General Data Envelopment Analysis Research Articles

Regret-based cross efficiency evaluation method in a general two-stage DEA system

Cross efficiency (CE) evaluation in data envelopment analysis (DEA) has significant advantages in ranking decision making units (DMUs). A variety of CE evaluation methods with different secondary goals are proposed in traditional black-box DEA models. At present, some scholars have studied the CE evaluation approaches in two-stage DEA systems. However, these studies commonly think of decision makers (DMs) as perfectly rational and ignore the influence of DMs’ psychological factors on the evaluation results. To conquer these limitations, this study introduces regret theory to portray DMs’ psychological preferences and investigates two-stage CE evaluation models based on regret theory. We bring in the comprehensive perceived utility of DMUs by combining direct utility and indirect utility at first, and then develop the regret-based two-stage cross efficiency (RTCE) models in a centralized and a decentralized decision environments respectively. The efficiency of Chinese “double first-class” universities are evaluated to verify our models and a completely ranking of them can be obtained. Finally, a comparative analysis is conducted to illustrate the effectiveness of our proposed models.

A Novel General Data Envelopment Analysis Based Approach for MCDM Issues of Hydrogen Energy under a Fuzzy Environment

Multi-criteria decision-making (MCDM) issues related to hydrogen energy usually involve weight consideration of evaluation criteria, ambiguous evaluation information provided by experts, and lacking or incomplete evaluation information. Conventionally, the MCDM calculation method cannot effectively and simultaneously process evaluation information. To effectively address this issue, this study proposed a novel general data envelopment analysis (DEA)-based approach for MCDM issues of hydrogen energy under a fuzzy environment. The proposed general DEA-based approach integrates the typical DEA method, analytic hierarchy process (AHP) method, hesitant fuzzy linguistic term set (HFLTS), and the soft set to process the MCDM problems under a fuzzy environment. For the numerical verification, this study used the case of hydrogen energy key technologies ranking, as an important development reference for carbon reduction to further verify the correctness and reasonableness of the proposed approach. The calculation results were also compared with those from the typical DEA method, typical AHP/DEA method, and the fuzzy AHP/DEA method. The numerical verification results show that the proposed method can effectively process the MCDM problems under a fuzzy environment than listing different calculation methods.

A generalized inverse DEA model for firm restructuring based on value efficiency

Abstract We present a novel general inverse data envelopment analysis model for assessing the restructuring of decision-making units (DMUs) while observing predetermined value efficiency targets, under two distinct scenarios: merger and acquisitions and split. By considering the set of efficient DMUs as the Decision Maker’s set of Most Preferred Solutions, virtual new units with desired targets for value efficiency scores and input and output levels can be computed. The innovations of this paper are threefold. First, a comparison between the proposed value efficiency and previous technical efficiency approaches reveals improvement in the estimation of restructured input/output levels. Second, the proposed approach is capable of handling the decision-maker’s preferences during restructuring. Third, an algorithm to determine the worst case-scenario for restructuring is presented. An applied case study in banking operations is presented to illustrate the validity and applicability of the proposed method.

Assessing the performance of industrial water resource utilization systems in China based on a two-stage DEA approach with game cross efficiency

While shouldering the burden of economic development, China's industrial sector has significant water consumption and wastewater discharge, which has intensified the country's water shortage. To improve the efficiency of industrial water resource utilization system, data envelopment analysis (DEA) has been widely used to assess the performance of the system. The current network DEA approaches adopted to investigate the system all belong to the self-evaluation mode, and existing network DEA cross-efficiency evaluation approaches have shortcomings. Therefore, a two-stage DEA approach with game cross efficiency is proposed to evaluate the system. First, according to the operation process of the system, this paper decomposes the system into a general two-stage network structure: water use stage and wastewater treatment stage. Second, the DEA game cross-efficiency model is improved to the general two-stage DEA game cross-efficiency model to evaluate the overall efficiency of the system. Third, given the overall efficiency, an efficiency decomposition model is proposed to determine a set of weights for each decision-making unit to evaluate water use efficiency and wastewater treatment efficiency. Finally, the rationality of the proposed approach is illustrated by model comparison, and the efficiencies of industrial water resource utilization systems in 31 regions of China from 2010 to 2015 are evaluated based on the proposed approach. The results indicate that, from the overall efficiency perspective, no region in China is always evaluated as being overall efficient and the overall efficiencies of 17 regions show an increase before a decreasing trend or decreasing trend during the study period. In 11 regions, wastewater treatment efficiency is far lower than water use efficiency, and in 11 other regions, both sub-stages are inefficient. In terms of the three areas, the eastern area has the highest water use efficiency, the central area has the lowest efficiency of both sub-stages, and the western area has the highest wastewater treatment efficiency. Some recommendations are presented to ensure China's sustainable development.

