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.

Evaluation of Energy Efficiency and Analysis of Influencing Factors of Company CW’s Manufacturing Workshops

In this work,the Slacks-Based Measure(SBM)model within Data Envelopment Analysis was employed to establish a set of indicators for evaluating the energy efficiency of manufacturing workshops.The energy efficiency of 12 Company CW’s manufacturing workshops from 2016 to 2022 was assessed.The findings indicated that aside from a few workshops operating at the production frontier,the rest exhibit significant fluctuations in energy efficiency and generally low energy efficiency.Subsequently,a combined GRA-Tobit analysis model was introduced to identify factors influencing the energy efficiency of Company CW’s manufacturing workshops.Regression analysis revealed that technological investments,employee quality,workshop production scale,investment in clean energy,and the level of pollution control all significantly impact the energy efficiency of Company CW’s manufacturing workshops.By evaluating the energy efficiency of Company CW’s manufacturing workshops and studying their influencing factors,this research aids company managers in understanding the energy efficiency of the manufacturing process.It optimizes the combination of various production elements,thereby offering effective guidance for improving the energy efficiency issues of the company’s manufacturing workshops,which can contribute to enhancing the corporation’s overall energy efficiency.

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.

The Correlation of Hospital Operational Efficiency and Average Length of Stay in China: A Study Based on Provincial Level Data

Objective: To measure the hospital operation efficiency, study the correlation between average length of stay and hospital operation efficiency, analyze the importance of shortening average length of stay to the improvement of the hospital operation efficiency and put forward relevant policy suggestion. Methods: Based on China provincial panel data from 2003 to 2012, the hospital operation efficiencies are calculated using Super Efficiency Data Envelopment Analysis model, and the correlation between average length of stay and hospital operation efficiency is tested using Spearman rank correlation coefficient test. Results: From 2003 to 2012, the average of national hospital operation efficiency was increasing slowly and the hospital operations were inefficient in most of the areas. The national hospital operation efficiency is negatively correlated to the average length of stay. Conclusion: Measures should be taken to set average length of stay in a scientific and reasonable way, improve social and economic benefits based on the improvement of 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.

Overall profit Malmquist productivity index under data uncertainty

The calculation of the overall profit Malmquist productivity index(MPI)requires precise and accurate information on the input,output,input-output prices of each decision making unit(DMU).However,in many situations,some inputs and/or outputs and input-output prices are imprecise.As such,we consider the overall profit MPI problem when the input,output,and input-output prices are imprecise and vary over intervals,showing that method(MCM 54:2827–2838,2011)has some shortfalls.To remedy these shortfalls,we propose another method for measuring the overall profit MPI when the inputs,outputs,and price vectors vary over intervals.That is,to calculate the overall profit efficiency intervals,cone-ratio data envelopment analysis models can be applied to the incorporated information as weight restrictions.Further,we provide a new approach to calculating the upper bound of the overall profit efficiency of each DMU.A numerical example is provided for illustrating the proposed method.

Efficiency Comparison and Influencing Factor Analysis of Dairy Farms over/at Different Scales:Based on the Survey Data of 263 Scale Farms in 22 Provinces of China

China's dairy farming has presented a striking development in recent years.Under the dual constraints of environment and resources,it is of practical significance to increase the output of dairy farming and ensure the healthy and stable development of the dairy industry,by accurately comparing the differences in the farming efficiency of dairy farms at different scales and grasping key factors influencing the farming efficiency.This study,through the cost analysis of 263 scale farms across 23 provinces and regions of China in 2019,reaches a result that the cost of a single cow in a certain scale farm increases with the enlargement of the scale,and shows an inverted-U shaped curve with the relatively large scales(1001-2000 cows)at the highest point.It measures the farming efficiency of dairy farms at different scales through the data envelopment analysis and finds that the scale efficiency and allocation efficiency of scale farms in China are relatively high,while the technology efficiency and cost efficiency are relatively low.The efficiency of different scale farms is obviously different,where the cost efficiency,allocation efficiency and scale efficiency show a U-shaped curve as the scale enlarges(with the relatively large scale as the lowest point),while the technology efficiency gradually decreases as the scale expands.It is concluded that for the scale farms,feed conversion ratio and forage-to-concentrate ratio have a significantly negative impact on the scale efficiency,while the labor cost,number of employees,and depreciation of fixed assets are negatively correlated to the technology efficiency and cost efficiency of dairy farming.

