Two-stage Data Envelopment Analysis Model Research Articles

Efficiency assessment of two-stage systems with fixed-sum outputs: A noncooperative DEA model with uncertain stage priority

Exogenous constraints such as fixed-sum output can affect the efficiency assessment of traditional two-stage data envelopment analysis (DEA) models. To address this issue, several studies have evaluated the DEA efficiencies for two-stage systems with fixed-sum output. They have proposed centralized models based on cooperative game theory and models under global mindset. However, in many cases, the first and second stages play a noncooperative game, and information on stage priority is often unobservable. In this study, we develop a noncooperative two-stage fixed-sum output DEA model with uncertain stage priority for calculating the overall system and stage efficiencies. Instead of stage priority as an endogenous variable, with aid of acceptaiblty analysis, we analyze the dominance relationship among decision-making units (DMUs) and provide a robust ranking by considering all possible stage priorities. We also conduct an empirical analysis with data from commercial banks to demonstrate the effectiveness of the developed model. After 10,000 groups of stage priority iterations, we report a robust ranking of commercial banks in which Hefei branch ranks first with 100 % probability

Comprehensive intuitionistic fuzzy network data envelopment analysis incorporating undesirable outputs and shared resources

The economic growth rate is intricately linked to the efficiency and effectiveness of the banking industry. A widely applicable mathematical technique for such assessments is Data Envelopment Analysis (DEA), which evaluates the relative efficiency of Decision-Making Units (DMUs) by comparing their inputs and outputs. Traditional DEA treats DMUs as black boxes, neglecting internal processes that contribute to inefficiencies in individual DMUs. Additionally, it assumes precise values for inputs and outputs that do not apply to real-world problems. This study introduces a comprehensive network series of two-stage DEA, incorporating shared inputs and intermediate measures, undesirable outputs, external inputs and outputs, initial inputs, and terminal outputs. The network two-stage DEA is extended to intuitionistic fuzzy circumstances to address uncertainty. In this extension, a non-linear intuitionistic fuzzy number, namely a parabolic intuitionistic fuzzy number, represents higher-order imprecise datasets. An illustrative example validates the proposed methodology, and comparisons with existing methods are conducted. Moreover, the methodology is applied to assess the efficiency of Indian public sector banks, demonstrating its applicability and showcasing the efficacy of the procedures and algorithms used. Decision-makers can make better choices using optimal efficiency values to gain insights into inputs, intermediate measures, and outputs.•The research study focused on a network two-stage DEA model, incorporating undesirable outputs and shared resources in the presence of uncertainty.•The methodology involves solving the network two-stage DEA model using parabolic intuitionistic fuzzy numbers.•The experimental analysis involves assessing the efficiency of Indian public sector banks.

Evaluation of bank efficiency by considering the uncertainty of nonperforming loans

Research of banking operations has recently attracted increasing interest among bank managers and scholars, especially research on the evaluation of bank efficiency. As a prominent factor, nonperforming loans are always considered when measuring bank efficiency. Actually, the complex structures and uncertainty of non-performing loans have been neglected in previous studies. In our study, a new robust two-stage DEA (data envelopment analysis) model is proposed to analyze bank efficiency while considering the structure and uncertainty of nonperforming loans. The proposed model was utilized to assess Chinese commercial banks’ performance. Results indicated traditional model may overestimate banks’ performances, which will mislead bank decision-makers seeking to implement improvement strategies. Moreover, the majority of banks performed better in producing deposits compared with earning profits. Lastly, gaps between small medium banks and state-owned banks are still larger when considering the structure and uncertainty of nonperforming loans. Specific recommendations are proposed for each type of bank.

