Traditional Data Envelopment Analysis Research Articles

Estimating the productivity of US agriculture: The Fisher total factor productivity index for time series data with unknown prices

AbstractIn this paper, we propose a straightforward way to estimate the Fisher ideal total factor productivity (TFP) index (FI) in cases where price information is unavailable, using ‘shadow prices’ derived from data envelopment analysis (DEA). A Monte Carlo experiment shows that the shadow price Fisher ideal TFP index (SPFI) can effectively estimate the ‘true’ FI with relatively small (and stable) errors. The empirical application to the US agriculture sector (1948–2017) further suggests that the SPFI is a (superior) alternative to the traditional Malmquist DEA, especially in dealing with unbalanced panel or time series data when price data are unknown.

Healthcare performance analytics based on the novel PDA methodology for assessment of efficiency and perceived quality outcomes: A machine learning approach

Efficient resource allocation in healthcare organizations remains a complex challenge, exacerbated by the intricate data structure and myriad variables involved. While traditional methods like Data Envelopment Analysis have been employed, these often lack the requisite discriminatory power for accurate evaluation. This study introduces the PDA methodology, a fusion of Principal Component Analysis, Data Envelopment Analysis, and Analysis of Variance algorithms, developed in a machine learning environment. To further optimize discriminative power, the Particle Swarm Optimization Algorithm was included. By applying the PDA methodology to hospitals in the Apulia region of Italy, we found that facilities with better perceived quality tend to be more efficient. Furthermore, we identified significant variations in efficiency based on network affiliation and hospital level. Machine learning algorithms, including linear regressions and neural networks, confirmed that our methodology outperforms traditional Data Envelopment Analysis models in precisely distinguishing between varying levels of hospital efficiency. In conclusion, this work provides a fresh perspective for future research and policy decisions in the healthcare domain, demonstrating how the use of advanced and machine learning algorithms can result in more accurate evaluations and targeted interventions.

Comprehensive intuitionistic fuzzy network data envelopment analysis incorporating undesirable outputs and shared resources

The economic growth rate is intricately linked to the efficiency and effectiveness of the banking industry. A widely applicable mathematical technique for such assessments is Data Envelopment Analysis (DEA), which evaluates the relative efficiency of Decision-Making Units (DMUs) by comparing their inputs and outputs. Traditional DEA treats DMUs as black boxes, neglecting internal processes that contribute to inefficiencies in individual DMUs. Additionally, it assumes precise values for inputs and outputs that do not apply to real-world problems. This study introduces a comprehensive network series of two-stage DEA, incorporating shared inputs and intermediate measures, undesirable outputs, external inputs and outputs, initial inputs, and terminal outputs. The network two-stage DEA is extended to intuitionistic fuzzy circumstances to address uncertainty. In this extension, a non-linear intuitionistic fuzzy number, namely a parabolic intuitionistic fuzzy number, represents higher-order imprecise datasets. An illustrative example validates the proposed methodology, and comparisons with existing methods are conducted. Moreover, the methodology is applied to assess the efficiency of Indian public sector banks, demonstrating its applicability and showcasing the efficacy of the procedures and algorithms used. Decision-makers can make better choices using optimal efficiency values to gain insights into inputs, intermediate measures, and outputs.•The research study focused on a network two-stage DEA model, incorporating undesirable outputs and shared resources in the presence of uncertainty.•The methodology involves solving the network two-stage DEA model using parabolic intuitionistic fuzzy numbers.•The experimental analysis involves assessing the efficiency of Indian public sector banks.

Estimating the eco‐efficiency of urban waste services towards sustainable waste management

AbstractAssessing the eco‐efficiency of municipalities regarding the provision of solid waste services is a useful tool for improving its sustainability. However, robust, and reliable methods are needed to benchmark the performance of municipalities. Data envelopment analysis (DEA) methods typically used to assess the eco‐efficiency of municipal solid waste (MSW) service providers. However, the variables used in the eco‐efficiency assessment bear distinct weights for each individual unit, limiting thus interpretation. Therefore, benchmarking the performance of MSW service providers becomes challenging because different conditions are applied. Thus, this study uses a common set weights DEA (DEA‐CSW) model assess the eco‐efficiency of different municipalities in providing MSW services. Eco‐efficiency scores were estimated by integrating total costs, recycled waste and unsorted waste as input, desirable outputs and undesirable outputs, respectively. The empirical application of the model demonstrated that when using DEA‐CSW, only one municipality (out of 36) was eco‐efficient in managing MSW. The weightings for inputs and outputs were allocated based on the degree of satisfaction estimated for each municipality. Satisfaction ranged from 0.829 to 1.000 indicating that none of the municipalities were heavily penalized based on the eco‐efficiency scores estimation when allocating common weights. In conclusion, this study demonstrates that compared to traditional DEA models, the DEA‐CSW approach is more adequate at benchmarking the performance of municipalities regarding the provision of MSW services.

