Efficiency Of Decision Making Units Research Articles

Performance Measurement: Machine Learning as a Complement to DEA for Continuous Efficiency Estimation

Data Envelopment Analysis (DEA) is a well-established non-parametric technique for performance measurement to access the efficiency of Decision-Making Units (DMUs). However, its inability to predict the efficiency values of new DMUs without re-conducting the analysis on the entire dataset has led to the integration of Machine Learning (ML) in previous studies to address this limitation. Yet, such integration often lacks a thorough evaluation of ML's adaptability in replacing current DEA process. This paper presents the results of an empirical study that employed eight ML models, two DEA variants, and a dataset of S&P500 companies. The findings demonstrated ML’s remarkable precision in predicting efficiency values derived from a single DEA run and comparable performance in predicting the efficiency of new DMUs, thus eliminating the need for repeated DEA. This discovery highlights ML’s robustness as a complementary tool for DEA in continuous efficiency estimation, rendering the practice of re-conducting DEA unnecessary. Notably, boosting models within the Ensemble Learning category consistently outperformed other models, highlighting their effectiveness in the context of DEA efficiency prediction. Particularly, CatBoost demonstrated its superiority as the top-performing model, followed by LightGBM in the second position in most cases. When extended to five enlarged datasets, it shows that the model exhibits superior R² values in the CRS scenario.

Ranking DMUs by using interval efficiencies in data envelopment analysis

Efficiency is a relative measure that allows assessment across different ranges. Evaluating the performance of decision-making units (DMUs) from an optimistic perspective yields the best relative efficiency (optimistic efficiency), which establishes an efficiency frontier. Conversely, evaluating from a pessimistic perspective produces the worst relative efficiency (pessimistic efficiency) and creates an inefficiency frontier. This study examines the efficiency of DMUs in two scenarios and proposes models for adjustment coefficient. The pessimistic and optimistic efficiencies are adjusted to the lower and upper bounds of the DMUs based on the adjustment coefficient, enabling determination of efficiency intervals for all DMUs, as well as evaluation and ranking. A Hurwicz criterion-based approach is introduced and applied to compare and rank the interval efficiencies of DMUs. Two numerical examples are examined using the proposed DEA adjustment coefficient models to demonstrate its potential application and validity.

Advancing Efficiency Sustainability in Poultry Farms through Data Envelopment Analysis in a Brazilian Production System.

The production efficiency factor is widely used to measure the zootechnical performance of a batch of broilers. The unit cost of production brings new elements to improve efficiency evaluation and financial sustainability for this activity in agriculture. This research aims to evaluate the production efficiency level of the crop to maximize the return on investment. This study uses Data Envelopment Analysis (DEA) with the computational processing of the SIAD software (Integrated Decision Support System). The variables selected were poultry housing, age at slaughter, feed consumed, mortality, and unit cost. The chosen output variable was the total available weight. The analysis spans 31 decision-making units (DMUs) composed of integrated producers, unveiling a frontier of efficiency delineated by the most exemplary DMUs. Notably, only two DMUs, specifically DMU 4 and DMU 23, approached the threshold of maximum relative efficiency. This research illuminates the critical role of unit cost in enhancing the assessment of production efficiency and financial sustainability within the agriculture environment. By setting benchmarks for efficient management and operational protocols, our findings serve as a cornerstone for improving practices among less efficient DMUs, contributing significantly to the literature on agricultural efficiency and offering actionable insights for the poultry farming sector.

An Application of Data Envelopment Analysis and Game Theory for Appraisal of Balanced Scorecard Indexes in Media Industry

Todays, the media industry encompasses all businesses that allow information to be shared (traditional and digital media). Media is vast, large, and ever-growing, and is an incredibly popular sector at the minute, and an extremely interesting area to research work in. This paper considered a news agency of media organization as a Decision-Making Unit (DMU). The aim of the study was to evaluate the role of Balanced Scorecard (BSC) indexes on measuring the efficiency of DMU. This was done by a new hybrid model of Data Envelopment Analysis (DEA), cooperative game theory and Shapley value index. The initial values of the DEA model were selected from among the BSC indexes in four perspectives (i.e., financial, customer, internal processes, and growth and learning). Finally, the proposed model was experimented on a case study and the computational results were obtained. The results showed that the profitability ratio with a Shapley value of 2.903 and the percentage of satisfied audiences with a Shapley value of 0.404 had the highest and lowest reflection in performance assessment, respectively. The rest of the results were presented and discussed in detail. This study can reveal scientific orientation to increase organizational performance to media managers and policymakers.