Inverse two-stage data envelopment analysis with interval measures for resource planning

PurposeAssessing inputs and outputs is a significant aspect of taking decisions while there are complex and multistage processes in many examinations. Due to the presence of interval performance measures in various real-world studies, the purpose of this study is to address the changes of interval inputs of two-stage processes for the perturbations of interval outputs of two-stage systems, given that the overall efficiency scores are maintained.Design/methodology/approachActually, an interval inverse two-stage data envelopment analysis (DEA) model is proposed to plan resources. To illustrate, an interval two-stage network DEA model with external interval inputs and outputs and also its inverse problem are suggested to estimate the upper and lower bounds of the entire efficiency and the stages efficiency along with the variations of interval inputs.FindingsAn example from the literature and a real case study of the banking industry are applied to demonstrate the introduced approach. The results show the proposed approach is suitable to estimate the resources of two-stage systems when interval measures are presented.Originality/valueTo the best of the authors’ knowledge, there is no study to estimate the fluctuation of imprecise inputs related to network structures for the changes of imprecise outputs while the interval efficiency of network processes is maintained. Accordingly, this paper considers the resource planning problem when there are imprecise and interval measures in two-stage networks.

Two-Stage Data Envelopment Analysis Models with Negative System Outputs for the Efficiency Evaluation of Government Financial Policies

The main purpose of this study is to provide a comparative analysis of several possible approaches to applying data envelopment analysis (DEA) in the case where some decision making units (DMUs) in the original sample have negative system outputs. In comparison to the traditional model of Charnes, Cooper, and Rhodes (CCR) and the CCR model with a scale shift to measure second-stage outputs, the range directional measure (RDM) model produces the most appropriate results. In this paper, an approach is proposed for estimating returns to scale. The study applies a two-stage DEA model with negative second-stage outputs to assess the public support for research, development, and demonstration projects in the energy sector in 23 countries over the period from 2010 to 2018. The assessment of government performance depends on its contribution to the growth of energy efficiency in the national economy and the reduction of its carbon intensity. Intermediate outputs (patents in the energy sector) are included in the analysis as both outputs of the first stage and inputs of the second stage. Taking the similarity between the calculations obtained without stage separation and the system efficiency calculations from the two-stage model as a measure of model adequacy, the RDM model shows the highest similarity scores.

Efficient water use and reusing processes across Spanish regions: A circular data envelopment analysis with undesirable inputs

Efficiency is a fundamental element of the transition towards a sustainable use of natural resources among which water has a prominent role. Spain is among the European countries facing considerable water shortage problems, particularly within its southern regions. The current paper introduces an efficiency evaluation model based on Data Envelopment Analysis (DEA). The model incorporates a subset of outputs as undesirable inputs to account for the circularity of the production process by means of treated and reused water. The main differences existing between the circular approach proposed, a standard two-stage DEA model and a dynamic Slacks-Based Measure process will be carefully illustrated. In particular, the drawbacks faced by these latter techniques to consistently incorporate circularity into their optimization structures will be demonstrated both formally and numerically. The malleability of the current approach and its capacity to generate consistent identifiable categories among the regions evaluated within a circular production setting will be studied in detail. The analysis performed demonstrates significant structural differences in production capacity and efficiency across regions, with the inefficient ones displaying a considerable subpar use of resources through their production processes. The prevalence of inefficiency in several northern regions is partially compensated through their treatment and reutilization of water. However, this is not the case for the southern ones, which face stricter constraints and more inefficient production processes. The subsequent implications for efficiency are examined and policies aimed at enhancing the structural quality of the corresponding production systems suggested.

How to Comprehensively Evaluate Firm Performance from Operational, Financial, and Sustainability Perspectives? A Two-Stage Data Envelopment Analysis Approach

ABSTRACT This study proposes a two-stage modeling framework to evaluate the efficiency of firm performance based on sustainability (environmental, social, and governance (ESG)), operational and financial measures. Diverging from previous studies, this study conceptualizes firm performance as two serially linked stages, with operational performance as the first stage and market performance as the second stage. Acknowledging that ESG activities may reflect firm value and that these activities depend on a firm’s operational performance, ESG scores are modeled simultaneously as an output of the operational performance stage and as an input for the market stage. Under this performance appraisal framework, two-stage data envelopment analysis models capturing overall and stage-level efficiency are constructed. The application of the proposed modeling framework is demonstrated using a sample of large Saudi listed firms as a case study of an emerging market. The main conclusion is that ESG legislation, regulations, and disclosure guidelines should be well defined in emerging markets to increase the overall efficiency of listed firms’ performance.

