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.

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.

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.

Optimization of energy consumption and environmental impacts of chickpea production using data envelopment analysis(DEA)and multi objective genetic algorithm(MOGA)approaches

Energy consumption in agricultural products and its environmental damages has increased in recent centuries.Life cycle assessment(LCA)has been introduced as a suitable tool for evaluation environmental impacts related to a product over its life cycle.In this study,optimization of energy consumption and environmental impacts of chickpea production was conducted using data envelopment analysis(DEA)and multi objective genetic algorithm(MOGA)techniques.Data were collected from 110 chickpea production enterprises using a face to face questionnaire in the cropping season of 2014-2015.The results of optimization revealed that,when applying MOGA,optimum energy requirement for chickpea production was significantly lower compared to application of DEA technique;so that,total energy requirement in optimum situation was found to be 31511.72 and 27570.61 MJ ha^-1 by using DEA and MOGA techniques,respectively;showing a reduction by 5.11%and 17%relative to current situation of energy consumption.Optimization of environmental impacts by application of MOGA resulted in reduction of acidification potential(ACP),eutrophication potential(EUP),global warming potential(GWP),human toxicity potential(HTP)and terrestrial ecotoxicity potential(TEP)by 29%,23%,10%,6%and 36%,respectively.MOGAwas capable of reducing the energy consumption from machinery,farmyard manure(FYM)diesel fuel and nitrogen fertilizer(the mostly contributed inputs to the environmental emissions)by 59%,28.5%,24.58%and 11.24%,respectively.Overall,the MOGA technique showed a superior performance relative to DEA approach for optimizing energy inputs and reducing environmental impacts of chickpea production system.

Application of Integrated Multiple Criteria Data Envelopment Analysis to Humanitarian Logistics Network Design

This paper considers a humanitarian logistics network(HTLN)design problem,including the emergency relief facilities(ERFs)location-allocation decision for the efficient distribution of emergency supplies from the ERFs to the affected areas.A goal programming(GP)approach is applied to consider the multiple objectives simultaneously.Solving the GP model with a given weight assigned to each goal yields a single HTLN scheme,so there will be various schemes available by solving the GP with multiple values of the weights.For evaluating these schemes and identifying the most efficient one,we apply the data envelopment analysis(DEA)methods considering each scheme as a decision-making unit(DMU).Since the classical DEA(C-DEA)intrinsically aims to identify efficient DMUs and the efficient frontier,the use of C-DEA may not lead to a full ranking in many situations.There are several independent evaluation approaches to increasing discriminating power.Among them,this study integrates the multiple criteria DEA(MC-DEA)with the following three DEA methods,(i)stratification DEA(S^DEA),(ii)cross-efficiency DEA(CE-DEA),and(iii)super-efficiency DEA(SE-DEA),to make the most use of each method's strengths.Through a case study of designing the HTLN system for South Carolina,the procedure of implementing the integrated multiple criteria DEA(IMC-DEA)method is demonstrated.It is observed that the IMCDEA method performs well in terms of designing the HTLN system and would help the decision-makers consider more efficient options and make a final decision.

Efficiency measurement of fertilizer-manufacturing organizations usingFuzzy data envelopment analysis

The aim of the paper is to benchmark the performance of the Indian fertilizermanufacturing organizations based on the ranking of efficiencies using a fuzzy data envelopment analysis(FDEA).FDEA has been used to find the relative efficiency and ranking of the fertilizer-manufacturing organizations.The last few years’data have been converted into the fuzzy inputs and outputs as minimum,mean,and maximum values,respectively.The performance of the fertilizer manufacturing organizations is based on the output maximization model of DEA.The frontier organizations set the benchmark for the lagging organizations for further improvement in the performance.This method can also be used to incorporate the data of the several years for multiple inputs and outputs instead of consideration of data of only one year.The proposed approach in this study may help organizations to improve its efficiency to fulfill its goal.

Evaluation and Ranking DMUs in the Presence of Both Undesirable and Ordinal Factors in Data Envelopment Analysis

In the last decade,ranking units in data envelopment analysis(DEA) has become the interests of many DEA researchers and a variety of models were developed to rank units with multiple inputs and multiple outputs.These performance factors(inputs and outputs) are classified into two groups:desirable and undesirable.Obviously,undesirable factors in production process should be reduced to improve the performance.Also,some of these data may be known only in terms of ordinal relations.While the models developed in the past are interesting and meaningful,they didn t consider both undesirable and ordinal factors at the same time.In this research,we develop an evaluating model and a ranking model to overcome some deficiencies in the earlier models.This paper incorporates undesirable and ordinal data in DEA and discusses the efficiency evaluation and ranking of decision making units(DMUs) with undesirable and ordinal data.For this purpose,we transform the ordinal data into definite data,and then we consider each undesirable input and output as desirable output and input,respectively.Finally,an application that shows the capability of the proposed method is illustrated.