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.

A new parallel framework algorithm for solving large-scale DEA models

With the rapid development of social informatization and platform economy, evaluating high-frequency and large-scale data has attracted widespread attention. One relevant and current research topic deals with finding high-quality decision-making units (DMUs) and scoring each DMU using a shorter computing time. The Framework method (Khezrimotlagh et al., 2019) has the fastest computing time so far. We propose a new parallel framework algorithm in this study. This algorithm effectively reduces the calculation time for finding all efficient DMUs and evaluate all DMUs in the BCC (Banker, Charnes and Cooper) model, the CCR (Charnes, Cooper and Rhodes) model, FG (Färe and Grosskopf) model and ST (Seiford and Thrall) model. The proposed algorithm has a reasonable selection method and optimal numbers of initial hull which can decrease the running time effectively. The extensive experimental results presented in this study show that when the input and output data are generated by uniform approach or normal approach, the density will increase with the increase of input and output dimensions, and show a growth trend like that of the S curve, which is similar to the distribution function of the Gamma distribution. We also tested our method using a real-life dataset. Compared with the previous methods, our method is shown to be more suitable for the input and output data generated by normal approach and decreases the calculation time by at least 12.52%. Furthermore, it has strong advantages in decreasing calculation time of solving the CCR model irrespective of whether the input data and output data are uniformly distributed or normally distributed.

Enchanting performance measurement and management with data envelopment analysis: Insights from bibliometric data visualization and analysis

While the breadth of applicative uses of data envelopment analysis (DEA) has increased over time, this non-parametric frontier methodology has proven effective for measuring how efficient decision-making units (DMUs) are. One of its uses is performance measurement in various organizations — from universities and banks to investment funds and entrepreneurial small and medium-sized enterprises. Following a search inquiry in the Scopus and Web of Science databases, we found no bibliometric analysis and keyword co-occurrence network visualization of just the use of DEA for performance management. With this study, we attempt to investigate the DEA literature for performance measurement and management, considering articles in scientific peer-reviewed journals, which are indexed in the Web of Science database. The analysis and visualization of the bibliometric data are based on 89 articles from the start of the century onward. We present the annual trends of published articles, journals, authors, and countries leading the scientific discussion and citation analysis. A detailed keyword visualization analysis was performed and is discussed in this article alongside the paths for future hotspots of the use of DEA for performance management. The findings have implications for both the academic community and practitioners, business leaders, managers, and policy-makers.

Maximum slacks-based measure of efficiency in network data envelopment analysis: A case of garment manufacturing

The conventional slacks-based measure (SBM) model is widely applied to measure the relative efficiency of a set of decision making units (DMUs) because the measured efficiency is not affected by weakly efficient frontiers. This model seeks the target point on the production frontier that is farthest to the assessed DMU to calculate efficiency, which requires more effort for the DMU to reach to become efficient. This paper develops a model to calculate the maximum SBM efficiency for general network production systems. Different from the conventional minimum SBM efficiency that is always less than the radial efficiency for inefficient DMUs, the maximum SBM efficiency can be greater than the radial efficiency. The measured efficiency satisfies the monotonicity property. The efficiencies of the component divisions of the network system can also be calculated at the same time. A garment manufacturing company whose major operations comprise cutting and sewing is studied using the developed model. The results show that the average maximum SBM efficiency is 35 % higher than the average minimum SBM efficiency and the sewing operation contributes more to the system efficiency than the cutting operation does.

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.

Intertemporal environmental efficiency assessment in China: A new network-based dynamic super-efficiency measure.

In order to make a complete ranking of intertemporal environmental efficiency in a dynamic manner, this paper combines the network-based dynamic data envelopment analysis (DEA), super-efficiency with the unified efficiency under natural and managerial disposability, and designs a dynamic DEA model and the corresponding dynamic super-efficiency DEA model. Compared with previous studies, the proposed measure can fully rank the overall environmental efficiency of all decision making units (DMUs) in a dynamic manner, and more importantly, it provides the information about when and what factors lead to inefficiency or efficiency of DMUs. The proposed models are applied to examine the environmental efficiency of 30 provinces in China from 2008 to 2017. The results show that there are significant regional differences of environmental efficiency in China. In addition, slack analysis shows that most eastern efficient provinces have no obvious advantages in energy consumption, labor and waste water emission; most central and western efficient provinces have no advantages in sulfur dioxide (SO2) emissions and GDP. To improve overall efficiency, eastern inefficient provinces should mainly focus on reducing energy consumption, SO2 emissions and labor, and increasing capital investment in right years, central and western inefficient provinces can focus on reducing SO2 emissions and labor in most years, most of provinces need to increase gross domestic capital formation.

