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.

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.

Efficiency assessment of coal mine safety input by data envelopment analysis

In recent years improper allocation of safety input has prevailed in coal mines in China, which resulted in the frequent accidents in coal mining operation. A comprehensive assessment of the input efficiency of coal mine safety should lead to improved efficiency in the use of funds and management resources. This helps government and enterprise managers better understand how safety inputs are used and to optimize allocation of resources. Study on coal mine＇s efficiency assessment of safety input was con- ducted in this paper. A C^2R model with non-Archimedean infinitesimal vector based on output is established after consideration of the input characteristics and the model properties. An assessment of an operating mine was done using a specific set of input and output criteria. It is found that the safety input was efficient in 2002 and 2005 and was weakly efficient in 2003. However, the efficiency was relatively low in both 2001 and 2004. The safety input resources can be optimized and adjusted by means of projection theory. Such analysis shows that, on average in 2001 and 2004, 45% of the expended funds could have been saved. Likewise, 10% of the safety management and technical staff could have been eliminated and working hours devoted to safety could have been reduced by 12%. These conditions could have Riven the same results.

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.

Prediction Model of Data Envelopment Analysis with Undesirable Outputs

Data envelopment analysis (DEA) has become a standard non parametric approach to productivity analysis, especially to relative efficiency analysis of decision making units (DMUs). Extended to the prediction field, it can solve the prediction problem with multiple inputs and outputs which can not be solved easily by the regression analysis method.But the traditional DEA models can not solve the problem with undesirable outputs,so in this paper the inherent relationship between goal programming and the DEA method based on the relationship between multiple goal programming and goal programming is explored,and a mixed DEA model which can make all factors of inputs and undesirable outputs decrease in different proportions is built.And at the same time,all the factors of desirable outputs increase in different proportions.

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.

Data Envelopment Analysis on Evaluating the Efficiency of Public Hospitals in Tianjin,China

Public hospitals are the most important components of health systems and account for a large proportion of health resources in China. However, few researches on the efficiency assessment of public hospitals have been conducted in Tianjin, China. On the basis of the data of annual health service report in 2013 from the Ministry of Health, we measured the relative efficiency of the tertiary general public hospitals in Tianjin and estimated the magnitudes of output increase and/or input reduction by using data envelopment analysis to improve hospital efficiency. The main findings of this study indicate that more than half of the sample hospitals operate at a technical and scale efficiency, and the prevalent scale inefficiency is increasing returns to scale. Moreover, it is a prominent issue that health resource constraint and resource waste coexist. Health policy-makers and hospital administrators would need to address these problems by taking comprehensive measures such as optimizing the allocation of health resources, implementing hierarchical diagnosis and treatment, as well as innovating medical-service operating mechanism of public hospital to improve the people's wellbeing.

AIDS Treatments Efficiency Analysis Based on Cost Efficiency Data Envelopment Analysis Model

Three data envelopment analysis (DEA) models were used to analyse the relative efficiencies of four AIDS treatments in AIDS Clinical Trial Group (ACTG) Study 193A(1 309 patients in total, classified into 4 age groups). Results from the output-oriented BCC model show that Treatment 4 ( 600 mg of zidovudine plus 400 mg of didanosine plus 400 mg of nevirapine) is particularly efficient for age group 14—25, but not efficient for the older age groups; Treatment 1 (600 mg of zidovudine alternating monthly with 400 mg of didanosine)and Treatment 2 (600 mg of zidovudine plus 2.25 mg of zalcitabine) are efficient for the age groups 35—45 and 45— ; age group 25—35 does not have a particularly efficient treatment, but Treatments 1 and 2 are relatively good. The cost efficiency BCC model, which takes the treatment cost into account, gives similar results as the output-oriented model. Results from the indirect output-oriented BCC model, which allows the replacement among medicines, show that the efficiency of Treatment 2 has greatly decreased compared with that of the output-oriented model, and a set of optimal medicine amounts for different age groups is obtained.