Can industrial transfer improve urban innovation efficiency?

Investigating whether industry transfers to different cities and regions contribute to innovative efficiency improvement is a critical issue in addressing the development of urban innovation. Using the implementation of national industrial relocation demonstration zones (NIRDZ) in China as a quasi-natural experiment, this study empirically assesses the impact of industrial relocation upon urban innovation efficiency. This study first measures the urban innovation efficiency of 194 prefectural cities during 2005–2019 using a two-stage data envelopment analysis model. Then, a multiperiod difference-in-differences model is used to evaluate the innovation effects of national-level demonstration zones for undertaking industrial transfers. The results are as follows. First, industrial relocation does contribute to urban innovation efficiency. This conclusion is supported by a series of robustness tests confirming that the NIRDZ pilot policy indeed contributes to this efficiency, including a placebo test, propensity score matching, shortened time window, winsorized outliers, and lag treatment. Secondly, a regional heterogeneity analysis shows that the pilot policy significantly promotes innovation efficiency of cities located in the central region, but there is an insignificant effect in western region cities. The analysis of city size heterogeneity shows that the pilot policy promotes innovation efficiency more significantly in small cities. In contrast, the promotion effect on big cities is not significant. Third, when considering the potential impact mechanisms, the NIRDZ policy positively affects urban innovation efficiency by enhancing the informatization level and improving economic development. Based on the analysis above, this study recommends establishing an effective mechanism for industrial transfer, realizing the transfer between different regions and cities according to local conditions, and deepening the NIRDZ policy implementation. Policymakers should also increase investment in the construction of an informatization platform, plan resource usage rationally, promote regional integration development, change the philosophy of education, and recognize how the NIRDZ policy influences urban innovation through economic development and informatization.

Efficiency analysis of Chinese universities with shared inputs: An aggregated two-stage network DEA approach

Evaluating the resource utilization efficiency of a country's universities is a prerequisite for implementing a balanced development strategy. Universities often share some resources such as the teachers and fixed assets used for teaching and research. Data envelopment analysis (DEA), as a non-parametric method for performance evaluation of decision-making units (DMUs), has been used for measuring the operating efficiency of universities with shared inputs based on radial measures under multiplier DEA models. However, few existing studies consider non-radial measures and different perspectives of external and internal evaluations. From both external and internal perspectives, we propose aggregated two-stage DEA models to measure the efficiency scores of 52 Chinese universities in 2014. The main results indicate that: (1) both internal and external evaluations yield relatively high average operating efficiency, with around 53 % of universities being efficient. The allocation ratios of shared inputs for the same university differ according to the internal and external evaluations. (2) Heterogeneity analysis reveals that 985 universities are less efficient than non-985 universities, and comprehensive universities operate more efficiently than science and engineering universities. (3) There are efficiency differences between 985 and non-985 universities in the teaching stage. Science and engineering as well as comprehensive universities also differ in the teaching efficiency.

Grey clustering and grey ranking of bank branches based on grey efficiency

PurposeCompetition in the banking sector is more complex than in the past, and survival has become more difficult than before. The purpose of this paper is to propose a grey methodology for evaluating, clustering and ranking the performance of bank branches with imprecise and uncertain data in order to determine the relative status of each branch.Design/methodology/approachIn this study, the two-stage data envelopment analysis model with grey data is applied to assess the efficiency of bank branches in terms of operations. The result of grey two-stage data envelopment analysis model is a grey number as efficiency value of each branch. In the following, the branches are classified into three grey categories of performance by grey clustering method, and the complete grey ranking of branches are performed using “minimax regret-based approach” and “whitening value rating”.FindingsThe results show that after grey clustering of 22 branches based on grey efficiency value obtained from the grey two-stage DEA model, 6 branches are assigned to “excellent” class, 4 branches to “good” class and 12 branches to “poor” class. Moreover, the results of MRA and whitening value rating models are integrated, and a complete ranking of 22 branches are presented.Practical implicationsGrey clustering of branches based on grey efficiency value can facilitate planning and policy-making for branches so that there is no need to plan separately for each branch. The grey ranking helps the branches find their current position compared to other branches, and the results can be a dashboard to find the best practices for benchmarking.Originality/valueCompared with traditional DEA methods which use deterministic data and consider decision-making units as black boxes, in this research, a grey two-stage DEA model is proposed to evaluate the efficiency of bank branches. Furthermore, grey clustering and grey ranking of efficiency values are used as a novel solution for improving the accuracy of grey two-stage DEA results.