A comprehensive neutrosophic model for evaluating the efficiency of airlines based on SBM model of network DEA

This research aims to provide an innovative framework for evaluating airline performance through the networking of decision-making units (DMUs) and neutrosophic data. As a consequence, we propose a comprehensive methodology for assessing the efficiency of these decision-making units. Network data envelopment analysis (DEA) models deal with measurements of relative efficiency of DMUs when the insight of their internal structures is available. In network models, sub-processes are connected by links or intermediate products. Links have the dual role of output from one division or sub-process and input to another one. Therefore, improving the efficiency score of one division by increasing its output may reduce the score of another division because of increasing its input. To address this conflict, we proposed a new approach in Slack-Based Measure (SBM) framework and neutrosophic logic, which provide deeper insights regarding the sources of inefficiency. Our approach is a new network model, in which the intermediate products are classified into two groups of “input-type”, and “output-type” that their excesses and shortfalls directly concern with the objective function. The results of the illustrated case and analysis show that the constructed model may successfully produce performance assessments. By taking into account the number of slacks or surpluses of these products in the objective function, the proposed model gives analysts and managers a more accurate assessment of network structure efficiency. In this paper, we present a new model in the field of network data envelopment analysis with SBM approach in a neutrosphonic environment, in which for the first time the nature of intermediate products in terms of input or output is investigated. Also, the proposed framework is the first attempt to performance evaluation in neutrosophic network DEA.

Discrete-Event Simulation (DES) and Banker, Chames and Cooper Data Envelopment Analysis (BCC-DEA) Models in Improving the Allocation Officers in Outpatient Department

This study aims to propose an improvement model for the queuing system and determine the best and most appropriate allocation suggestion for officers at the outpatient department of a public clinic in Johor. In this study, Arena Simulation Software and Lingo Software were used. Discrete-Event Simulation (DES) and Banker, Chames, and Cooper Data Envelopment Analysis (BCC-DEA) models were used to determine the best improvement model across various alternatives. The Min-Max of officers was suggested as an improvement model. The mathematical formulation has been programmed and tested in the Lingo 19.0 software, and Decision-Making Units (DMU) would be suggested. After that, each DMUs were run in Arena Simulation Software. Then, the input and output of each DMUs were determined. The researcher used BCC Model Input-Oriented to reduce the input required to produce the optimal output. The mathematical formulation has been programmed again and tested in the Lingo 19.0 software. Based on the results, DMU is considered an efficient choice if the value θ_0 is one (θ_0= 1). DMU is considered an inefficient alternative if the value θ_0 is not one (θ_0 ≠ 1). The input-oriented BCC model needs to identify the most effective and efficient DMU because they have multiple DMUs that are rated as efficient. So, the Super Efficiency model was used to identify the most efficient and suitable DMU. The mathematical formulation has been programmed again and tested in the Lingo 19.0 software to identify the Super Efficiency model

Setting closer targets based on non-dominated convex combinations of Pareto-efficient units: A bi-level linear programming approach in Data Envelopment Analysis

Data Envelopment Analysis (DEA) very often sets unrealistic targets, which require from the decision-making units (DMUs) a huge amount effort, perhaps non-assumable, for their achievement. For the identification of best practices in the benchmarking, this paper proposes considering as peers not only DEA efficient DMUs but also those that are Pareto efficient, and allowing for reference sets spanning convex combinations that are not dominated by observed DMUs. It is therefore an approach that somehow relaxes the convexity in DEA, and sets targets representing best practices in the sense that they define a course of action leading to results that are not worse than those of the real plans. A bi-level linear programming (BLP) DEA model is developed which finds the closest targets from a convex combination of the DMUs in a reference set satisfying such non-dominance requirement. This approach has proven to be successful in setting targets that require an effort significantly smaller than that needed to achieve the closest targets on the strong efficient frontier of both the DEA and the free disposal hull (FDH) technologies. In the empirical illustration, we have observed reductions in the order of 40 percentage points on average in the total effort required for their achievement, thus setting more realistically implementable directions for improving performance towards best practices than those provided by conventional DEA and FDH.