基于三阶段数据包络分析模型的苏浙沪皖经济圈医院运行效率研究

目的分析2019年苏浙沪皖经济圈内27个城市医院运行效率,为优化苏浙沪皖卫生资源配置和规划提供参考。方法选取苏浙沪皖27个城市医院指标数据,运用三阶段数据包络分析(data envelopment analysis,DEA)模型法,在控制环境变量和剔除随机效应后效率分析。结果苏浙沪皖经济圈医院综合技术效率、纯技术效率和规模效率均值分别为0.941、0.948和0.992。结论苏浙沪皖经济圈内医院运行效率有所差异,环境变量对医院运行效率影响较大,对外部的资源配置存在敏感性不同的差异,应统筹区域医疗资源,提高医院运行效率。

基于DEA方法的江苏省制造业上市企业创新绩效研究

基于道格拉斯生产函数,构建了企业创新绩效评价指标体系,运用DEA-CCR、DEA-BCC、DEA-Malmquist模型测算了2018—2020年169家江苏省制造业上市企业静态效率和动态效率。研究表明,江苏省制造业上市企业研发投入呈现逐年递增趋势,但创新绩效整体没有达到最优状态,主要是由于纯技术效率较低所致,需要提升资源配置效率;且受疫情影响创新绩效整体上经历了一个从增长到衰退的过程,相对来说企业技术进步率大于技术效率变化率。

Integrity-Management Characteristics and Efficiency Evaluation of Oil and Gas Pipelines

Pipeline integrity is a cornerstone of the operation of many industrial systems, and maintaining pipeline integrity is essential for preventing economic losses and ecological damage caused by oil and gas leaks. Based on integritymanagement data published by the US Pipeline and Hazardous Materials Safety Administration, this study applied the k-means clustering and data envelopment analysis(DEA) methods to both explore the characteristics of pipeline-integrity management and evaluate its efficiency. The k-means clustering algorithm was found to be scientifically valid for classifying pipeline companies as either low-, medium-, or high-difficulty companies according to their integrity-management requirements. Regardless of a pipeline company's classification, equipment failure was found to be the main cause of pipeline failure. In-line inspection corrosion and dent tools were the two most-used tools for pipeline inspection. Among the types of repair, 180-day condition repairs were a key concern for pipeline companies. The results of the DEA analysis indicate that only three out of 34 companies were deemed to be DEA-effective. To improve the effectiveness of pipeline integrity management, we propose targeted directions and scales of improvement for non-DEA-effective companies.

上海市静安区区级医院慢性肾衰竭患者住院总费用负担评价

目的 对上海市静安区2015—2019年区级医院慢性肾衰竭患者住院总费用负担进行评价,探讨导致住院总费用负担增加的主要因素,为控制住院总费用、减轻患者本人和社会经济压力提供可行性建议。方法 利用基于松弛变量的数据包络分析法对住院总费用技术效率进行测算。结果 各年度的住院总费用技术效率均低于0.8,其中2015年技术效率值最高,而2019年技术效率值最低。各类医疗费用中治疗费和检查化验费技术效率值较低。不同医院之间技术效率值存在显著差异。结论 慢性肾衰竭患者住院总费用负担呈逐年上升趋势。慢性肾衰竭住院患者药费支出较为合理。降低治疗费和检查化验费是控制住院总费用的关键。各医疗机构诊疗行为的不同是造成疾病经济负担差异的重要因素。

Analysis of Economic Efficiency of Wildlife Law Enforcement in Serengeti Ecosystem Tanzania