A Two-Stage Dea Model of Super Sbm and Malmquist for Analyzing Innovation and Energy Sustainability Efficiency of Asian Countries

The relationship between innovation and energy sustainability is deeply interconnected, as innovation plays a crucial role in achieving long-term solutions for energy challenges. Innovation involves the introduction of new concepts, products, or techniques that drive economic progress and enhance quality of life. On the other hand, energy sustainability focuses on ensuring the availability of cost-effective and reliable energy resources while mitigating environmental impacts. In Asia, the most populous and diverse region in the world, the correlation between innovation and energy sustainability holds significant importance. The region faces the complex task of balancing rapid economic growth and urbanization with the imperative to adopt sustainable energy practices. To assess performance and identify best practices, two key global indicators, namely the Global Innovation Index (GII) and the Energy Trilemma Index (ETI), can provide valuable benchmarks. This study aims to evaluate the efficiency of innovation and energy sustainability among 32 Asian countries using a two-stage Data Envelopment Analysis (DEA) model that incorporates the Super Slacks-based Measure (Super SBM) and Malmquist approaches. Additionally, hierarchical cluster analysis will be applied to group these countries based on their efficiency scores. By examining efficiency levels, influential factors, and the impact of the innovation-energy sustainability relationship on economic growth, this research can assist policymakers in making informed decisions. Furthermore, this study seeks to contribute to the existing body of knowledge by conducting a comprehensive investigation into the relationship between innovation and energy sustainability in the Asian region. Keywords: efficiency; innovation; energy; GII; ETI; sustainability; DEA; Super SBM; Malmquist; clustering; Asia

The Three Dimensions of Small Accommodation Businesses and Their Efficiency

Measuring efficiency and determining factors that may influence it are very important steps to improve the businesses’ competitive position, growth, and sustainability. This paper aims to investigate the efficiency of small accommodation businesses located in Greek non-coastal areas and to determine a set of factors that may affect it, from the perspective of the three dimensions of family businesses (family, business, ownership). The method adopted, in order for the research objective aim to be fulfilled, is the two-stage Data Envelopment Analysis model. In the first stage, the efficiency was estimated from a sample of 150 businesses. In the second stage, the influence of various factors on the examined efficiency was investigated by implementing a Bootstrap Truncated regression. The results showed that the majority of the examined businesses presented a low level of efficiency. Regarding the determination of the factors, it occurred that the manager’s age, ownership form, and business type influenced the relative efficiency level in contrast to the factors of the business’s age, the manager’s sex and education level, the state of succession, as well as the manager’s agricultural employment. By fulfilling the aim of this study, a significant contribution to the relative literature and especially to the hospitality field is offered.

Customer satisfaction and airport efficiency in Brazil: a hybrid NDEA-AHP approach

PurposeThis paper aims to measure and unveil the relationship between customer satisfaction and efficiency levels in the most relevant Brazilian airports.Design/methodology/approachThe authors utilize a two-stage network DEA (data envelopment analysis) and AHP (analytic hierarchy process) model as the cornerstones of the study. The first stage of the network productive structure focuses on examining the infrastructure efficiency of the selected airports, while the second stage assesses their business efficiency.FindingsAlthough the results indicate that infrastructure and business efficiency levels are heterogeneous and widely dispersed across airports, controlling the regression results with different contextual variables suggests that the impact of efficiency levels on customer satisfaction is mediated by a set of socio-economic and demographic (endogenous) and regulatory (exogenous) variables. Furthermore, encouraging investment in airports is necessary to achieve higher infrastructural efficiency and scale efficiency, thereby improving customer satisfaction.Originality/valueThere is a scarcity of studies examining the relationships among customer satisfaction, privatization and airport efficiency, particularly in developing countries like Brazil.