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.

Performance Evaluation of Hospitals under Data Uncertainty: An Uncertain Common-Weights Data Envelopment Analysis.

In the context of healthcare systems, the performance evaluation of hospitals plays a crucial role in assessing the quality of healthcare systems and facilitating informed decision-making processes. However, the presence of data uncertainty poses significant challenges to accurate performance measurement. This paper presents a novel uncertain common-weights data envelopment analysis (UCWDEA) approach for evaluating the performance of hospitals under uncertain environments. The proposed UCWDEA approach addresses the limitations of traditional data envelopment analysis (DEA) models by incorporating the uncertainty theory (UT) to model the inherent uncertainty in input and output data. Also, by utilizing a common set of weights (CSW) technique, the UCWDEA method provides a more robust and reliable assessment of hospital performance. The main advantages of the proposed UCWDEA approach can be succinctly summarized as follows. Firstly, it allows for the comparison of all hospitals on a consistent basis to calculate a realistic efficiency score, rather than an overly optimistic efficiency score. Secondly, the uncertain common-weights DEA approach exhibits linearity, enhancing its applicability. Thirdly, it possesses the capability to extend its utility under various other prevalent uncertainty distributions. Moreover, it enhances the discriminatory power of results, facilitates the ranking of hospitals in the presence of data uncertainty, and aids in identifying the sensitivity and stability levels of hospitals towards data uncertainty. Notably, in order to showcase the pragmatic application and efficacy of the uncertain common-weights DEA model, a genuine dataset has been utilized to evaluate the efficiency of 20 public hospitals in Tehran, all of which are affiliated with the Iran University of Medical Sciences. The results of the experiment demonstrate the efficacy of the UCWDEA approach in assessing and ranking hospitals amidst uncertain conditions. In summary, the research outcomes can offer policymakers valuable insights regarding hospital performance amidst data uncertainty. Additionally, it can provide practical recommendations on optimizing resource allocation, benchmarking performance, and formulating effective policies to augment the overall efficiency and effectiveness of healthcare services.

Weighing in on the average weights: Measuring corporate social performance (CSP) score using DEA

This study develops a new DEA approach to incorporate such market-level information (i.e., average weights over firms) to create a composite corporate social performance (CSP) measure. The new model addresses the challenge that stakeholder expectations—expressed as the CSP weights of different CSP dimensions—are usually unknown at the firm level, but some reliable estimates of the average weights (across firms) are available at the industry or market level. Distinct from the traditional DEA, the new approach can incorporate constraints on the average values of weight distributions and is built on a computational framework new to the literature. The new model is compared with the traditional CSP approach, using longitudinal investment data by socially responsible funds (SRF). The regression results show evidence that the traditional CSP score, which is widely used in the management literature, may not be a reliable CSP score: firms with higher CSP scores tend to have lower SRF investment (in both the number of SRF and total shares). In contrast, the DEA-based CSP scores show the correct and positive correlation with SRF investment. Overall, this paper contributes to the literature by presenting a more reliable CSP approach and a new, generalizable DEA model. This is also the first empirical work documenting the potential validity issue of the traditional CSP scores.

Dynamic DEA with Common Weights: A Case Study of Iranian Airlines

The traditional data envelopment analysis (DEA) models allow each decision-making unit (DMU) to designate the most advantageous weights to maximize its relative efficiency score. Furthermore, for evaluating the performance of DMUs with consecutive processes during specified periods, dynamic data envelopment analysis (DDEA) has received considerable attention from researchers. Considering the dynamic effects, this paper develops a novel dynamic DEA approach based on the analysis of weight restrictions to achieve a common set of weights in dynamic structures. Essentially, the contribution of this research is fourfold: (1) Generating strictly positive weights. (2) Evaluating overall and periodic efficiencies simultaneously. (3) Preventing weight dissimilarity using the proposed Model. (4) Simplifying the comparison and ranking of each unit in a dynamic network nature. To elucidate the details of the proposed approach, the real data set of fourteen Iranian airlines is used to analyze their dynamic performance levels during the period 2018–2020. The results highlight that Iran Air Tour has had the best total efficiency in the years under evaluation. The findings further demonstrate the superiority and applicability of the proposed method in analyzing the dynamic structures with the carryover flows that link the consecutive periods.

