and lowering costs. We conclude by offering several new research directions for future studies.

Development of intuitionistic fuzzy cost efficiency model in data envelopment analysis

Data envelopment analysis (DEA) is a non-parametric linear programming (LP) based technique to measure the relative efficiencies of decision-making units (DMUs). The conventional DEA models assume that input-output data is crisp, which may not always be feasible in practical situations due to the presence of ambiguity and imprecision. Therefore, to handle uncertain and imprecise data, the concept of intuitionistic fuzzy sets (IFS) has been introduced. In this study, the relative efficiencies of DMUs with uncertain data will be determined. For this reason, the conventional cost efficiency (CE) model of DEA is extended to IF environment. Also, the lower and upper-cost efficiency models are developed using α-cut and β-cut approach. The data for inputs, outputs and input prices are considered intuitionistic fuzzy numbers (IFNs), in particular triangular intuitionistic fuzzy numbers (TIFNs). To demonstrate the practical application of the proposed intuitionistic fuzzy cost efficiency models (IFCEMs), a numerical example is presented.

Efficiency analysis of engineering colleges in India: Decomposition into parallel sub-processes systems

Analyzing engineering colleges in India with Data Envelopment Analysis (DEA) is the focus of this study. Engineering colleges pioneer in teaching and research, creating two sub-processes within engineering education. Thus, our study considers each engineering college to comprise two parallel non-homogenous sub-processes, such as teaching and researching. Unlike the conventional DEA models, where the system is treated as a black box, this work attempts to independently assess the impact of each parallel sub-process so that it is possible to identify specific changes in the respective processes to improve the overall efficiency. In particular, our study analyzed the efficiency of engineering colleges based on the National Institute Ranking Framework (NIRF) data. Further, the comparison of the efficiency scores from teaching and research indicates that, on average, the institutes are more efficient in teaching than researching. The current study helps policymakers set priorities and course corrections for performance improvement programs of engineering colleges in India.

Maintenance groups evaluation under uncertainties: a novel stochastic free disposal hull in the presence of lognormally distributed data

Maintenance groups play an essential role in the successful operation of large companies and factories. Additionally, data envelopment analysis (DEA) is known as a valuable tool for monitoring the performance of maintenance groups. Especially, in contrast to the conventional DEA models that impose the convexity assumption into the technology, the free disposal hull (FDH) model provides a method for assessing the efficiency without the assumption of convexity and can be considered a valuable tool for determining one of the observed groups as the benchmark for each maintenance group. Meanwhile, because of the stochastic structure of data with lognormal distribution in the maintenance groups, this paper extends the FDH model in stochastic data with the lognormal distribution. Moreover, the method’s capabilities are confirmed based on some theorems, and a simulation study that illustrated the properties of the developed procedure is also performed. The developed methodology is applied to assess the performance of 21 maintenance groups of AZCO under uncertainty conditions.

Embedding Best-Worst Method into Data Envelopment Analysis

In real-life applications, there generally exist Decision Makers (DMs) who have preferences over outputs and inputs. Choosing appropriate weights for different criteria by DMs often arises as a problem. The Best-Worst Method (BWM) in Multiple Criteria Decision-Making (MCDM) depends on very few pairwise comparisons and just needs DMs to identify the most desirable and the least desirable criteria. Unlike MCDM, Data Envelopment Analysis (DEA) does not generally assume a priority for an output (an input) over any other outputs (inputs). The link between DEA and MCDM can be introduced by considering Decision-Making Units (DMUs) as alternatives, outputs as criteria to be maximized, and inputs as criteria to be minimized. In this study, we propose a linear programming model to embed DEA and BWM appropriately. We first propose a modified BWM linear programming model to satisfy all conditions that DMs can assume. We then illustrate how a conventional DEA model can be developed to include the BWM conditions. From our approach, the MCDM problem to obtain the optimal weights of different criteria are measured. At the same time, the relative efficiency scores of DMUs corresponding to the MCDM criteria are also calculated. We provide the foundation of measuring the efficiency scores when most desirable and the least desirable inputs and outputs are known. To show the process of the proposed approach, a numerical example (including 17 DMUs with seven inputs and outputs) is also discussed.