Influences of Talent Cultivation and Utilization on the National Human Resource Development System Performance: An International Study Using a Two-Stage Data Envelopment Analysis Model

To enhance national competitiveness, countries are committed to building a National Human Resource Development (NHRD) system to develop talents. However, studies have rarely investigated the internal development process of the NHRD system and the performance at the system and sub-system levels. Thus, this study constructed the performance evaluation model of the NHRD system from a two-stage process efficiency perspective that first cultivates talents and then uses the talents produced to create value. In addition, considering the problem of international talent flow and the time-lag effect, the bad output and the time-lag between inputs and outputs were incorporated into the model. The subjects included 60 countries, including Argentina, China, and OECD member countries. The results reveal that countries that excel at nurturing talents do not necessarily have the ability to effectively use talents to create value. Only having high-efficiency talent cultivation cannot strengthen competitiveness. Sensitivity analysis was also conducted to identify the input that affects talent cultivation and utilization efficiency, which could be used as a reference for competitiveness and NHRD performance improvement.

A bootstrapping dynamic two-stage SBM model: An application to assess industrial water use and health risk systems

Despite the great number of applications of bootstrapping data envelopment analysis (DEA) with a one-stage structure, there are limited attempts for approximating the distribution of the DEA estimator considering the two-stage structure across multiple periods. This research develops the dynamic two-stage non-radial DEA model based on smoothed bootstrap and subsampling bootstrap. Then, we run the proposed models on assessing the efficiency of China's industrial water use and health risk (IWUHR) systems and compare them with the bootstrapping results on standard radial network DEA. The results are as follows. (1) The proposed non-radial DEA model based on smoothed bootstrap can adjust original over-estimated and under-estimated values. (2) China's IWUHR system has good performance, and its HR stage performs better than the IWU stage for 30 provinces from 2011 to 2019. The poor performance of the IWU stage in Jiangxi and Gansu needs to be noticed. The provincial differences of the detailed bias-corrected efficiencies expand in the later period. (3) The rankings of IWU efficiency in the three regions are in agreement with that of HR efficiency: eastern, western, and central regions in this order. Particular attention should be paid to the downward trend of the bias-corrected IWUHR efficiency in the central region.

Using social media for efficient brand marketing: An evaluation of Chinese Universities using Bilibili

As the higher education market becomes increasingly competitive, Chinese universities are competing to develop brand marketing programmes on social media platforms, with significant differences in performance. This paper divides universities’ social media marketing processes into two stages: the production-operation stage and the marketing communication stage. It constructs a two-stage data envelopment analysis (DEA) model to evaluate the brand marketing efficiency of 296 Chinese universities on the Bilibili video-sharing platform to provide strategic proposals for social media marketing. The results show that 10 universities perform efficiently in the production-operation stage, while 11 universities perform efficiently in the marketing communication stage. The gap in marketing efficiency is relatively large across Chinese universities. Most universities perform unsatisfactorily because of their redundant input or insufficient output. To improve the brand marketing efficiency on Bilibili, universities should pay more effort into quality rather than quantity of input, produce high-quality videos continuously and build and maintain fan loyalty.