Multi-sector environmental efficiency and productivity: A general Leontief optimization method

For efficiency evaluation purposes, a multi-sector economy is always regarded as a “black box” in which the linkages among sectors are not considered. This leads to biased efficiency evaluation and failure to identify the sources of inefficiency. To solve these problems, this paper proposes a general Leontief optimization method for environmental performance estimation. The proposed method can assess the environmental benefits that result from the adjustment of input coefficients and environmental factor intensities. Moreover, this study proposes two models under different elasticity of input substitution assumptions. The difference in environmental efficiency between the two assumptions is defined here as the substitution efficiency. Further, a new Luenberger environmental productivity indicator is constructed that contains a new element reflecting the effect of input substitution. To demonstrate the new method, a numerical example is used to compare the estimation results between the general Leontief optimization method and the traditional data envelopment analysis method. Then, the environmental performance associated with CO2 emissions and energy consumption in China is studied over two years, i.e., 2012 and 2017. By fully opening the “black box” of how to improve environmental efficiency, this study provides a reference with regard to cost-effective specific measures for policymakers in China.

A New Resource Allocation Multiple Criteria Decision-Making Method in a Two-Stage Inverse Data Envelopment Analysis Framework for the Sustainable Development of Chinese Commercial Banks

The resource allocation of commercial banks is a multiple-criteria decision-making issue with complex internal structure, and traditional inverse data envelopment analysis cannot meet its decision-making needs. A two-stage structure with undesirable outputs is constructed to describe the operations of a Chinese commercial bank, and then a new two-stage inverse data envelopment analysis with undesirable outputs is proposed to address its resource allocation multiple criteria decision-making issue. The new method can be used to calculate the minimum input increment required to achieve the goals of desirable and undesirable output under a certain efficiency, and then a specific resource allocation plan can be obtained to promote the sustainable development of commercial banks. Finally, the new method is applied to the resource allocation of 16 Chinese listed commercial banks in 2013, and the application results fully demonstrate the effectiveness of the new method.

Congestion: relation between traditional DEA congestion and two-stage processes congestion

Congestion is a kind of inefficiency because it causes the decision-making units (DMUs) to be inefficient and reduces their output. Identifying inefficient DMUs and determining the cause of their inefficiencies has been one of the most important reasons for referring to the internal structure of DMUs and analyzing the effect of intermediate products on subDMUs (or stages) performance. In this paper, to characterize the cause of the DMU’s congestion, we refer to its internal structure as a two-stage network data envelopment analysis (DEA) and decompose the DMU’s congestion into black-box (BB) and two-stage structure congestion. Also, inputs have two separate and simultaneous roles; the black-box’s inputs role and the stage1’s input role, so three congestion types occur. Thus, we sought to analyze the relation between two types of initial inputs congestion, and intermediate products congestion, and express their effects on BB congestion. Finally, we define three congestion definitions and model the relation between two types of input congestion, intermediate products congestion and BB inputs congestion. Finally, a practical example illustrates the proposed method.

Measuring the Efficiency of Turkish Research Universities via Two-Stage Network DEA with Shared Inputs Model

The efficiency of universities, which have a network structure of production process, is an essential component of performance measurement in education. However, most previous studies use traditional Data Envelopment Analysis (DEA), which disregards the network structure of the production process in universities. This study adopts a two-stage Network Data Envelopment Analysis (NDEA) with shared inputs model to assess the overall, teaching and research efficiencies of Turkish research universities. The findings show that only 6 out of 23 research universities are efficient, and some universities with lower world rankings are more efficient than those with higher rankings. On the other hand, no significant difference was found between the efficiency levels of regions with a high level of socio-economic development and regions with a relatively low level of socio-economic development. The study also evaluates the effects of different priority scenarios on efficiency and the optimal allocation of shared inputs between sub-processes. This study provides guidance for universities seeking to improve their performance and for the Council of Higher Education (CHE) in determining incentives for research universities. It also promotes the use of multi-stage NDEA with shared inputs model over traditional DEA for accurate efficiency assessment in the field of education.

Cross-efficiencyBasedonGeneralized-DEAandItsApplication

Traditional DEA selects automatically inner Decision-Making Units (DMUs) as the reference set. However, some applications might need specified units. Based on generalized DEA and cross-efficiency DEA, a cross-GDEA model is constructed in this paper, which not only considers any specified reference set in efficiency evaluation but also ranks distinguishably all DMUs. A numerical example and comparative analysis are given to illustrate the reasonableness of the cross-GDEA model. Comparative analysis with several established DEA models reveals the superior flexibility and generality of our method. Furthermore, an application aiming at measuring the multiple-factor carbon productivity of Western China is given to verify the applicability of the cross-GDEA model. Results show the proposed approach can contribute to advancing the theoretical and practical research of DEA.