Low-carbon city pilot and carbon emission efficiency: Quasi-experimental evidence from China

Abstract This paper identifies the causal effect of low-carbon city pilot (LCCP) policy on carbon emission efficiency (CEE). Specifically, we first develop a general nonconvex metafrontier data envelopment analysis model to calculate CEE. We also provide a quasi-experimental evidence using a unique dataset of 251 cities in China during the years 2003 to 2018. Specifically, difference-in-differences (DID) and spatial DID (SDID) estimators are used as the main empirical strategy. We find that the LCCP policy improved CEE by 1.7% which are both economically and statistically significant. Further, its impact on neighbor untreated cities is about 64% of that on the treated cities. Scenario analysis documents that the average carbon dioxide emissions should be mitigated by approximately 8.37 million tons with a CEE increase of 1%, 8.84 million tons with a 2% increase, and 9.31 million tons with a 3% increase. Our findings also indicate that a 1% increase in years relative to a city's carbon dioxide emissions peak year commitment associates with a 1.3% increase in CEE.

Efficiency of Indian banks with non-performing assets: evidence from two-stage network DEA

This paper addresses the concerns regarding the sustainability of the banking sector in India prompted by the recent unintended high level of non-performing assets (NPAs). It uncovers the linkage between NPAs and banking efficiency by integrating NPAs into the measurement of bank efficiency to provide a holistic efficiency profile of the Indian banking sector. We apply the general two-stage data envelopment analysis of Kao [16] by incorporating NPAs as an exogenous output from the first stage, and the empirical results identify an efficiency gap of 16.2% due to NPAs in the Indian banking sector for the year 2016. Further, it also documents that the efficiency gap/loss is increasing over the years and differs according to the shareholding pattern of the banks.

DEA under big data: data enabled analytics and network data envelopment analysis

This paper proposes that data envelopment analysis (DEA) should be viewed as a method (or tool) for data-oriented analytics in performance evaluation and benchmarking. While computational algorithms have been developed to deal with large volumes of data (decision making units, inputs, and outputs) under the conventional DEA, valuable information hidden in big data that are represented by network structures should be extracted by DEA. These network structures, e.g., transportation and logistics systems, encompass a broader range of inter-linked metrics that cannot be modelled by conventional DEA. It is proposed that network DEA is related to the value dimension of big data. It is shown that network DEA is different from standard DEA, although it bears the name of DEA and some similarity with conventional DEA. Network DEA is big data enabled analytics (big DEA) when multiple (performance) metrics or attributes are linked through network structures. These network structures are too large or complex to be dealt with by conventional DEA. Unlike conventional DEA that are solved via linear programming, general network DEA corresponds to nonconvex optimization problems. This represents opportunities for developing techniques for solving non-linear network DEA models. Areas such as transportation and logistics system as well as supply chains have a great potential to use network DEA in big data modeling.

NETWORK DATA ENVELOPMENT ANALYSIS WITH COMMON WEIGHTS: AN APPLICATION TO THE SUSTAINABILITY MEASUREMENT OF OECD COUNTRIES

This work considers a general common-weights network data envelopment analysis (DEA) model which is applicable to most network systems, except those with feedbacks and cycles. The principle of compromise, of the technique for order preference by similarity ideal solution (TOPSIS), is employed to find the common set of weights in the general network DEA model. The proposed method is applied to assess the environmental sustainability performance of the Organization for Economic Co-operation and Development (OECD) countries. Our results show that most countries have a large difference in the rank of efficiencies between the eco-efficiency and production efficiency stages, which reveals the source that causes the low environmental sustainability scores of the whole process.