Law enforcement remains to be the main strategy used to combat poaching and account for high budget share in protected area management. Studies on efficiency of wildlife law enforcement in the protected areas are limited. This study analyzed economic efficiency of wildlife law enforcement in terms of resource used and output generated using three different protected areas (PAs) of Serengeti ecosystem namely Serengeti National Park (SENAPA), Ikorongo/Grumeti Game Reserves (IGGR) and Ikona Wildlife Management Area (IWMA). Three years (2010-2012) monthly data on wildlife law enforcement inputs and outputs were collected from respective PAs authorities and supplemented with key informant interviews and secondary data. Questionnaire surveys were conducted to wildlife law enforcement staff. Shadow prices for non-marketed inputs were estimated, and market prices for marketed inputs. Data Envelopment Analysis (DEA) was used to estimate economic efficiency using Variable Return to Scale (VRS) and Constant Return to Scale (CCR) assumptions. Results revealed that wildlife law enforcement in all PAs was economically inefficient, with less inefficiency observed in IWMA. The less inefficiency in IWMA is likely attributed to existing sense of ownership and responsibility created through community-based conservation which resulted in to decrease in law enforcement costs. A slacks evaluation revealed a potential to reduce fuel consumption, number of patrol vehicles, ration and prosecution efforts at different magnitudes between studied protected areas. There is equal potential to recruit more rangers while maintaining the resting time. These finding forms the bases for monitoring and evaluation with respect to resource usage to enhance efficiency. It is further recommended to enhance community participation in conservation in SENAPA and IGGR to lower law enforcement costs. Collaboration between protected area, police and judiciary is fundamental to enhance enforcement efficiency. Despite old dataset, these findings are relevant since neither conservation policy nor institution framework has changed substantially in the last decade.

基本公共卫生服务效率及其影响因素

目的基于2017年武汉市13个地区基层医疗卫生机构的横断面数据,分析武汉市基本公共卫生服务效率及其主要影响因素。方法采用松弛测度(slack-based-measure,SBM)-超效率数据包络分析(data envelopment analysis,DEA)模型,对武汉市基本公共卫生服务效率进行测算,通过Tobit回归分析进一步探讨其影响因素。结果2017年武汉市13个地区基本公共卫生服务的超效率、纯技术效率、规模效率几何均数分别为1.073、1.213、0.884。其中76.9%的地区为DEA有效,若非DEA有效地区能达到DEA有效,全市可少开办11家基层医疗卫生机构、减少1451张病床、节省6983万元基本公共卫生服务补助经费。60岁及以上老年人比例、平均期望寿命、每千人口卫生技术人员数、每千人口床位数对武汉市基本公共卫生服务效率的影响具有统计学意义。结论武汉市基本公共卫生服务效率地区差异较大,规模效率是制约基本公共卫生服务效率的关键因素。60岁及以上老年人比例越高、平均期望寿命越长、每千人口卫生技术人员数越多,基本公共卫生服务效率越低;每千人口床位数越多,基本公共服务效率越高。针对这些因素,需提高老年人健康管理水平,优化机构人员配置,合理调整机构规模,重视基本公共卫生服务的公益性。

Sources of China's Economic Growth:An Analysis Based on Nonparametric Accounting Method

This paper improves the slacks-based method for estimating inefficiency,derives the criteria for the selection of the weights of output and input inefficiencies in the objective function,and creates a new nonparametric method for accounting economic growth.Based on this method,the paper estimates the sources of China s economic growth from 1978 to 2013.Our findings suggest that factor input and especially capital is a major source of economic growth for China as a whole and its major regions,and that economic growth in recent years is increasingly dependent on capital.For a rather long period of time before 2005,China s northeast,central and western regions lagged behind the eastern region in terms of economic growth,and TFP and factor input are major reasons behind such regional growth disparities.Although other regions have narrowed their disparities with and even overtaken the eastern region in terms of economic growth,the key driver is the rapid increase in the contribution of factor input.Advanced technologies of eastern region should be utilized to promote TFP progress in other regions,which is vital to economic growth in these regions and China as a whole.