Variable Returns To Scale Model Research Articles

Analisis Efisiensi Bank Umum Persero Menggunakan Metode Data Envelopment Analysis (DEA)

The purpose of this study is to analyze the efficiency of state-owned commercial banks and to analyze their development. Where efficiency is a parameter in measuring performance for banks. The Data Envelopment Analysis approach was used in this study with a quantitative method. Where there are two models used, namely the VRS (Variable Return to Scale) model and the CRS (Constant Return to Scale) model. State-owned commercial banks are the sample in this study for the period 2019 to 2022. Capital, Third Party Funds (DPK), and operational costs are used as variable inputs. Meanwhile, credit is used as a variable output. Based on the results of the analysis, it shows that based on the VRS model, the efficiency of state-owned commercial banks was obtained in almost all years except in 2019. Furthermore, the results of the analysis using the CRS model, several banks obtained efficiency results and several banks obtained inefficiency results. Even based on the average efficiency that existed during the study period, all of them experienced inefficiency, it's just that the efficiency value was at 0.9. The difference in the results of the two models used is because the VRS model overrides the production scale factor, while the resulting CRS model value is Overall Technical Efficiency

Factor affecting technical efficiency of the banking sector: Evidence from Ethiopia

An efficient bank is more robust to shocks, fosters competitiveness, and promotes stability of the financial system. This study estimates Ethiopia’s commercial banks’ level of efficiency and its determinants during the period 2014–2020. Data Envelopment Analysis (DEA), Malmquist DEA, and Tobit regression were employed to analyze the data. The result indicated that the average efficiency score of banks in the constant returns to scale (CRS), variable returns to scale (VRS), and scale efficiency (SE) models were 95.5%, 99.85%, and 96.95% , respectively. Furthermore, in the VRS model, a state bank is more efficient than private banks. During the study period, the Total Factor Productivity (TFP) of Banks improved by 1%. According to the Tobit model, the efficiency of banks grows with an increment in the number of branches, bank size, and credit risk. However, when, liquidity risk and the log of the fixed asset increase, bank efficiency will decrease. The level of capitalization, log of GDP, and inflation, on the other hand, do not influence bank efficiency. Therefore, banks should pay close attention to aspects that influence technical efficiency.

Variable returns to scale DEA\u2014Taguchi approach for ternary additives optimization in expansive soil subgrade enhancement

In this study, variable returns to scale (VRS) data envelopment analysis was integrated into the Taguchi approach to optimize ternary additives for expansive soil enhancement. The ternary additives selected were sawdust ash (SDA), quarry dust (QD) and ordinary Portland cement (OPC). The additives were set as the input variables while multiple responses obtained from the experiments performed with the Taguchi orthogonal array were set as the output variables. Each row in the orthogonal array were defined as a decision making unit (DMU) in the optimization process and output-oriented VRS model was used to obtain the efficiency score for each DMU. Next, benevolent formulation was utilized to obtain the multipliers for the inputs and outputs which were subsequently used to determine the cross efficiency scores for each DMU. The cross-efficiency scores were used to construct the cross-efficiency matrix. Thereafter, the mean cross-efficiency score (MCES) was determined for each DMU. Parameter level that maximizes the MCES was chosen as the optimal level for that parameter. Optimum combination of additives was found at A6 B2 C3. Lastly, confirmatory experiments performed by blending the soil with the optimum combination of additives showed the effectiveness of this method in the enhancement of expansive soil properties.

