Data envelopment analysis for scale elasticity measurement in the stochastic case:with an application to Indian banking

In the nonparametric data envelopment analysis literature,scale elasticity is evaluated in two alternative ways:using either the technical efficiency model or the cost efficiency model.This evaluation becomes problematic in several situations,for example(a)when input proportions change in the long run,(b)when inputs are heterogeneous,and(c)when firms face ex-ante price uncertainty in making their production decisions.To address these situations,a scale elasticity evaluation was performed using a value-based cost efficiency model.However,this alternative value-based scale elasticity evaluation is sensitive to the uncertainty and variability underlying input and output data.Therefore,in this study,we introduce a stochastic cost-efficiency model based on chance-constrained programming to develop a value-based measure of the scale elasticity of firms facing data uncertainty.An illustrative empirical application to the Indian banking industry comprising 71 banks for eight years(1998–2005)was made to compare inferences about their efficiency and scale properties.The key findings are as follows:First,both the deterministic model and our proposed stochastic model yield distinctly different results concerning the efficiency and scale elasticity scores at various tolerance levels of chance constraints.However,both models yield the same results at a tolerance level of 0.5,implying that the deterministic model is a special case of the stochastic model in that it reveals the same efficiency and returns to scale characterizations of banks.Second,the stochastic model generates higher efficiency scores for inefficient banks than its deterministic counterpart.Third,public banks exhibit higher efficiency than private and foreign banks.Finally,public and old private banks mostly exhibit either decreasing or constant returns to scale,whereas foreign and new private banks experience either increasing or decreasing returns to scale.Although the application of our proposed stochastic model is illustrative,it can be potentially applied to all firms in the information and distribution-intensive industry with high fixed costs,which have ample potential for reaping scale and scope benefits.

Frame Work of Data Envelopment Analysis—A Model to Evaluate the Environmental Efficiency of China'S Industrial Sectors

Objective To evaluate the environmental and technical efficiencies of China＇s industrial sectors and provide appropriate advice for policy makers in the context of rapid economic growth and concurrent serious environmental damages caused by industrial pollutants. Methods A data of envelopment analysis （DEA） framework crediting both reduction of pollution outputs and expansion of good outputs was designed as a model to compute environmental efficiency of China＇s regional industrial systems. Results As shown by the geometric mean of environmental efficiency, if other inputs were made constant and good outputs were not to be improved, the air pollution outputs would have the potential to be decreased by about 60% in the whole China. Conclusion Both environmental and technical efficiencies have the potential to be greatly improved in China, which may provide some advice for policy-makers.

Fuzzy data envelopment analysis approach based on sample decision making units

The conventional data envelopment analysis （DEA） measures the relative efficiencies of a set of decision making units with exact values of inputs and outputs. In real-world prob- lems, however, inputs and outputs typically have some levels of fuzziness. To analyze a decision making unit （DMU） with fuzzy input/output data, previous studies provided the fuzzy DEA model and proposed an associated evaluating approach. Nonetheless, numerous deficiencies must still be improved, including the α- cut approaches, types of fuzzy numbers, and ranking techniques. Moreover, a fuzzy sample DMU still cannot be evaluated for the Fuzzy DEA model. Therefore, this paper proposes a fuzzy DEA model based on sample decision making unit （FSDEA）. Five eval- uation approaches and the related algorithm and ranking methods are provided to test the fuzzy sample DMU of the FSDEA model. A numerical experiment is used to demonstrate and compare the results with those obtained using alternative approaches.

Bootstrapping Data Envelopment Analysis of Efficiency and Productivity of County Public Hospitals in Eastern, Central, and Western China after the Public Hospital Reform