An Exploration of Prediction Performance Based on Projection Pursuit Regression in Conjunction with Data Envelopment Analysis: A Comparison with Artificial Neural Networks and Support Vector Regression

Data envelopment analysis (DEA) is a leading approach in performance analysis and discovering newer benchmarks, and the traditional DEA models cannot forecast the future efficiency of decision-making units (DMUs). Machine learning, such as the artificial neural networks (ANNs), support vector machine/regression (SVM/SVR), projection pursuit regression (PPR), etc., have been viewed as beneficial for managers in predicting system behaviors. PPR is especially suitable for small and non-normal distribution samples, the usual cases in DEA analysis. This paper integrates DEA and PPR to cover the shortcomings we faced while using DEA and DEA-BPNN, DEA-SVR, etc. This study explores the advantages of combining these complementary methods into an integrated performance measurement and prediction model. Firstly, the DEA approach is used to evaluate and rank the efficiency of DMUs. Secondly, we establish two DEA-PPR combined models to describe the DEA efficiency scores (also called the production function) and the DEA-efficient frontier function. The first combined model’s input variables are input–output indicators in the DEA model, and the output variable is the DEA efficiency. In the second model, its input variables are input or output indicators in the DEA model, and the output variable is the optimal input indicator for input-oriented DEA or the output indicator for output-oriented DEA. We conducted positive research on two examples with actual data and virtual small, medium-sized, and large samples. Compared with the DEA-BPNN and DEA-SVR models, the results show that the DEA-PPR combined model has more vital global optimization ability, better convergence, higher accuracy, and a simple topology. The DEA-PPR model can obtain robust results for both small and large cases. The DEA-BPNN and DEA-SVR models cannot obtain robust results for small and medium-sized samples due to overfitting. For large samples, the DEA-PPR model outperforms DEA-BPNN, DEA-SVR, etc. The DEA-PPR combined model possesses better suitability, applicability, and reliability than the DEA-BPNN model, the DEA-SVR model, etc.

An efficiency-based interactive dynamic technique with interval-valued hesitant fuzzy constraint cone for rescue route planning

This paper develops an efficiency-based interactive dynamic technique to design the post-disaster rescue route by combining the data envelopment analysis (DEA), traveling salesman problem (TSP) and interval-valued hesitant fuzzy constraint cone (IVHFCC). The traditional DEA potentially presumes that the weights of the input (output) criteria are unrestricted, resulting in its inapplicability to some complex decision problems. To restrict the weights of input (output) criteria legitimately, this paper constructs an IVHFCC based on expert’s subjective preferences in the form of interval-valued hesitant fuzzy sets. This paper defines the additive consistent normal interval-valued hesitant fuzzy preference relation (NIVHFPR) and analyses its desirable properties. Based on these properties, three linear programming models are proposed to repair the incomplete NIVHFPR, judge the additive consistency of the repaired NIVHFPR and generate the additive consistent NIVHFPR. By incorporating the TSP, DEA and the constructed IVHFCC, an efficiency-based interactive dynamic model is originally proposed to generate the optimal rescue route for the rescue team. Some desirable properties of this efficiency-based interactive dynamic model are analyzed. The validity of this model is demonstrated with a real post-disaster rescue route planning problem of Wenchuan earthquake. Some comparative analyses are provided to show the superiorities of the proposed technique.

A hybrid approach combining data envelopment analysis and recurrent neural network for predicting the efficiency of research institutions

The traditional data envelopment analysis (DEA) method relies solely on current and historical performance and is unable to predict future efficiency. To overcome this limitation, we propose a novel prediction model called the input–output memory network (IOMN), which extends the Recurrent Neural Network (e.g., Long Short-Term Memory (LSTM) and Gate Recurrent Unit (GRU) to forecast the input and output variables in future periods. We then combined the IOMN with the DEA-Malmquist index to evaluate the efficiency of Decision-Making Units (DMUs) from the past to the future. To demonstrate the effectiveness of our proposed model, we conducted a case study of 15 research institutions in the Chinese Academy of Sciences (CAS) and compared its performance with those of linear regression (LR) and support vector regression (SVR) methods. The comparative results show that the IOMN significantly outperformed both the LR and SVR methods. Finally, we fed the past and predicted future data into the DEA-Malmquist index to examine the productivity efficiency trends in research institutions over time. Our results indicate that the annual mean of total factor productivity (TFP) continued to fluctuate at approximately 1 during the observation period. In the future, the geometric mean of TFP will decline slightly by 2.3%, the geometric mean of efficiency change (EC) will decline by 5%, and the geometric mean of technical change (TC) will increase by 2.9%.