A fuzzy rough network data envelopment analysis approach for evaluating the sustainability of supply chains: a case study in the pasta industry

ABSTRACT Evaluation of the sustainability of supply chains is a complex decision-making problem. One of the techniques, which are used for assessing the sustainability of supply chains is data envelopment analysis (DEA). Conventional DEA models consider decision making units (DMUs) as black boxes that consume a set of inputs to produce a set of outputs and do not take into consideration the internal interactions of DMUs. Also, they assume inputs and outputs are crisp. In this research, the network DEA (NDEA) model for assessing the sustainability of supply chains in the presence of fuzzy rough data is developed. The main contribution of this paper is to develop a novel NDEA model in the existence of internal and external uncertainties. To validate the proposed model, a case study for evaluating the sustainability of the supply chain in the pasta industry is presented.

A Decomposed Data Analysis Approach to Assessing City Sustainable Development Performance: A Network DEA Model with a Slack-Based Measure

This paper deals with urban sustainable development in China. We propose a network data envelopment analysis (DEA) model with a slack-based measure (SBM) to analyze the eco-efficiency of 284 Chinese cities, enabling us to find a way to open the “black box” in conventional DEA models and introduce social well-being factors into the model, and depict the role of local government in providing public service and improving social well-beings. We set up a framework of urban development by dividing the process of into two steps. The first stage is a production system translating inputs and natural resources into GDP and waste production, which will be inputs to the second stage for distribution and consumption to realize social welfare and environmental protection. The results show eco-efficiency of Chinese cities experienced a significant decrease from 2005 to 2016, which should be mainly attributed to the distribution and consumption processes. Structural differences are described by regions, administrative level and clusters. These results are compared with an existing urban sustainability index system developed by McKinsey and an ANOVA approach is conducted to reveal differences between cities across regions and clusters. This article sheds new light on the understanding of urban sustainable construction and development in China regarding the service performance of local government.

Scale characteristics of variable returns-to-scale production technologies with ratio inputs and outputs

Applications of data envelopment analysis (DEA) often include inputs and outputs represented as percentages, ratios and averages, collectively referred to as ratio measures. It is known that conventional DEA models cannot correctly incorporate such measures. To address this gap, the authors have previously developed new variable and constant returns-to-scale models and computational procedures suitable for the treatment of ratio measures. The focus of this new paper is on the scale characteristics of the variable returns-to-scale production frontiers with ratio inputs and outputs. This includes the notions of the most productive scale size (MPSS), scale and overall efficiency as measures of divergence from MPSS. Additional development concerns alternative notions of returns to scale arising in models with ratio measures. To keep the exposition as general as possible and suitable in different contexts, we allow all scale characteristics to be evaluated with respect to any selected subsets of volume and ratio inputs and outputs, while keeping the remaining measures constant. Overall, this new paper aims at expanding the range of techniques available in applications with ratio measures.

Evaluating the Efficiency of Decision Making Units in Fuzzy two-stage DEA Models

Data envelopment analysis (DEA) is an optimization method to assess the efficiency of decision-making units with multiple-inputs/multiple-outputs assumption. Most real-life issues contain more than one stage unit which needs multiple-stage data envelopment analysis models to be solved. Moreover, the inputs and outputs of the units are rarely measured accurately in real-life problems, hence fuzzy data envelopment analysis approaches can be significantly helpful in calculating efficiency scores. In this study, an approach for evaluating the performance of decision-making units (DMUs) in fuzzy two-stage DEA models is developed. The developed model is a parametric program based on alpha-cuts. The dependence on alpha allows the manager to compare and rank DMUs based on his/her degree of certainty and after the selection of alpha, our proposed model becomes linear. Furthermore, a theorem is proposed and proved for conventional multiplicative two-stage DEA models with the assumption of Variable Returns to Scale. This theorem can be used to evaluate the correctness of the results. Finally, by two illustrative examples, the ability of the proposed approach to solve fuzzy two-stage DEA models is shown, and the obtained results are compared to that of some other methods in this field.

Achievements of the European Union member states toward the development of sustainable agriculture: A contribution to the structural efficiency approach

The ranking of decision-making units can be performed by measuring their efficiency. However, the discriminatory power of efficiency measures is sometimes compromised, and complete rankings are not attained. Additionally, environmental performance must be considered when assessing the sustainability of operations. This paper applies the “average contribution to structural efficiency” index to measure the environmental performance of the European Union Member States’ agricultural sectors. The contribution index considers all of the possible combinations of observations when assessing states’ environmental performance. This process allows for a complete ranking of the countries under consideration. The agricultural performance of Bulgaria, Denmark, France, the Netherlands, Romania, Slovakia and Slovenia, as measured by the conventional data envelopment analysis, approached the production frontier. Therefore, these countries could not be ranked based on the conventional data envelopment analysis model. The application of the contribution index showed that Romania, the Netherlands, Bulgaria, Slovakia and Slovenia were ranked as the best-performing countries. In addition, France and Belgium showed positive contributions to structural efficiency, although they were not classified as efficient countries. Therefore, cooperation with these countries would allow other countries to exploit their agricultural resources in a more productive and sustainable manner.