Evaluation of Urban Health Efficiency in Japanese Cities Using Network Data Envelopment Analysis

Urban health efficiency is influenced by both urban planning decisions and the functioning of the public health system. However, there is currently a lack of effective methods to simultaneously examine urban planning and public health when assessing urban health efficiency. This study proposes a two-stage network data envelopment analysis (DEA) model for evaluating urban health efficiency. The urban planning and public health sectors act as interconnected stages where the public facilities and living quality are mediating variables. The urban health efficiencies of 303 Japanese cities are examined using the proposed model, showing that most Japanese cities still have room for urban planning improvement with pure technical efficiency ranging between 0.7 and 0.9. At the same time, most public health sectors of Japanese cities reach pure technical efficiencies larger than 0.95 but are limited by the scale efficiency. Further analysis points out that public health sectors are in decreasing-return-to-scale, meaning that excessive urban scale adversely affects urban health efficiency. Furthermore, cities that joined the Alliance for Healthy Cities (AFHC) performed better on average, suggesting that information sharing and national and international networking can boost urban health. The study shows that the proposed two-stage network DEA model can be applied to analyze urban health efficiency and identify the impact of technology and urban scale in different stages.

Analysis of environmental performance and interactivity of ports and regions

The port is the basic support for regional economic development and the global allocation of resources. With the rapid development of China's economy and growing ecological awareness, the assessment of port and regional efficiency has received unprecedented attention. In the current context of the COVID-19 pandemic, how the port and its region will be coordinated under the common goal of development has become a hot topic. In this study, the port subsystem (P-subsystem) and the regional subsystem (R-subsystem) are unified into the port–region system (PR system), and a new meta-frontier two-stage data envelopment analysis model is constructed to evaluate the P-subsystem efficiency and the environmental efficiency of the PR system. This research also measures the port–regional coordination level using the coordination index and explores the inefficiency of the PR system with the help of management improvement and technology improvement indices. Main results show that the overall efficiency of the Chinese PR system is increasing. The technological level of the PR system in coastal areas is close to the optimal level. The inefficiency of the Chinese PR system is mainly affected by management inefficiency. The coordination of regional and port development in China is also poor. Finally, on the basis of the research findings, this study provides targeted countermeasure suggestions to promote the efficiency enhancement and coordinated development of the PR system.

Port environmental efficiency assessment using the one-stage and two-stage model DEA: comparison of Koper and Dublin ports

Ports are important and central hubs for logistical activities in transportation chains that contribute to economic growth. Nevertheless, port activities are associated with undesirable impacts such as energy consumption and air pollutant emissions. Various policy instruments and measures have been developed and adopted to reduce energy consumption and emissions from ports. In an effort to manage all undesirable impacts of port operations, the search for best practices has proven to be an effective approach. This study examines one- and two-stage Data Envelopment Analysis (DEA) models for measuring port environmental efficiency. The adequacy of the models was analyzed using two case studies, i.e., the port of Koper and port of Dublin. The results of the study provided the best practices and the main differences between one-stage and two-stage models. Distance metrics were used to identify the necessary improvements of inefficient decision-making units (DMUs) to achieve the best practices.

Environmental efficiency assessment of Dublin Port using two-stage non-radial DEA model

The operation of a port is of critical economic importance because of its role in international trade. However, increased operations increase the port's environmental impact and contribute to climate change and global warming. Dublin Port is one of the busiest ports in Ireland, and throughput is expected to increase as the economy continues to grow. Achieving a balance between growing economic activity and reducing environmental impacts is critical to a sustainable future. The efficiency of the port considering operation, economic, and environmental factors can be evaluated using the well-known nonparametric model of Data Envelopment Analysis (DEA). In this study, a novel two-stage non-radial DEA model is used to evaluate the environmental efficiency of Dublin Port considering landward and seaward operations. The proposed two-stage model DEA isolates the efficiency of the two port sides and calculates the overall efficiency. The model minimizes Dublin Port's annual CO2 emissions by reducing a combination of variables that can be realistically controlled by engineering and policy measures. The analysis was extended to account for possible variations in a number of key environmental output factors to compensate for the lack of real-world data availability. The study found that the number of terminals and capital expenditures have significant impacts on the port's environmental efficiency. Small adjustments or reductions in key indicators can improve Dublin Port's efficiency. This methodology can be applied to other ports in growing economies that use similar indicators to assess their environmental efficiency.