A data envelopment analysis-based clustering approach under dynamic situations

Cluster analysis is one of the most useful tools for exploring the underlying structure of a given data set and is being applied in a wide variety of engineering and scientific disciplines. And Data Envelopment Analysis (DEA) is a data-driven tool for the efficiency evaluation of homogeneous decision-making units (DMUs). Few studies paid attention to the combination of the clustering approach and DEA. The paper proposes a method of clustering DMUs by the production function under dynamic situations. The paper determines the reference vector using the extreme efficient DMUs, defines the asymmetric dissimilarity, and realizes the clustering by a hierarchical algorithm. The numerical experiments are illustrated to examine the validity of the proposed method, and the experiments show that the method gives reasonable results. The proposed method is the first study for clustering time-varying DMUs by the production function.

Development of Bi-Objective Fuzzy Data Envelopment Analysis Model to Measure the Efficiencies of Decision-Making Units

The proposed bi-objective fuzzy data envelopment analysis (BOFDEA) model is a new approach to assess the performance efficiency of decision-making units (DMUs) in uncertain environments using α-cuts. The model is based on fuzzy data envelopment analysis (FDEA) and considers two objectives, and a solution method and ranking system are provided. Generally, the efficiency score obtained for a DMU using the α-cut approach is an interval. Intervals are partially ordered sets, due to which ranking intervals is a challenging task. The proposed BOFDEA model with α-cuts provides the efficiency of DMUs in the crisp form, not in the form of intervals. Due to this, ranking DMUs with the proposed method’s help becomes very easy and less computationally. The proposed model has been validated through numerical examples, and a real-world application in the education sector has been shown to demonstrate its practicality.

Benchmark Approach for Efficiency Improvement in Green Supply Chain Management with DEA Models

Nowadays, concerns about environmental issues are increasing. Therefore, companies and producers are under pressure from government rules and regulations on one hand, and on the other hand, maintaining customer satisfaction concerning cares about the environment. Green supply chain management (GSCM) is a procedure to increase efficiency and decrease environmental effects for companies that collaborate with customers and suppliers. According to GSCM, there is some research about applying green aspects of purchasing, design, manufacture, distribution, packaging, marketing, and reverse logistics of supply chains to improve their company’s performance regarding environmental issues. Moreover, recently, DEA as a nonparametric model is used to evaluate the efficiency and performance of supply chains as decision-making units (DMUs). However, previous studies on efficiency improvement in GSCM did not investigate the effect of some economic and environmental factors together such as service level, emissions (CO2), and size of the supply chains (arcs) on the efficiency of the whole supply system. These factors are essential as they can affect the manager’s ability to distinguish the true performance of a green supply chain. Thus, evaluating the efficiency of GSCM by DEA models and imposing the green principles to find out the efficient ones for increasing management performance is vital. Fulfilling the mentioned research gap, this paper developed a benchmark approach to verifying efficient DMUs and potential efficient DMUs which may improve costs and efforts to become efficient. In the case study, the benchmarks and potentially efficient DMUs are found by DEA standard models and slight adjustment is conducted for potentially efficient DMUs to change their status to efficient DMUs. Moreover, the effect of some green principles on the efficiency value of DMUs is verified using Tobit regression before and after the mentioned modification. A set of realistic results provided for the priority of potential DMUs modification confirmed the applicability of the proposed procedure.

Measuring Efficiencies of Dairy Buffalo Farms in the Philippines Using Data Envelopment Analysis

This study aimed to measure the efficiency scores of 75 dairy buffalo farms in the province of Nueva Ecija, Central Luzon, Philippines, using an input-oriented, variable-return-to-scale Data Envelopment Analysis (DEA) model. The farmer-informants or decision-making units (DMUs) were categorized as smallholders, family modules, and semi-commercial in operations. Personal interviews using structured questionnaires were done to gather various information on the socio-economic and management practices of the DMUs. Output in the form of volume and value of milk produced and inputs such as quantities and costs of biologics, feeds, forage, and labor were also collected and evaluated among individual DMUs. The efficiency scores were computed using PIM-DEA software, which identified fully efficient DMUs lying on the frontier line (scores of 1.0) and those enveloped by it (inefficient DMUs with scores of less than 1.0). The overall mean Technical Efficiency (TE), Allocative Efficiency (AE), and Economic Efficiency (EE) scores among the DMUs were 0.80, 0.81, and 0.65, respectively. Most of the inefficient DMUs were in the smallholder category. In sum, smallholder DMUs classified under low and moderate TE clusters should reduce their inputs by 53.31% and 40.01%, respectively, to become fully efficient. Likewise, higher lambda values among efficient peer DMUs indicate the best practice frontiers that the inefficient peer DMUs can benchmark with. Extension and advisory services can help promote the best management practices of the frontiers to improve the TE, AE, and EE of the inefficient DMUs.