Eco-efficiency measurement as an approach to improve the sustainable development of municipalities: A case study in the Midwest of Brazil

Global challenges related to energy consumption, water scarcity, deforestation, and environmental pollution have a direct impact on municipalities in Brazil and other countries around the world. Thus, the present study aims to evaluate eco-efficiency and its determinants in 41 Brazilian municipalities between 2014 and 2016 in the area covered by the Araguaia River Valley, in the Midwest of Brazil, Goiás state region. The Araguaia River Valley is considered of economic and especially environmental importance. It is located in one of the main Brazilian river basins, adjacent to states comprising the Legal Amazon, one of the world's most important biomes. To measure the eco-efficiency rate, we applied Data Envelopment Analysis (DEA) via the model of output-oriented variable returns to scale (VRS). Variables used as input include Energy Consumption, Water Consumption, Number of Inhabitants, Fleet of Vehicles, Territorial Area, Deforested Area, and output is the ratio between GDP per capita and Deforested Area. In the second stage, we used Tobit regression with eco-efficiency rate as the dependent variable. For the analyzed period, results show low mean eco-efficiency in the VRS model, with values of 0.45 (2014) and 0.48 (2016). Results indicate that the municipalities of Castelândia in 2014, and Santo Antônio da Barra in 2016, achieved a sustainable balance between environmental and economic variables, contributing to conservation. That suggests that these municipal areas be a benchmark for the others and to local and national public managers, as well as the effective DEA technology applicability in calculating eco-efficiency. In contrast to these two cases, the Mineiros municipality (Araguaia River headwater area) obtained a very low eco-efficiency score. This is extremely concerning since this is an important and sensitive area in this region. In the second stage of the research, the Tobit model indicates that Deforested Area in 2014 and 2016 was significant and negatively correlated with the dependent variable, while Water Consumption (2016) was positively correlated with eco-efficiency. However, the robustness test shows the significant and negative correlation between Water Consumption and eco-efficiency in both years, additionally, the test confirms the results for the Deforested Area variable. These results are important to support policymakers and public managers in the development of more sustainable and eco-efficient municipalities worldwide.

Multivariate returns to scale production frontiers

In this study, we develop multivariate returns to scale (MRTS) and illustrate the advantages of MRTS over the existing standard returns to scale (RTS) such as: constant RTS (CRS), variable RTS (VRS), nondecreasing RTS (NDRS), nonincreasing RTS (NIRS), and hybrid RTS (HRS). We explain theoretical reasonings for introducing MRTS when evaluating datasets with multiple inputs and multiple outputs. We demonstrate how to generate an MRTS production possibility set (PPS) and show its differences with the existing standard RTS PPSs. A linear programming model is proposed to estimate the frontier of the MRTS PPS and measure the corresponding radial efficiency scores of units. The proposed score for each unit is neither less than the corresponding score of the standard radial CRS model nor greater than the corresponding score of the standard radial VRS model. We propose a specific-to-general approach that users should consider when evaluating their datasets.

The Extent, Dynamics, and Potential Predictors of Technical Efficiency and Capacity Utilisation in Small-Scale Fisheries in Oman

This paper investigates the extent, dynamics, and factors influencing technical efficiency (TE) and capacity utilisation (CU) in small-scale fisheries (SSF) using a two-stage data envelopment analysis (DEA) approach covering the period 2010–2012. A considerable extent of boat-level technical inefficiency, capacity underutilisation and scale inefficiency were evident. On average, TE and CU levels under the constant returns to scale (CRS) and variable returns to scale (VRS) models declined over time. The TE and CU scores of 2010 remained unaltered with the addition of ‘fishing time’ as an input to the model. The proportion of boats with unitary scale efficiency (SE) decreased from 26 % in 2010 to 12 % in 2012. The underutilisation rates of the inputs ‘crew’ and ‘fishing time’ ranged from 15.5 % to 31.6 % and 15.8 % to 28.6 %, respectively. Among the species category, the extent of excess capacity was 70 % to 156 % and 47 % to 119 % under the CRS and VRS models, respectively. The second-stage DEA results indicated that the explanatory variables ‘fishing location’, ‘catch per unit of effort’ (CPUE), ‘fuel costs’ and ‘crew share’ significantly influenced CU under the CRS model. In contrast, the significant influence of subsidies and other operating costs were noted under the VRS model. For the TE case, ‘age’, ‘education’, ‘subsidy’ and ‘CPUE’ were found to be significant under the CRS and VRS models. Other significant variables were found in the study under CRS and VRS models. Finally, the results from the descriptive and empirical analysis under the two-stage DEA model are discussed together with policy implications.