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.

Evaluating banking efficiency with data envelopment analysis:evidence from Chongqing,P.R.China

Data envelopment analysis was applied to determine relative efficiencies of state-owned and joint-stock banks in Chongqing,P. R. China,during the years 1996 to 2000. We found that state-owned banks have low levels of efficiency when compared with joint-stock banks,but some joint-stock bank branches have low efficiency scores. Efficiency difference testing by using the Mann-Whitney rank order statistic indicates that the efficiency gap between state-owned and joint-stock banks is insignificant,which is characteristic of regional banks. We also presented some factors that may affect bank efficiency,and offer suggestions to improve bank management and efficiency.

Effectiveness of the Global Banking System in 2010： A Data Envelopment Analysis Approach

The current crisis has revealed the weaknesses of the global financial in general and its banking system in particular and puts forward a requirement for assessing the effectiveness and stability of the banking sectors across countries. Based on available data from 64 countries over the world, the author tried to evaluate the effectiveness of the banking sectors in those countries through the view point of the data envelopment analysis approach to define how the global banking systems is under the effect of the current crisis. Findings from the research showed that banking systems in advanced economies are still more effective than in developing countries. Moreover, it explained the effect of the current financial crisis, the role of public finance （and the government）, and the development of the （privately） commercial banks to the effectiveness of the banking sectors. The research also explained some determinants that can affect the effectiveness of the banking system, including inflation, bank concentration, and level of economic development.

Public and Private Investment in the Port Sector in Mexico, 2000-2010： A Study Through Data Envelopment Analysis

Knowing the level of efficiency of investment applied in ports of Mexico is relevant information for the design of port policies that contribute to its development and thus to greater freight movement. The objective of this paper is to analyze the technical efficiency obtained from International Mexican Ports, through the use of the technique of Data Envelopment Analysis （DEA）. It uses data regarding public and private investment in ports applied during the period 2000-2010 and its influence on the number of Twenty-foot Equivalent Unit （TEU）. Because it has been applied the DEA-CCR （the linear programming model） model input oriented, thus not only the efficiency is calculated in ports, but benchmarking is also obtained to determine the efficient ports that serve as reference to those who were found to be inefficient. The results obtained showed that Manzanillo and Progreso were the most efficient ports. On the other hand, the ports that were not efficient for any of the years reviewed were Mazatlan and Lazaro Cardenas. Generally, public investment has been increasing over the period, and public policies are not designed to allow the ports to have an international projection.

Comparison of Efficiencies of Enterprises Engaged in Food Sector in Turkey by Data Envelopment Analysis Taking Account of Their Efficiencies and Rantability Rates

Enterprises are in competition with other enterprises operating in their fields. In today＇s world, enterprises need to increase their efficiency and productivity, the values of which, if below market conditions, they need to raise. Data Envelopment Analysis, widely utilized in efficiency and productivity measurements is a method that measures the efficiency of one unit relatively, taking more than one input determines the efficiency of units with similar inputs and outputs and output simultaneously. DEA interactively Thus, not only the efficient units are determined, but an opinion is offered as to how the inefficient units can be improved. In this study, 12 enterprises that were among the first 500 enterprises in Turkey in 2008, active in Istanbul Stock Exchange and operating in food sector through Data Envelopment Analysis. In the model, activity rates were used as input values, rantability rates were used as output values. In conclusion of simultaneous analysis of input and output values, efficient and inefficient enterprises were determined.