China implemented the public hospital reform in 2012. This study utilized bootstrapping data envelopment analysis（DEA） to evaluate the technical efficiency（TE） and productivity of county public hospitals in Eastern, Central, and Western China after the 2012 public hospital reform. Data from 127 county public hospitals（39, 45, and 43 in Eastern, Central, and Western China, respectively） were collected during 2012–2015. Changes of TE and productivity over time were estimated by bootstrapping DEA and bootstrapping Malmquist. The disparities in TE and productivity among public hospitals in the three regions of China were compared by Kruskal–Wallis H test and Mann–Whitney U test. The average bias-corrected TE values for the four-year period were 0.6442, 0.5785, 0.6099, and 0.6094 in Eastern, Central, and Western China, and the entire country respectively, with average non-technical efficiency, low pure technical efficiency（PTE）, and high scale efficiency found. Productivity increased by 8.12%, 0.25%, 12.11%, and 11.58% in China and its three regions during 2012–2015, and such increase in productivity resulted from progressive technological changes by 16.42%, 6.32%, 21.08%, and 21.42%, respectively. The TE and PTE of the county hospitals significantly differed among the three regions of China. Eastern and Western China showed significantly higher TE and PTE than Central China. More than 60% of county public hospitals in China and its three areas operated at decreasing return scales. There was a considerable space for TE improvement in county hospitals in China and its three regions. During 2012–2015, the hospitals experienced progressive productivity; however, the PTE changed adversely. Moreover, Central China continuously achieved a significantly lower efficiency score than Eastern and Western China. Decision makers and administrators in China should identify the causes of the observed inefficiencies and take appropriate measures to increase the efficiency of county public hospitals in the three areas of China, especially in Central China.

Robust data envelopment analysis based MCDM with the consideration of uncertain data

The application of data envelopment analysis （DEA） as a multiple criteria decision making （MCDM） technique has been gaining more and more attention in recent research. In the practice of applying DEA approach, the appearance of uncertainties on input and output data of decision making unit （DMU） might make the nominal solution infeasible and lead to the efficiency scores meaningless from practical view. This paper analyzes the impact of data uncertainty on the evaluation results of DEA, and proposes several robust DEA models based on the adaptation of recently developed robust optimization approaches, which would be immune against input and output data uncertainties. The robust DEA models developed are based on input-oriented and outputoriented CCR model, respectively, when the uncertainties appear in output data and input data separately. Furthermore, the robust DEA models could deal with random symmetric uncertainty and unknown-but-bounded uncertainty, in both of which the distributions of the random data entries are permitted to be unknown. The robust DEA models are implemented in a numerical example and the efficiency scores and rankings of these models are compared. The results indicate that the robust DEA approach could be a more reliable method for efficiency evaluation and ranking in MCDM problems.

Data envelopment analysis procedure with two non-homogeneous DMU groups

The classic data envelopment analysis（DEA） model is used to evaluate decision-making units＇（DMUs） efficiency under the assumption that all DMUs are evaluated with the same criteria setting. Recently, new researches begin to focus on the efficiency analysis of non-homogeneous DMU arose by real practices such as the evaluation of departments in a university, where departments argue for the adoption of different criteria based on their disciplinary characteristics. A DEA procedure is proposed in this paper to address the efficiency analysis of two non-homogeneous DMU groups. Firstly, an analytical framework is established to compromise diversified input and output（IO） criteria from two nonhomogenous groups. Then, a criteria fusion operation is designed to obtain different DEA analysis strategies. Meanwhile, Friedman test is introduced to analyze the consistency of all efficiency results produced by different strategies. Next, ordered weighted averaging（OWA） operators are applied to integrate different information to reach final conclusions. Finally, a numerical example is used to illustrate the proposed method. The result indicates that the proposed method relaxes the restriction of the classical DEA model,and can provide more analytical flexibility to address different decision analysis scenarios arose from practical applications.

Integrating dual-role variables in data envelopment analysis

Traditional data envelopment analysis（DEA） theory assumes that decision variables are regarded as inputs or outputs,and no variable can play the roles of both an input and an output at the same time.In fact,there exist some variables that work as inputs and outputs simultaneously and are called dual-role variables.Traditional DEA models cannot be used to appraise the performance of decision making units containing dual-role variables.The paper analyzes the structure and properties of the production systems comprising dual-role variables,and proposes a DEA model integrating dual-role variables.Finally the proposed model is illustrated to evaluate the efficiency of university departments.