Framework for logistics performance index construction using DEA: an application for soybean haulage in Brazil

Freight transportation is vital to a nation’s long-term development and its performance needs to be carefully evaluated to ensure the effectiveness, efficiency, and equity of haulage infrastructure decisions. The previous attempts at benchmarking the transportation corridors and route efficiency through Data Envelopment Analysis (DEA) models violated homogeneity assumptions or did not provide an appropriate robustness analysis. The present paper integrates index creation and general DEA guidelines, and proposes a framework for the creation of a long-distance cargo haulage performance index, advancing towards the limitations of the previous efforts. The methodology is applied to the context of soybean transportation, one of the relevant Brazilian exporting products, during the harvest of 2015/2016, from the main mid-sized producing regions to the key exporting ports, by land transportation. The proposed approach and findings can provide insights into public and private long-term investment strategies and infrastructure policies in Brazil and other developing countries in a similar context.

A conic relaxation model for searching for the global optimum of network data envelopment analysis

Network data envelopment analysis (DEA) models the internal structures of decision-making units (DMUs). Unlike the standard DEA model, multiplier-based network DEA models are often highly non-linear and cannot be converted into linear programs. As such, obtaining a non-linear network DEA's global optimal solution is a challenge because it corresponds to a nonconvex optimization problem. In this paper, we introduce a conic relaxation model that searches for the global optimum to the general multiplier-based network DEA model. We reformulate the general network DEA models and relax the new models into second order cone programming (SOCP) problems. In comparison with linear relaxation models, which is potentially applicable to general network DEA structures, the conic relaxation model guarantees applicability in general network DEA, since McCormick envelopes involved are ensured to be finite. Furthermore, the conic relaxation model avoids unnecessary linear relaxations of some nonlinear constraints. It generates, in a more convenient manner, feasible approximations and tighter upper bounds on the global optimal overall efficiency. Compared with a line-parameter search method that has been applied to solve non-linear network DEA models, the conic relaxation model keeps track of the distances between the optimal overall efficiency and its approximations. As a result, it is able to determine whether a qualified approximation has been achieved or not, with the help of a branch and bound algorithm. Hence, our proposed approach can substantially reduce the computations involved.

Rank reversal issues in DEA models for China’s regional energy efficiency assessment

Energy efficiency (EE) is an important strategy for China to save energy and reduce energy-related emissions. With significant regional diversities in China, it is important to conduct the EE assessment at the regional level. Usually, the regional EE assessment is applied to 30 regions in Mainland China using the data envelopment analysis (DEA) technique. With the “Belt and Road” strategy initiated by the Chinese government, it is reasonable and necessary to take Hong Kong, Macao, and Taiwan into consideration. However, such data expansion for China’s regional EE assessment using DEA can reverse the relative rankings of some decision-making units, which is called the “rank reversal” phenomenon. In this paper, we illustrate in theory that rank reversal occurs in general DEA models, and apply the most popular five DEA models to assess China’s regional energy efficiency from 2000 to 2014. The empirical study shows that the 30 regions in Mainland China have the least rank reversal when Tone’s slack-based model (SBMT) is adopted. The main cause of ranking reversal is the addition of decision-making units lying on production frontier. Better understanding of the rank reversal phenomenon is critical for the energy efficiency assessment using DEA to inform the policy makings.