Performance Assessment of European Football Teams： Using Stochastic Data Envelopment Analysis Model

Data Envelopment Analysis （DEA） is a powerful mathematical optimization method widely used for measuring, evaluating and improving the performance of Decision Making Units （DMUs）. These used in the various forms, such as hospitals, government agencies, educational institutions, air force, bank branches, business finns, sport teams and even people including the performance of countries, regions, etc. Recently DEA has been extended to examine the performance through the different sport types. In this paper, a Stochastic Input Oriented Data Envelopment Analysis （SIODEA） Model is conducted for measuring and evaluating the relative efficiency scores of football teams selected from different European countries during 2014/2015 season each with some of inputs are stochastic with normally distributed and recent inputs are deterministic and outputs, to shed light on the professional football teams performance.

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.

A point-wise minimization model for data envelopment analysis considering environmental variables

Environmental variables are widely recognized as a cause of differences in efficiency measurement.However,the existing literature on data envelopment analysis(DEA)in environmental factors ignores the impact of demand on output.To address this gap,we propose the Point-wise Minimization DEA model(PWMDEA),which considers contextual variables that affect demand and lead to differences in efficiency.The model obtains efficiency value by considering the minimum of virtual inputs and virtual demand.Then,efficiency is evaluated by minimizing the ratio of above minimum to virtual output.This one-step model avoids issues of multi-stage assumptions and requires less data,making it more applicable.Moreover,we demonstrate the accuracy of our new model by conducting simulations with given true efficiency values.The simulation results demonstrate that our model has the lowest ranking error when the output is affected by multiple inputs or when demand has a significant impact.In addition,we evaluate the efficiency of healthcare in 31 Chinese provinces by considering two environmental factors.The results suggest that provinces with lower financial investments or population loss received higher rankings from our proposed model.These findings provide plausible explanations and demonstrate the practical usefulness of our model.

Combining data envelopment analysis and Random Forest for selectingoptimal locations of solar PV plants

Solar photovoltaic (PV) energy has emerged as a potential alternative to carbon-based energies to meet theParis agreement commitment. This study investigates the effect of environmental variables on the efficiencyof solar PV panels. Data Envelopment Analysis (DEA) is used to estimate efficiencies of 91 solar PV panelslocated in Australia during the time period 2010–2020. The effects of environmental variables on the estimatedefficiencies are quantified using the truncated regression model. Random forest is then used to predict efficiencyof solar PV panel in every city of Australia. The results allow to determine the most suitable location and regions for solar PV energy production in Australia. This study provides an interesting and easily interpretabletool for policy decision makers.

Efficiency and Productivity of County-level Public Hospitals Based on the Data Envelopment Analysis Model and Malmquist Index in Anhui, China

Background： China began to implement the national medical and health system and public hospital reforms in 2009 and 2012, respectively. Anhui Province is one of the four pilot provinces, and the medical reform measures received wide attention nationwide. The effectiveness of the above reform needs to get attention. This study aimed to master the efficiency and productivity of county-level public hospitals based on the data envelopment analysis （DEA） model and Malmquist index in Anhui, China, and then provide improvement measures for the future hospital development. Methods： We chose 12 country-level hospitals based on geographical distribution and the economic development level inAnhui Province. Relevant data that were collected in the field and then sorted were provided by the administrative departments of the hospitals. DEA models were used to calculate the dynamic efficiency and Malmquist index factors for the 12 institutions. Results： During 2010-2015, the overall average relative service efficiency of 12 county-level public hospitals was 0.926, and the number of hospitals achieved an effective DEA for each year from 2010 to 2015 was 4, 6, 7, 7, 6, and 8, respectively, as measured using DEA. During this same period, the average overall production efficiency was 0.983, and the total productivity factor had declined. The overall production efficiency of five hospitals was 〉1, and the rest are 〈1 between 2010 and 2015. Conclusions： In 2010-2015, the relative service efficiency of 12 county-level public hospitals in Anhui Province showed a decreasing trend, and the service efficiency of each hospital changed. In the past 6 years, although some hospitals have been effective, the efficiency of the county-level public hospitals in Anhui Province has not improved significantly, and the total factor productivity has not been effectively improved. County-level public hospitals need to combine their own reality to find their own deficiencies.