How to improve the future efficiency of Covid-19 treatment centers? A hybrid framework combining artificial neural network and congestion approach of data envelopment analysis

Covid-19 virus (severe acute respiratory syndrome coronavirus 2, SARS-CoV-2) threatens the health of human beings worldwide, imposing a concern for the world and prompting governments to control the contagion. Although vaccination is a proper tool to control the transmission, the efficient allocation of limited health-care resources to massive patients can improve the effectiveness of medical services. Relying on the Artificial Neural Network (ANN), the aim of this research is to enhance the future efficiency of Covid-19 treatment centers by forecasting their efficiency and providing benchmarks. To do this, we use the congestion approach of data envelopment analysis (DEA) based on the theory of economies of scale principles. In the traditional input-oriented DEA, inefficient decision-making units (DMUs) can become efficient merely by reducing the inputs. However, this may not always be true in real-world applications such as improving the efficiency of COVID-19 treatment centers (DMUs). Meaning that the treatment centers with less congested inputs (e.g., ventilators, test equipment, pulmonologists, and nurses, etc.) normally have higher mortality rates. For this reason, in this study, we take the congested inputs approach into account to provide proper benchmarks for the inefficient treatment centers. According to the congestion approach of DEA, an optimum increase in congested inputs can lead to a greater than a proportional increment in outputs. In other words, if more respiratory equipment, pulmonologists, patient rooms, nurses and beds, etc. are allocated to Covid-19 treatment centers, not only the number of deaths (undesirable outputs) are decreased, but also the number of recoveries (desirable outputs) are increased. Such an optimal rise in the congested inputs is determined in pairwise comparisons derived from the model. Accordingly, in this study, first, considering the congestion approach of DEA and historical data of five periods, we identify the initial efficiency of Iranian Covid-19 treatment centers. Then, by running ANN, we forecast the future inputs and outputs, the overall efficiency, and rank of the treatment centers. By doing this, the prospective efficient and inefficient DMUs are identified, and appropriate benchmarks are determined.

Investigating the Sustainability of Return to Scale Classification in a Two-Stage Network Based on DEA Models

Purpose. The purpose of this study is to sensitivity analysis analyze the returns to scale in two-stage network based on DEA models. The main focus of the firms has always been to obtain the maximum output with the least available resources, which points to the improvement of the firm’s performance and the importance of returns to scale and technical improvement. Design/Methodology/Approach. This study examines the sensitivity of returns to scale classifications in a two-stage DEA network. A new input-oriented model was progressed to identify the efficient decision-making units in the two-stage network, after which a new method of determining the returns to scale classifications in the efficient DMUs in two-stage network (constant, increasing, or decreasing returns to scale) was established. Findings. The stability of the returns to scale classifications in the two-stage network was analyzed. A stability region for changes in primary inputs and final outputs is only determined especially for DMUs that are efficient so that it maintains the classification of the returns to scale units. The results are shown by numerical examples. Practical Implications. The sensitivity analysis of returns to scale classifications is one of the most significant issues in data envelopment analysis (DEA), which plays an essential role in management decisions. Originality/Value. Using this model can help improve the performance of companies by using new tools and also improve the quality of work and increase acceptance competition.

Measurement of DEA-Based ICT Development Efficiency Level with Modified CCR Method

Data Envelopment Analysis (DEA) is the use of non-parametric mathematical programming that is useful for measuring the efficiency of the Decision Making Unit (DMU) of an organization. This study uses the Cooper and Rhodes (CCR) method known as the DEA-CCR multiplier which aims to determine the weight value of each input and output variable of the DMU being evaluated, but it is not sufficient to measure efficiency optimization. To get an efficient value of the weight value of each DMU as a reference to get updated DMU input and output values. So that the DMU efficiency value is obtained which is evaluated. The results of this study show how to modify the Multiplier Model-CCR into the Envelopment Model-CCR. Then displays the efficient level DMU which is evaluated as a result of the weight each DMU gets from the results of processing the LINDO application. Illustrations of changes in input variables and output variables are displayed in the form of tables and figures before and after the changes. The modified DEA-CCR model can also complete DMU super efficiency, effectiveness and productivity.