Modifying the convexity condition in Data Envelopment Analysis (DEA)

Conventional Data Envelopment Analysis (DEA) models are based on a production possibility set (PPS) that satisfies various postulates. Extension or modification of these axioms leads to different DEA models. In this paper, our focus concentrates on the convexity axiom, leaving the other axioms unmodified. Modifying or extending the convexity condition can lead to a different PPS. This adaptation is followed by a two-step procedure to evaluate the efficiency of a unit based on the resulting PPS. The proposed frontier is located between two standard, well-known DEA frontiers. The model presented can differentiate between units more finely than the standard variable return to scale (VRS) model. In order to illustrate the strengths of the proposed model, a real data set describing Iranian banks was employed. The results show that this alternative model outperforms the standard VRS model and increases the discrimination power of (VRS) models.

Classifying dual role variables in DEA: The case of VRS

Data envelopment analysis is a mathematical programming methodology commonly used to evaluate the relative efficiencies of each of a set of decision-making units in terms of a selected set of input and output variables. In many situations, however, it can happen that certain variables can play roles of either inputs or outputs. This dual-role or classification concept was examined in earlier research for settings where the production possibility set was defined in terms of a constant returns to scale (CRS) technology. The current article extends the classification models to those cases where a variable returns to scale (VRS) technology is present. We show that if one simply adds a free-in-sign variable to the CRS model, the resulting VRS model can be unbounded. To alleviate this circumstance, we develop an altered version of the conventional VRS model which is shown to be feasible and bounded. We provide numerical examples to demonstrate the applicability and strength of the proposed methodology.

Measurement of Ministry/Institution Budget Performance Efficiency Using Data Envelopment Analysis (DEA)

Efficiency is one of the tools used by the Government to measure the success of an activity. Based on PMK Number 214/ PMK.02/2017 it is regulated regarding the measurement and Evaluation of Budget Performance for the implementation of Work Plans and Ministries/Institutions Budgets. To measure budget performance achievement based on aspects of implementation 4 (four) variables i.e. budget absorption, output achievements, efficiency, and consistency of budget absorption towards planning, are used. This study aims to measure the efficiency level of Ministries/Institutions budget performance using Data Envelopment Analysis (DEA). However, the variables used are not only based on measurement aspects of implementation according to PMK Number 214/PMK.02/2017 but also the number of satker (satuan Kerja). The approach used in the DEA model is Constant Return to Scale (CRS) model and Variable Return to Scale (VRS) model. This study uses the DEA model approach by comparing the results of the CRS model with VRS model. Based on DEA results, the number of Ministries/Institutions that have efficient scores is less than the number of Ministries/Institutions with inefficient scores. In addition, based on the value of slacks in each Ministries/Institutions, the variables that need to be improved are the coordination among satkers in when they are recording their performance achievements in the SMART application. Other variables that also require improvements are the ministry/agency’s willingness to revise their Disbursement Plan (RPD) after each budget revision and the speed at which they spend their budget once DIPA is stipulated.