What explains the technical efficiency of banks in Tunisia?Evidence from a two‑stage data envelopment analysis

In this study we examine the potential determinants of technical efficiency for the Tunisian commercial banking sector over the period of 1995–2017.First,we estimate banking technical efficiency with a radial and non-radial bootstrap data envelopment analysis.For the radial technique,we use an input-oriented approach and for non-radial we use the Range Adjusted Measure(RAM).Second,we use a double bootstrapping regression technique to estimate the influence of a set of eventual determinants on technical efficiency.Finally,based on all possible regressions,we gauge the overall effect of each determinant.Our results reveal that the input-oriented and RAM approach gave somewhat similar results.We found that the return on equity,the expense to income ratio,the loan to deposit ratio,and the growth rate are insignificant to Tunisian banking technical efficiency.In particular,banking technical efficiency increases with capitalization and inflation,whereas,it decreases with size,number of bank branches,management to staff ratio,and loan to asset ratio.In addition,we identified evidence supporting the moderate success of the last decade of reforms and a noticeable one for the post-revolution reforms in helping improve banking technical efficiency.The post-revolution reforms,largely revolving around reinforcing the rules of good governance and banking supervision,coupled with the restructuring of public banks,were found to be insufficient to raise overall banking technical efficiency despite improvement in the technical efficiency of private banks.

An Efficiency Assessment of Tuberculosis Treatment on Health Centers: A Data Envelopment Analysis Approach

This study utilized Data Envelopment Analysis (DEA) in assessing the efficiency of health center in tuberculosis (TB) treatment. Assessing the efficiency of health center treating TB is a vital and sensitive topic, because there is a cumulative amount of public funds devoted to healthcare. In this research, a DEA model has been correlated to evaluate and assess the efficiency of 17 health centers. The researchers selected the health budget and the number of health workers as input variables likewise, the number of people served, number of TB patients served, and TB patients treated (%) as output variables. Based on the result of the study, only five (5) health centers out of seventeen (17) have 100% efficiencies throughout the 2 years period. It is recommended that other health centers should learn from their efficient peers recognized by the DEA model so as to increase the overall performance of the healthcare system. Likewise, health centers should integrate Health Information Technology to deliver healthier care for their patients.

Assessing the Relative Efficiency of Health Systems in Sub-Saharan Africa Using Data Envelopment Analysis

We assess the relative efficiency of health systems of 35 countries in sub-Saharan Africa using Data Envelopment Analysis. This method allows us to evaluate the ability of each country to transform its sanitary “inputs” into health “outputs”. Our results show that, on average, the health systems of these countries have an efficiency score between 72% and 84% of their maximum level. We also note that education and density of population are factors that affect the efficiency of the health system in these countries.

Energy Efficiency Analysis of White Button Mushroom Producers in Alburz Province of Iran: A Data Envelopment Analysis Approach

The aim of this study was to determine energy consumption pattern and specifically to measure and benchmark the efficiency for white button mushroom production in Alburz province of Iran. The data used in this study were collected by interviewing mushroom producers in the region. In the surveyed farms, average yield and total energy consumption were calculated as around 208.46 kg·ton-1 compost and 133.25 MJ·ton-1, respectively. The results revealed that fossil fuel (40.43%), compost (30.45%) and electricity (27.42%) consumed the bulk of energy. The results of DEA approach also showed that 12 and 14 farmers had efficiency score of unity. Electricity and fossil fuel were found to be used in excess in target mushroom production farms. Moreover, we came to the conclusion that the total energy consumption can be reduced to 120.15 MJ·ton-1 for mushroom production in which diesel fuel energy (50.89 MJ·ton-1), FYM (37.32 MJ·ton-1) and electricity (30.34 MJ·ton-1) energies were considerably significant.

A New Approach for Ranking Efficient Units in Data Envelopment Analysis and Application to a Sample of Vietnamese Agricultural Bank Branches

This paper proposes a new approach for ranking efficiency units in data envelopment analysis as a modification of the super-efficiency models developed by Tone [1]. The new approach based on slacks-based measure of efficiency (SBM) for dealing with objective function used to classify all of the decision-making units allows the ranking of all inefficient DMUs and overcomes the disadvantages of infeasibility. This method also is applied to rank super-efficient scores for the sample of 145 agricultural bank branches in Viet Nam during 2007-2010. We then compare the estimated results from the new SCI model and the exsisting SBM model by using some statistical tests.