Assessing efficiency profiles of UK commercial banks: a DEA analysis with regression-based feedback

Data envelopment analysis (DEA) has witnessed increasing popularity in banking studies since 1985. In this paper, we propose a new DEA-based analysis framework with a regression-based feedback mechanism, where regression analysis provides DEA with feedback that informs about the relevance of the inputs and the outputs chosen by the analyst. Unlike previous studies, the DEA models used within the proposed framework could use both inputs and outputs, only inputs, or only outputs. So far, the UK banking sector remains relatively under researched despite its crucial importance to the UK economy. We use the proposed framework to address several research questions related to both the efficiency of the UK commercial banking sector and DEA analyses with and without regression-based feedback. Empirical results suggest that, on average, the commercial banks operating in the UK—whether domestic or foreign—are yet to achieve acceptable levels of overall technical efficiency, pure technical efficiency, and scale efficiency. On the other hand, DEA analyses with and without a linear regression-based feedback mechanism seem to provide consistent findings; however, in general DEA analyses without feedback tend to over- or under-estimate efficiency scores depending on the orientation of the analyses. Furthermore, in general, a linear regression-based feedback mechanism proves effective at improving discrimination in DEA analyses unless the initial choice of inputs and outputs is well informed.

Performance evaluation of general network production processes with undesirable outputs: A DEA approach

Performance evaluation of production systems with network structure has been widely studied in recent data envelopment analysis (DEA) literature. Production systems in which outputs of some stages are consumed as the inputs of some other stages in producing final outputs. In real world applications, production processes are often complex and may produce not only desirable but also undesirable intermediate or final outputs. In this paper modelling a general network DEA is considered in the presence of undesirable outputs. A weak disposable production set consistent with undesirable outputs is introduced and some network DEA models are also proposed for performance evaluation of the production units. The proposed method is illustrated by some numerical example, including an empirical application.

Assessment of urban sustainability efficiency based on general data envelopment analysis: a case study of two cities in western and eastern China.

Sustainable urban development focuses on enhancing urban well-being, while also balancing the demands of urban social and economic development, natural resource consumption, and environmental pollution. This work used general data envelopment analysis to assess the urban sustainability efficiency (USE) and sustainability potential (SP) in Lanzhou and Xiamen, two cities that are characteristic of urban areas in western and eastern China. The assessment indicator system included important natural and urban welfare factors as input and output indices, respectively. The results showed that overall urban sustainability efficiency increased in Lanzhou and Xiamen from 1985 to 2010, but that the sustainability of natural resources clearly decreased. The urban sustainability efficiency of Xiamen was higher than that of Lanzhou, and the sustainability potential of Xiamen was lower than that of Lanzhou; this indicates that Xiamen performed better in terms of urban sustainable development. The urban sustainability efficiency in Xiamen has increased with increasing urban population, and the rate and scale of economic development have been higher than in Lanzhou. The assessment and analysis performed in this study show that cities with different natural resources and development characteristics have different forms, patterns, and trajectories of sustainable development.

Towards a new model to benchmark firms’ operating efficiency: A data envelopment analysis approach

The purpose of the study was to construct two similar data envelopment analysis (DEA) models. The first contains only published accounting-based data and the second added weighted average cost of capital (WACC), a primary market-based determinant, as an input variable. The efficiency scores of firms according to the two models are compared to determine whether there is a significant difference between the two models’ results. In total, 206 company years were analysed. This includes all the manufacturing firms which published financial statements on the Johannesburg Security Exchange (JSE) from 2011 to 2013. The study found that there is a good chance that the efficiency score of a firm will be significantly lower when WACC is added as a variable. Therefore, ignoring WACC in a general benchmarking DEA model may provide a misleading, too optimistic, sugar-coated answer to firms’ managers with regard to their firms’ relative operating efficiency. The study contributes to the existing body of literature by revealing evidence that WACC is an important component in a DEA model that aims to benchmark firms’ operating efficiency. Therefore, accounting-based data should be used in conjunction with WACC, a primary market-based determinant, which adds a further dimension to the benchmarking model.