Input-use Efficiency of Irrigation Farmers in Southwest Nigeria

This study estimated the technical and water-use efficiency of irrigation farmers in Southwest Nigeria. A multistage sampling procedure was employed to interview one hundred and eighty-five irrigation farmers. Descriptive statistics, Data Envelopment Analysis Program (DEAP) and Tobit regression model were used to describe and analyze the determinants of inefficiency among irrigation farmers. The result of the descriptive statistics showed that there were more male farmers (82.2%) with a mean household size of 3.7. The mean area of irrigated land was 1.29ha. with about 84 percent of farmers cultivating on rented land. The average income from irrigation farming was N 38,650.27 per month. The sprinkler irrigation (Centre Pivot) was used by 85.4% of the farmers. The water fee for farmers was N 10,000 and the average cost of diesel for irrigating their farmland was estimated to be N 34,400 per production. The variation in input use and the output produced is considerably large. The DEAP results showed that on average, the farmers achieved only 79% Constant Return to Scale (CRS) technical efficiency, 85% Variable Return to Scale (VRS) technical efficiency and 22% water use efficiency. The Tobit regression results showed that farmers’ characteristics like age (0.008), household size (0.048), area of land irrigated (0.000), income (0.075) and drip irrigation method (0.041) were significant under CRS, whereas gender, education, experience, labour and sprinkler irrigation method were not significant. Under VRS model, significant variables includes age (0.032), gender (0.003), education (0.080), experience (0.059) and area of land irrigated (0.000), while gender (0.004), household size (0.086), education (0.027), experience (0.045), area of land irrigated (0.000) and labour (0.089) were significant for sub-vector VRS. It appears that farmers have little incentives to use water in an efficient way. In this sense, a public-private partnership could trigger better management of irrigation facilities and efficient water use among farmers.

Application of data envelopment analysis in environmental impact assessment of a coal washing plant: A new sustainable approach

The main problem of traditional methods of environmental impact assessment (EIA) is that in most of the existing algorithms and methods, such as Leopold, Folchi and RIAM, the main attention is to the destructive effects of the proposed plan, and the advantages of the industrial project are less noticeable. This has led to a permanent challenge between environmental organizations and industrial stakeholders. Data envelopment analysis (DEA) is a new approach of assessing the industrial units. Besides, it considers the positive economic and social impacts of the project and provides a comprehensive assessment of the industrial unit. With this approach, the environmental impacts of an industrial unit have been considered as “inputs” and its positive economic and social impacts considered as the “outputs” of the DEA models. Therefore, the problem of impact assessment changes into a DEA model. In the present study, the Alborz Sharghi Coal washing plant in northern Iran has been considered as a case study for implementing the DEA-EIA approach, and 19 plant activities and 11 environmental components have been used to evaluate the environmental effects of the plant. To solve the EIA problem, two commonly used DEA approaches, called CRS (constant returns to scale) and VRS (variable returns to scale), have been used. The DEA results identified the critical environmental components of the plant that should be considered seriously. Also, drawing the “potential improvement” diagram in the DEA method is an effective tool for determining the high risk activities of the factory and applying them in development plans. Besides, using the VRS model with maximize-output approach showed that some of the plant activities had the most differences with optimal mode and these components should be considered in future development plans. Finally, it can be concluded that, assessing the environmental impacts of the mineral industries with VRS maximize-output approach, is closer to the concept of sustainable development and cost-benefit analysis.

An Entropy-Based Cross-Efficiency under Variable Returns to Scale

Cross-efficiency evaluation is an effective methodology for discriminating among a set of decision-making units (DMUs) through both self- and peer-evaluation methods. This evaluation technique is usually used for data envelopment analysis (DEA) models with constant returns to scale due to the fact that negative efficiencies never happen in this case. For cases of variable returns to scale (VRSs), the evaluation may generate negative cross-efficiencies. However, when the production technology is known to be VRS, a VRS model must be used. In this case, negative efficiencies may occur. Negative efficiencies are unreasonable and cause difficulties in calculating the final cross-efficiency. In this paper, we propose a cross-efficiency evaluation method, with the technology of VRS. The cross-efficiency intervals of DMUs were derived from the associated aggressive and benevolent formulations. More importantly, the proposed approach does not produce negative efficiencies. For comparison of DMUs with their cross-efficiency intervals, a numerical index is required. Since the concept of entropy is an effective tool to measure the uncertainty, this concept was employed to build an index for ranking DMUs with cross efficiency intervals. A real-case example was used to illustrate the approach proposed in this paper.