Discriminating Among Relatively Efficient Units in Data Envelopment Analysis: A Comparison of Alternative Methods and Some Extensions

This paper concentrates on methods for comparing activity units found relatively efficient by data envelopment analysis (DEA). The use of the basic DEA models does not provide direct information regarding the performance of such units. The paper provides a systematic framework of alternative ways for ranking DEA-efficient units. The framework contains criteria derived as by-products of the basic DEA models and also criteria derived from complementary DEA analysis that needs to be carried out. The proposed framework is applied to rank a set of relatively efficient restaurants on the basis of their market efficiency.

The Treatment of Non-zero Slacks in Data Envelopment Analysis

The paper studies the non-zero slacks in data envelopment analysis. A procedure is developed for the treatment of non-zero slacks. DEA projections can be done just in one step.

Economic efficiency of radiology wards using data envelopment analysis: Case study of Iran

Background: In evaluating the activities and performance of radiology units, the main aim of applying feasible scientific methods is to use technological and human resources optimally. One of the suitable scientific methods in this field is determining the technical, economic, and allocative efficacy of these centers. We aimed to assess the economic efficiency of radiology units of hospitals affiliated to Shiraz University of Medical Sciences, southern Iran. Methods: In this descriptive-analytical cross-sectional study, the technical, economical, and allocative efficiency of 27 radiology units of public hospitals was assessed using data envelopment analysis. The input oriented envelopment form with the assumption of the varied outputs with respect to the scale was used. Related forms were filled using the existing information in the archives of radiology centers. Input variables in this study were the number of radiology devices, the number of expert personnel, the number of technicians, equipment maintenance and depreciation costs, and the salaries of the experts and technician. Output variables included the number of admitted patients and the number of photographic film. Then, data were analyzed using the DEAP software for calculating the various forms of efficiency. Results: The mean scores of economic, technical, and allocative efficiencies of radiology units were 0.749, 0.880, and 0.852, respectively. The final score of economical efficiency was lower than the technical and allocative efficiency scores. Only 15% of radiology units were economically efficient. Conclusion: Economical efficiency can be attained when resources are used in the best possible way and not wasted. Therefore, a combination of inputs that comprise the lowest costs should be selected.

Public Transit Performance Evaluation Using Data Envelopment Analysis and Possibilities of Enhancement

This study evaluates the operational performance of all routes of Sajha Bus Yatayat operating inside Kathmandu valley using Data Envelopment Analysis (DEA) in terms of efficiency and effectiveness score. This approach allows us to access the relative performance of transit system in absence of historical data and research to compare with. To explore the possibility of enhancing the performance, scenarios were created for relatively underperforming routes and long route problem by changing the most important input variable and output variables accordingly with regression model where it was relevant. Partial Least Squares (PLS) regression was used to determine the most influential input variables to the output variables. DEA was conducted to access the performance of all routes under these scenarios. Underperforming routes except the longest route under the first set of scenarios, emerge to be better performing efficiently without considerable negative deviation in effectiveness. The result of second set of scenarios for long route problem suggests that the longest route’s performance can be enhanced significantly upon proper route alignment. Scenarios development and evaluation can help lead transit companies to explore the strategies to facilitate operational performance enhancement.

Promoting Balance in Output Efficiencies for Cross-Efficiency Evaluation in Data Envelopment Analysis

Cross-efficiency evaluation is recognized as an effective way of efficiency assessment for a set of decision making units (DMUs) in the framework of data envelopment analysis (DEA). It has been generally suggested that secondary goals be introduced for cross-efficiency evaluation owing to the non-uniqueness of optimal solutions in self-evaluation. This paper develops a variety of secondary goals in the spirit of promoting balance in the output efficiencies of the DMU under evaluation. The proposed models attempt to make each output contribute as equally as possible to the self-evaluated efficiency. In this way, the weight flexibility can for one thing be reduced by the introduced secondary goals with selections from alternate optimal solutions, in addition to counting on the dilution of flexibility in the subsequent peer-evaluation. The proposed approach might be applicable to evaluation problems in which multiple outputs are considered important and balance is encouraged to put all dimensions into sufficient use. The effectiveness of the proposed approach and its comparisons with some relevant secondary goals are illustrated empirically using numerical examples.