How ecoefficient is European food consumption? A frontier‐based multiregional input–output analysis

AbstractThis paper presents an integrated approach combining the optimization‐based frontier model with a global multiregional input–output (MRIO) analysis for food consumption in Europe. The weighted and conventional data envelopment analysis models are coupled with production and consumption‐based environmental and economic footprint data obtained from the environmental footprint explorer database. Eco‐efficiency assessment is carried out using multiple undesirable environmental outputs such as carbon emission, total energy consumption, land use, material use, water use, and one desirable economic output, which is the gross value‐added (GVA). This assessment indicates an efficiency level of each economic activity associated with its environmental impacts and policies are made as a result of the efficiency level to propose an equilibrium between economic development and environmental impacts. Finally, a sensitivity analysis of each parameter, variability analysis between weighted and non‐weighted models, and performance improvement projections are presented. Based on the results, four countries become efficient when moving from production‐based accounting (PBA) to consumption‐based accounting (CBA). France, United Kingdom, Italy, and Sweden are efficient countries in both findings. Denmark caused the highest carbon emission from the production point of view. Germany is the largest importer in all environmental categories such as carbon emission, energy usage, material use, land use, and water use. Additionally, the weight‐restricted model indicated a noticeable difference concerning the eco‐efficiency scores under the PBA and CBA approach, where land use and material footprint categories were found to be the most sensitive parameters for eco‐efficiency scores. The authors believe that this integrated approach will aid in decision‐making and help build a composite eco‐efficiency score when comparing the performance of food consumption with multiple environmental and economic metrics.

Efficiency of South African water utilities: a double bootstrap DEA analysis

ABSTRACT Although the efficiency of the water sector has been studied extensively utilizing data envelopment analysis (DEA), most of the literature tends to use the conventional DEA model to compute efficiency scores. In addition, there are many studies that undertake a second stage regression of the efficiency scores against a set of covariates. However, such second-stage analyses are problematic due to potential serial correlation inherent in the estimated efficiency scores. To determine the bias-corrected efficiency scores of rural and urban water utilities in South Africa, this study uses a robust, non-parametric DEA bootstrapping model to generate them. Moreover, little is known about relative performance of the conventional DEA versus bias-corrected DEA. In addition, the truncated double-bootstrap regression results provide insights into the drivers of efficiency, including how water policies and the political and institutional contexts of water utilities can impact relative efficiencies. We found that there are significant differences between the rankings and efficiency scores generated by the conventional DEA model compared to the double-bootstrap DEA model, for both urban and rural samples. The regression model found the location and the ratio of metered to unmetered connections to be significant determinants of efficiency for both urban and rural water utilities.

The Environmental Efficiency Analysis Based on the Three-Step Method for Two-Stage Data Envelopment Analysis

This paper suggests that the efficiency of a system (decision-making unit) and its subsystem cannot be properly measured using a two-stage data envelopment analysis (DEA) model either in cooperative or non-cooperative evaluation. Indeed, the existing methods subjectively determine the status of the subsystems in the whole system. The two-stage DEA models, either cooperative game or non-cooperative game, are used to analyze the environmental efficiency. However, when the actual relationship between the two subsystems is inconsistent with the subjective relationship assumptions, the overall efficiency of the system and the efficiency of each subsystem will be biased. The conventional two-stage DEA models require predetermining the relationship between the subsystems within the system based on the subjective judgment of the decision-maker. Based on this, this paper proposes a three-step method to solve the two-stage DEA. First, the position relation among subsystems is determined according to the optimal weights through the model. According to the status relationship among subsystems, the decision units are grouped, and the two-stage DEA model of cooperative game or non-cooperative game is used to analyze the efficiency in each group. This method reduces the subjectivity of decision making and analyzes the efficiency of each decision unit applying the most appropriate two-stage DEA model to find the source of inefficiency. Finally, this paper verifies the rationality and validity of the method by analyzing the water use efficiency of industrial systems in China. It is found that most regions in China value economic development more than environmental protection (as evidenced by the DEA weights). What is more, the method proposed by the paper can be generalized for any two-stage DEA problem.