Efficiency Analysis of East Asian Zinc Smelters and the Effects of Capacity and Bonus Zinc on Efficiency

Non-ferrous metals are widely used as basic materials in various industrial fields, and zinc is a metal that is produced and used next to iron, aluminum, and copper. In this study, DEA (data envelopment analysis) was applied to measure the efficiency of 43 zinc smelters in three countries in East Asia: Korea, China, and Japan. The constant returns to scale (CRS) and the variable returns to scale (VRS) models, and the slack-based measure (SBM) were used for the analysis. As a result of the efficiency analysis, there were three efficient zinc smelters in the CRS model, 14 in the VRS model and 14 in the SBM. The average efficiency was 0.458 based on the SBM, which indicates that there is room for improvement in efficiency. In addition, the average scale efficiency value was 0.689, showing the scale to be inefficient. Therefore, it can be seen that the labor cost and the energy cost must be brought to an appropriate level. The Tobit regression analysis was used to analyze the causes of efficiency. The greater the capacity and the larger amount of bonus Zn of the refinery, the higher the efficiency of the refinery.

Economic growth and environmental degradation: a conditional nonparametric frontier analysis

This paper examines the effect of economic growth and the association of environmental degradation on economies’ technological change and technological catch-up. Using a conditional nonparametric frontier analysis to a sample of 73 economies over the time period 1980–2014, empirical evidence of the examined relationship is provided both under full and partial frontiers in the constant and variable returns to scale (VRS) models. Specifically, the newly proposed time-dependent conditional nonparametric frontier estimators have been applied. In our case the time-dependent conditional efficiency estimators allow us to model directly the effects of growth and time on economies’ estimated performance without requiring any specification of the production functional form and without assuming the separability condition between time, economic growth and the support of inputs and outputs. The overall results reveal that the efficiency results of full and partial frontiers tend to lead to the same results, except in the cases of full VRS models where energy use and carbon dioxide emissions are incorporated as an additional input and output, respectively. The results demonstrate that countries with a higher environmental efficiency are those that have signed the first agreement between nations (Kyoto Protocol) to mandate country-by-country reductions in greenhouse-gas emissions, while countries that have not signed are relatively inefficient. Ultimately, the empirical findings also suggest that the effect of economic growth is determined by economies’ development stage and geographical region.

Modified variable return to scale back-propagation neural network robust parameter optimization procedure for multi-quality processes

ABSTRACTSelecting the optimum process parameter level setting for multi-quality processes is cumbersome. Previous methods were plagued by complex computational search, unrealistic assumptions, ignoring the interrelationship between responses and failure to select optimum process parameter level settings. The methods of variable return to scale (VRS) back-propagation neural network (BPNN) previously adopted were limited by the use of weak models, poor discriminatory tendency and an inability to select the optimum parameter level setting. This study applied a modified VRS–adequate BPNN topology model in the robust parameter procedure to solve this problem. Here, standard VRS models are allowed to self-assess, leading to partitioning. The upper bound of the free variable of the VRS model is restricted and the VRS penalization coefficient is adopted to determine the optimum process parameter level setting. The effectiveness of the proposed model measured by the total anticipated improvement yielded the highest total improvement over the existing methods.

Integrated data envelopment-thermoexergetic optimization framework for multicomponent distillation system with multiexergetic response in the robust parameter design procedures

ABSTRACTIntegrated exergetic, data envelopment analysis (DEA)-robust parameter design framework is proposed to optimize and select thermo-feasible multicomponent distillation system which is a herculean task through reported exergy analysis techniques. It attempts to reduce the thermodynamic computational search for optimal sequence and to handle the effects of variations. Conventional exergetic analysis obtained the thermo-responses, variations are smoothened by robust signal-to-noise ratio procedures, variable return to scale (VRS) partitioning is imposed prior to the efficiency determination by the facet VRS model and penalization coefficient model is employed to select the optimum. The numerical illustration reveals its specificity and provides vivid and panoramic insight into actual efficient systems and those that need improvement. This study shows that exergetic analysis when integrated with DEA and robust parameter procedures can interrelate adequately, efficiently and effectively to optimize multicomponent distillation process and can be applied for optimizing energy-intensive systems especially those with multi-response processes.