Measuring West-Africa Ports Efficiency Using Data Envelopment Analysis

The present study measured the relative efficiency of five major commercial ports in West Africa, using three different Data Envelopment Analysis (DEA) methods, the CCR, BCC, and Windows I-C methods over the years 2005-2016. Seven input variables and one output variable were used in the model analysis. The CCR and BCC methods were used to evaluate the technical and scale efficiency while the Windows I-C method provided a comprehensive ranking of the studied ports. The results showed that the scale efficiency score of 89.53% indicated that on average the production scale of the ports had deviated from the most productive scale size (MPSS) by 10.47%. These results revealed that the source of the overall inefficiency is due to scale rather than pure technical inefficiency. Hence, in order to improve the overall efficiency, the two scaled inefficient ports of Abidjan and Cotonou should adjust their scale of operations. Then, further investigations were conducted to detect correlations between various variables used in this study. The research found that the absence of any correlation for non-significant variables and negative correlation for the significant variables throughout time resulted from the fact that these variables were not fully utilized. Meaning that they were not efficiently used to boost the container throughput on a scale basis, the research also found that a pandemic or insecurity could easily impact seaports activities with the case of the Ebola outbreak which strucked the West African region from the year 2013 to 2016, or the terrorism threats which prevailed in the region around the year 2012. Thus, for ports to stand out in the present fiercely competitive environment, ports authorities ought to analyze their operational scale to identify whether or not the production size is fitting before further port capacity expansion.

Assessment of Dry Port Efficiency in Africa Using Data Envelopment Analysis

This work involves the evaluation of dry port competitiveness through analysis of efficiencies for selected dry ports in Africa. Five dry ports were selected and analysis carried out over a period of four years. The dry ports considered were Mojo and Kality in Ethiopia, Mombasa in Kenya, Isaka in Tanzania and Casablanca in Casablanca, Morocco. Data Envelopment Analysis (DEA) was applied for this work. Container throughputs for the various ports under consideration were used as the output variable for the data analysis model, while the number of reach stackers, the number of tractors, the number of forklifts and the size of the dry port were used as the input variables. From the results, the Mombasa dry port was found to be the most efficient with an average score of approximately 1 over the period under consideration. Casablanca was the second efficient dry port with an average score of 0.762, while Isaka was the least efficient with an average score of 0.142. This research is significant since the African countries have embraced the dry port concept, as witnessed in the huge investments in this sector, and would serve to highlight areas that need improvement for the few existing dry port facilities, most of which are undergoing expansion as well as modernization.

Calculation of Agricultural Production Efficiency Based on a Three-stage Data Envelopment Analysis Model and Analysis of the Spatial-temporal Characteristics: A Case Study of the Yangtze River Economic Belt

In response to the strategic call for the " Great Protection" of the Yangtze River Economic Belt and to fulfill the important historical tasks assigned by the state to the provinces and cities of the area,the Yangtze River Economic Belt is adjusting the agricultural industry structure,optimizing the input-output ratio,and ensuring stable and sustainable agricultural production. Based on the combination of the three-stage Data Envelopment Analysis( DEA) model and cluster analysis,this study examined the Yangtze River Economic Belt from 2008 to 2018 to measure its agricultural production efficiency and to analyze its temporal and spatial characteristics. Studies showed that exogenous environmental factors significantly( P < 5%) impacted agricultural production efficiency in the Yangtze River Economic Zone,and there were temporal and spatial differences. These included:(1) after excluding environmental factors,the overall agricultural production efficiency of the Yangtze River Economic Zone had improved. Sichuan Province and Jiangsu Province were at the forefront of efficiency,whereas the agricultural production efficiency of Shanghai had declined obviously.(2) The agricultural production efficiency of the Yangtze River Economic Belt varied year by year,with fluctuating development. The middle reaches of the Yangtze River had advanced agricultural production efficiency more than the upstream and downstream regions,and the agricultural production efficiency of the individual provinces did not match their economic and social development.(3) Increases in labor,land,irrigation,and other input factors increased agriculture production efficiency,and there was no correlation between fiscal investment,per capita gross domestic product( GDP) and agricultural production efficiency,while the disaster-affected area had a significantly negative impact on agricultural production efficiency.