Modelling NPLs and identifying convergence phenomenon of banks: a case of pre-during and immediate after the crisis years in India

PurposeComparing conventional data envelopment analysis (DEA) model with contemporary Seiford and Zhu model, this study aims to evaluate the technical efficiency (TE) of Indian banks from 1998/99 to 2016/17 in the presence of non-performing loans (NPLs).Design/methodology/approachTo examine TE, this study has considered a novel approach, i.e. linear monotone decreasing transformation as suggested by Seiford and Zhu (2002), which treats undesirable output as a desirable output in the framework of Charnes, Cooper and Rhodes (CCR)-based output-oriented DEA approach. In particular, to remove the biasness from the estimated efficiency scores, Simar Wilson (1998, Algorithm #1) has been applied, which is perhaps the first attempt in this kind of literature till now. This study further tries to investigate the notion of sigma and unconditional β-convergence in TE using two-step system generalized method of moments model in dynamic panel framework.FindingsTreatment of NPLs using conventional DEA model misinterprets the TE scores, while a true picture emerges when the NPLs are correctly accounted as an undesirable output in banks’ loans production process. Efficiency has declined during the crisis years, but it recovered immediately after the crisis years in India. However, a sudden and steep deterioration in efficiency scores has been seen from 2013 till the most recent study period. Public sector banks and old private banks have reported higher average efficiency scores than new private banks (NPBs) and foreign banks (FBs) in India. However, FBs are the only commercial banks that maintained their efficiency levels during crisis years in India. This study also saw the persistence and presence of σ-convergence phenomena in TE for Indian banks, reflecting the ability to reach up to “Catch-up” phenomenon owing to the lower dispersion and persistence of convergence in TE by the Indian banks.Practical implicationsThe actual efficiency score can only be estimated when the NPL will be considered as an undesirable output rather than a desirable output when designing the loan production process of banks. Although the ownership clusters of all commercial banks in India need to formulate stricter policies to increase the level of assets quality and efficiency, but, NPBs need to pay some more efforts in this direction. This study’s outcome has the potential to provide useful information for regulators and policymakers, which suggests that in which direction or in which clusters improvement are needed to raise the level of asset quality and technical efficiency in the coming years.Originality/valueFor a long time, there has been the existence of trade-offs between researchers, like which is the best model for accounting for NPLs? Traditional or contemporary? Thus, our study aims to add knowledge to the limited stock of NPL modelling in the efficiency literature. Dynamic convergence in TE scores in Indian banks has yet not to be tested, which is another novelty of the study.

DeaR-Shiny: An Interactive Web App for Data Envelopment Analysis

In this paper, we describe an interactive web application (deaR-shiny) to measure efficiency and productivity using data envelopment analysis (DEA). deaR-shiny aims to fill the gap that currently exists in the availability of online DEA software offering practitioners and researchers free access to a very wide variety of DEA models (both conventional and fuzzy models). We illustrate how to use the web app by replicating the main results obtained by Carlucci, Cirà and Coccorese in 2018, who investigate the efficiency and economic sustainability of Italian regional airport by using two conventional DEA models, and the results given by Kao and Liu in their papers published in 2000 and 2003, who calculate the efficiency scores of university libraries in Taiwan by using a fuzzy DEA model because they treat missing data as fuzzy numbers.

A credibility approach on fuzzy slacks based measure (SBM) DEA model

Data Envelopment Analysis (DEA) is a multi-criteria technique based on linear programming to deal with many real-life problems, mostly in nonprofit organizations. The slacks-based measure (SBM) model is one of the DEA model used to assess the relative efficiencies of decision-making units (DMUs). The SBM DEA model directly used input slacks and output slacks to determine the relative efficiency of DMUs. In order to deal with qualitative or uncertain data, a fuzzy SBM DEA model is used to assess the performance of DMUs in this study. The credibility measure approach, transform the fuzzy SBM DEA model into a crisp linear programming model at different credibility levels is used. The results came from the fuzzy DEA model are more rational to the real-world situation than the conventional DEA model. In the end, the data of Indian oil refineries is collected, and the efficiency behavior of the companies obtained by applying the proposed model for its numerical illustration.