Pengukuran Efisiensi Kinerja Sekolah Dasar lewat Model Data Envelopment Analysis

This study aims to measure the performance efficiency of elementary schools in Special Capital Region of Jakarta, especially Central Jakarta district in the period 2014/2015 by using data envelopment analysis (DEA) approach. DEA is a non-parametric method to measure efficiency of decision making units (DMUs). DEA compares several homogeneous DMUs based on a number of inputs to produce the expected outputs. This study uses descriptive method using DMU as many as 103 public elementary schools that are A-accredited with three inputs and four outputs. Data is analyzed using DEAP version 2.1 application by comparing CRS (Constant Returns to Scale) model and VRS (Variable Returns to Scale) model. Results show that: 1) in CRS model, there are 8 public elementary schools (7.77 percent) have efficient performances while in VRS model there are 14 public elementary schools (13.59 percent) have efficient performances; 2) VRS model is better than CRS model in measuring the efficiency performance of public elementary schools in Central Jakarta.

Developing a Model for Determining Corporate Performance after Bank Acquisition

This is a panel study designed to develop a model to determine bank performance after acquisition. Data Envelopment Analysis (DEA) using Value Added Approach which adopted both Constant Returns to Scale (CRS) and Variable Returns to Scale (VRS) models was employed to determine efficiency scores of the banks. The study examined 62 banks from 30 countries acquired in 2006 and which had data with Fitch/IBCA/Bureau Van Dijk Bankscope database. The banks were divided into large and small groups. The study period was from 2007-2012. Results from the VRS model were used for further analyses. The Malmquist TFP was determined to identify key value drivers in the acquired banks. Five environmental variables namely Corruption Perception Index (CPI), Bank Industry Concentration (BIC), Total Assets, Gross Domestic Product (GDP) and Real Interest Rates were regressed on the efficiency scores using fractional regression models to determine their impact on efficiency scores. The “Spearman rho” correlation between efficiency scores and profitability ratios was established.

EFFICIENCY ANALYSIS OF MEAT PROCESSING INDUSTRY IN INDONESIA

This paper aims to analyze the efficiency of the meat processing industry in Indonesia large-scale and medium-year period 1990-2013. The method used data envelopment analysis (DEA) model of Variable Return to Scale (VRS) Input-oriented. It was found that, the estimation value Constant Return to Scale (CRS) model of efficiency with an average of 89.38 percent, which means that the industry is only able to optimize the resources available inputs to produce a production of 89.38 per cent, in other words there is still potential inputs that they can be optimized for 10.62 percent assuming all companies operating at an optimal scale. VRS model results by an average of 95.7 percent, which means that the efficiency is still below 100, there are inefficiencies at 4.3 percent, assuming the company is not operating at optimal scale due to factors existing constraints, medium scale efficiency (Scale) an average of 93.36 per cent less than 100 percent means that the industry is on a scale of inefficiency. The implications of negative growth efficiency or below 100 percent is the need for skills development of workers in order to adapt to technological upgrading and make the selection of efficient combination of inputs.

Comparison of Performance Efficiency of Improved Network Coding Multicast Algorithms using Data Envelopment Analysis

In this paper, comparison of multicast algorithms was carried out in terms of performance Efficiency using Constant Return to Scale (CRS) and Variable Return to Scale (VRS) Model. The Improved Network Coding Algorithm (INCA) which was developed to minimize the consumption of Bandwidth during multicasting was used. The aim of the INCA is achieving cost effective multicast in order to encourage group communication over the internet. Data Envelopment Analysis was applied on the results obtained from the INCA in order to determine their performance efficiency using a number of input parameters. Simulation results obtained showed that the VRS Model performs better than the CRS Model. General Terms Multicasting, Modeling, Decision Making Units, Algorithms, Bandwidth Utilization, Performance Efficiency