The optimal model of oilfield development investment based on Data Envelopment Analysis

The investment problem of oilfield development is to trade off the investment exploration investment and development investment.With low return on investment got by using the existing method to solve this problem,we construct an optimal model to improve it based on Data Envelopment Analysis(DEA)method and the relations about investment and proven reserves,investment and output as well as production cost.Data Envelopment Analysis(DEA)method is used to present a method to determine the optimal scale of productivity construction investment in unit production.The relation between total cumulated proven reserves and cumulative exploration investment is denoted as an exponential model.The relation among productions and remaining recoverable reserves as well as production cost may be described as an exponential operational cost function.Based on above two relation models and investment effectiveness coefficients of every block,we establish an optimal model whose objective function is net present value(NPV)profit maximum,whose constrain conditions include investment,reserve/production ratio,production and some equality constraints under the mode of sustainable development.It can be solved by genetic algorithms.The result of case study shows that this optimal investment of oilfield development has multi-stage investment structure under given conditions;the model can provide scientific basic theory for oil companies to make a long-term strategic program and investment plan in oil exploration and development,may decrease the subjective blindness in the investment and bring about a reasonable and orderly exploration and development of oil resources.

Directional congestion in the framework of data envelopment analysis

This studyfirst proposes a definition for directional congestion in certain input and output directions within the framework of data envelopment analysis.Second,two methods from different viewpoints are proposed to estimate the directional congestion.Third,we address the relationship between directional congestion and classic(strong or weak)congestion.Finally,we present a case study investigating the analysis performed by the research institutes of the Chinese Academy of Sciences to demonstrate the applicability and usefulness of the methods developed in this study.

A New Stochastic Model for Classifying Flexible Measures in Data Envelopment Analysis

The way to deal with flexible data from their stochastic presence point of view as output or input in the evaluation of efficiency of the decision-making units(DMUs)motivates new perspectives in modeling and solving data envelopment analysis(DEA)in the presence of flexible variables.Because the orientation of flexible data is not pre-determined,and because the number of DMUs is fixed and all the DMUs are independent,flexible data can be treated as random variable in terms of both input and output selection.As a result,the selection of flexible variable as input or output for n DMUs can be regarded as binary random variable.Assuming the randomness of choosing flexible data as input or output,we deal with DEA models in the presence of flexible data whose input or output orientation determines a binomial distribution function.This study provides a new insight to classify flexible variable and investigates the input or output status of a variable using a stochastic model.The proposed model obviates the problems caused by the use of the large M number and using its different values in previous models.In addition,it can obtain the most appropriate efficiency value for decision-making units by assigning the chance of choosing the orientation of flexible variable to the model itself.The proposed method is compared with other available methods by employing numerical and empirical examples.

Data envelopment analysis for highway asset investment assessment

Highway agencies have been using many of the elements of asset management with the support of various decision-making tools.To determine the most effective investment strategy with scarce resources,the integration,and hence better utilization,of existing tools and practices across asset classes is generally lacking.This paper applies data envelopment analysis(DEA)to benchmark different highway investment scenarios using existing data or data readily available through existing models.Three asset types,pavements,bridges,and traffic signage,are investigated.Asset investment analysis results from the Highway Economic Requirements System State Version(HERS-ST)application,the PONTIS bridge management system software,and purpose-built traffic signage spreadsheet are obtained to capture the changes of performance measures under various budget scenarios and are further used as the inputs for the DEA process to benchmark investment scenarios for each individual asset.Subsequently,the performance measures and budget levels are assembled in the Asset Manager-NT software,whose results are input into DEA to benchmark cross-assets resource allocation scenarios.Planning for the management of highway network is addressed via case studies in a systematic manner that recognizes the tradeoffs among different funding periods and objectives such as preserving existing investments,safety,roughness and user costs.This study has established a preliminary implementable framework of highway asset management by linking DEA approach and current widely used decision-making tools for more efficient investments within and cross assets,and better understand of the tradeoffs,costs and consequences of various asset management decisions.

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.