Integrating decision making conditions into DEA models

Data Envelopment Analysis (DEA) is a popular non-parametric technique for the assessment of efficiency of a set of homogeneous decision making units (DMUs) with the same set of inputs and outputs. In the conventional DEA models, it is assumed that all variables are fully controllable. However, in the real-world applications of DEA, some of the variables are completely uncontrollable or partially controllable. In this paper, we are concerned about partially controllable variables which are called semi-discretionary variables. In DEA models, in the presence of semi-discretionary variables, decision makers have partial control on these variables and the proportional changes are possible to some extent. Previous DEA models with semi-discretionary variables consider a certain level of control on the variables which is fixed and it is given by decision makers or a higher authority. Since this level is usually given by experts, it is possible that in some cases all experts may not come up with an agreement, so in this paper we consider variable instead of fixed level of control on each semi-discretionary variable. In the presence of semi-discretionary variables, the proportional changes in inputs and out-puts may not be feasible and as a result the obtained target value by conventional DEA models is not achievable for an inefficient DMU. Thus, we propose a bi-objective model to evaluate DMUs when modifying a variable to its target value should be managed by decision makers in a voting system. One of the advantages of the proposed model is including decision making conditions directly into a DEA model.

Eco-efficiency evaluation in wastewater treatment plants considering greenhouse gas emissions through the data envelopment analysis-tolerance model

The eco-efficiency evaluation in wastewater treatment plants (WWTPs) is used to know and improve the environmental and economic efficiency of these processes, systems, products, and services. The eco-efficiency evaluations in WWTP contemplate the inputs to be minimized, the desirable results to be maximized, and the undesired results to be minimized. Data envelopment analysis (DEA) is a widely used method to evaluate the eco-efficiency of WWTPs; integrating several approaches in a single index, traditional DEA models do not take into account the uncertainty in the data. This study evaluates the eco-efficiency of a sample of Catalan WWTPs, considering the uncertainty of the data (DEA tolerance model), and it is for the first time that together with CO2, other greenhouse gas (GHG) such as CH4 and N2O are considered as part of the process outputs. GHG emissions were quantified using methods reported in the literature. Seven hundred twenty-nine eco-efficiency scores were estimated for each WWTP instead of a single score like conventional DEA models, analyzing optimistic and pessimistic scenarios. The WWTPs were classified according to the estimated eco-efficiency scores, accounting for the uncertainty in each of the scenarios, and demonstrating the changes in the performance of the WWTPs in the different scenarios. Only two WWTPs were eco-efficient in all the scenarios evaluated. This approach provides essential information to improve efficiency and innovation in the wastewater sector.

Performance benchmarking of achievements in the Olympics: An application of Data Envelopment Analysis with restricted multipliers

Data envelopment analysis (DEA) is a useful tool for measuring the relative efficiencies of participating nations in the Olympic Games. DEA models with restricted multipliers have been used to refine efficiency evaluations by imposing additional information. Existing DEA models for evaluating Olympic medals do not focus on multiplier restrictions regarding input. To fill this research gap, this study incorporates a data fitting technique of medal prediction using ordinary least squares regression in input multiplier restrictions of the conventional DEA model. We show that the efficiency of the proposed model can be decomposed into the achievement ratio of substantial medal total and the unit value index of medals. Such decompositions can be used to analyze the effectiveness of host nations and athlete development initiatives. For an illustrative empirical application, we examine the target that the Brazilian Olympic Committee (BOC) set for the 2016 Summer Olympic Games (Rio 2016). Our results explain the extremely high feasibility of Brazil’s target of being in the top 10 medals table in Rio 2016.

Structural and operational management of Turkish airports: a bootstrap data envelopment analysis of efficiency

This paper explores the structural and operational dimensions of the efficiencies of airports. The two-stage procedure is suggested to assess the efficiencies of airports in this study. In the first-stage, Classification and Regression Tree, which is one of the machine-learning approaches used to divide the airports into homogeneous and thus comparable sub-groups. In the second stage, the bootstrap data envelopment analysis approach obtains more precise structural and operational efficiency scores. To illustrate the proposed framework use, we applied it to a real case associated with Turkish airports. The results demonstrate that this framework presents a more comprehensive assessment of airport performance rather than conventional data envelopment analysis models. Moreover, it provides to show the deficiencies of the structural and operational management of airports. The findings can help anywhere airport authorities as well as Turkish airport authorities.