Evaluating the technical efficiency of Saudi Arabian telecommunications companies using window DEA and AHP techniques

PurposeThis study aims to evaluate the efficiency of the three telecommunications companies in Saudi Arabia: Saudi Telecom Company (STC), Mobily and Zain over the period of 2010–2019. This evaluation is a step toward improving the performance of the Saudi telecommunications sector.Design/methodology/approachThree multicriteria decision-making (MCDM) techniques were used to calculate technical efficiency. These techniques include the traditional data envelopment analysis (DEA), window DEA and analytical hierarchy process (AHP). The three inputs used were total assets, operating expenses and capital expenditures, whereas the two outputs were sales revenue and total stockholders’ equity.FindingsSTC was ranked first using the three techniques, followed by Zain, and then Mobily. According to the DEA window analysis, these three companies were all efficient only in 2012. The efficiency was high in the initial years, 2010–2013, when it was above 0.90, and it dropped below 0.90 in the subsequent years, 2014–2019. In addition, the efficiency of STC remained high, with an average of 0.990. However, the average efficiencies of Zain and Mobily during this period were 0.807 and 0.804, respectively.Originality/valueThis is the first study to use the three MCDM techniques to evaluate the performance of telecommunications providers. The results show that window DEA is better than the other two techniques at evaluating performance over time, as it has a higher discrimination power than either the traditional DEA or AHP.

Performance Efficiency Measurement in Managing Elementary Schools by Using a Robust Data Envelopment Analysis

Efficiency is one of the determinants of the quality of education in schools. This study aimed to measure the performance of Indonesian provinces in managing elementary schools by using Data Envelopment Analysis (DEA). This research is evaluation-research using a quantitative approach. As many as 34 provinces in Indonesia were defined as DMUs by using six input variables, namely the number of schools, the number of teachers, the number of teachers certified more than the degree of bachelor, the number of students, the number of classes, and the number of libraries. Meanwhile, there were three output variables, namely the number of graduates, the number of schools that were A-accredited, and the average national exam. The robust data envelopment analysis (RDEA) applied the number of replications B=100, 500, and 1000. The results indicated that RDEA provided better accuracy and preciseness. Overall, all 34 provinces in Indonesia were found to have good performances in managing elementary schools where their efficiency scores were above 90% for both the traditional DEA and RDEA approaches. The implications of this research can be used as a study for stakeholders in making policies to improve the quality of education.

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.

Evaluating the efficiency of primary health care institutions in China: an improved three-stage data envelopment analysis approach

BackgroundPrimary health care (PHC) institutions are key to realizing the main functions of the health care system. Since the new health care reform in 2009, the Chinese government has invested heavily in PHC institutions and launched favorable initiatives to improve the efficiency of such institutions. This study is designed to gauge the efficiency of PHC institutions by using 2012–2020 panel data covering 31 provinces in China.MethodsThis study applied an improved three-stage data envelopment analysis (DEA) model to evaluate the efficiency of PHC institutions in China. Unlike the traditional three-stage DEA model, the input-oriented global super-efficiency slack-based measurement (SBM) DEA model is used to calculate the efficiency in the first and third stages of the improved three-stage DEA model, which not only allows the effects of environmental factors and random noise to be taken into account but also deal with the problem of slack, super-efficiency and the comparability of interperiod efficiency values throughout the efficiency measurement.ResultsThe results show that the efficiency of PHC institutions has been overestimated due to the impact of external environmental factors and random noise. From 2012 to 2020, the efficiency of PHC institutions displayed a downward trend. Moreover, there are significant differences in the efficiency of PHC institutions between regions, with the lowest efficiency being found in the northeast region. The efficiency of PHC institutions is significantly affected by residents’ annual average income, per capita GDP, population density, the percentage of the population aged 0–14, the percentage of the population aged 65 and older, the number of people with a college education and above per 100,000 residents, and the proportion of the urban population.ConclusionsSubstantial investment in PHC institutions has not led to the expected efficiency gains. Therefore, more effective measures should be taken to improve the efficiency of PHC institutions in China based on local conditions. This study provides a new analytical approach to calculating the efficiency of PHC institutions, and this approach can be applied to efficiency evaluation either in other fields or in other countries.