Determination of Efficient bandwidth utilization During Multicast using Data Envelopment Analysis

Data Envelopment Analysis (DEA) is an operational research tool that is used for measuring the performance efficiency of an algorithm or organization. In this paper, DEA is applied on the simulation results of an Improved Network Coding Algorithm (INCA) with two and three performance in order to establish the performance efficiency of the two algorithms in terms of bandwidth utilization during video conferencing over a wireless network. Most researches which focus largely on determining the effectiveness of the INCA in terms of bandwidth consumption during video conferencing. However, this approach which uses DEA, the simulation results showed that the INCA with two parameters is the most cost-Efficient algorithm in terms of performance than the INCA with three parameters. General Terms Data Envelopment Analysis, Improved Network Coding Algorithm, Multicast and Performance Efficiency.

Measuring efficiencies of parallel systems with shared inputs/outputs using data envelopment analysis

Purpose– The purpose of this paper is to measure the efficiencies of parallel subsystems with shared inputs/outputs. Each subsystem has not only a set of common inputs and outputs, but also some dedicated inputs and outputs as well as some shared inputs and outputs. A more general data envelopment analysis (DEA) approach is proposed to deal with this efficiency evaluation issue. Based on the proposed approach, mechanisms for shared inputs/outputs distribution and efficiency decomposition among sub-units are presented.Design/methodology/approach– To evaluate the efficiency of the parallel systems, this paper proposes a centralized DEA approach by assuming that the same input/output factor in a decision-making unit (DMU) has the same multiplier for all its sub-units. Furthermore, different proportions of shared inputs/outputs are imposed on sub-units within different DMUs in evaluating each DMU’s efficiency. The proposed approach is applied to evaluate the operational efficiencies of 18 railway firms in China.Findings– By using the proposed DEA approach, the efficiencies of the whole DMU and its sub-units can be measured at the same time, and the optimal allocation strategy of shared inputs/outputs can also be obtained. The proposed model is more reasonable and robust for measuring the operational performance of parallel systems with shared inputs and outputs. The efficiency of railway system in China is relatively low, and its inefficiency is largely caused by lower freight transportation performance. Great disparities among firms can be found in the passenger transportation efficiency and freight transportation efficiency.Research limitations/implications– This study develops the DEA model under the assumption of constant returns to scale, which can be directly extended to a situation with variable returns to scale.Practical implications– In this paper, the proposed approach is a more effective way to evaluate the efficiencies of parallel systems with shared inputs/outputs. With respect to the application, to improve the overall efficiency of China’s railway system, more efforts should be taken to improve its operational performance of freight transportation. Furthermore, firms’ disparities should also be considered when making these related policies.Originality/value– The proposed approach can evaluate the whole DMU and its sub-units at the same time. Considering simultaneously the common/dedicated/shared inputs/outputs, the proposed approach is more general than the existing approaches in the literature. In the described approach, the same type of input or output is assumed to have the same weight for all sub-units within one DMU. More importantly, the proposed model imposes different proportions of shared inputs/outputs on different DMUs’ sub-units when measuring the efficiency for each DMU.

Maintaining the Regular Ultra Passum Law in data envelopment analysis

The variable returns to scale data envelopment analysis (DEA) model is developed with a maintained hypothesis of convexity in input–output space. This hypothesis is not consistent with standard microeconomic production theory that posits an S-shape for the production frontier, i.e. for production technologies that obey the Regular Ultra Passum Law. Consequently, measures of technical efficiency assuming convexity are biased downward. In this paper, we provide a more general DEA model that allows the S-shape.

Output-specific input-assurance regions in DEA

The use of assurance region (AR) constraints to restrict multipliers in data envelopment analysis (DEA) is well-established, and has been discussed at length in the literature. The conventional assumption in imposing such restrictions is that they apply universally. Specifically, AR constraints on input multipliers are intended to control the relative importance of the individual inputs in terms of how they impact the entire bundle of outputs. In many settings the relative importance of inputs is different for some of the outputs than for others. A typical example of this in the financial services sector is where the importance of sales staff versus service staff is different in regard to sales outputs than is true for service outputs. In this paper we develop a general DEA framework that incorporates multiple input-AR structures that cater to multiple output classes. We examine the cases of both divisible and indivisible inputs, and as well as mutually exclusive and overlapping output sets. The concepts are applied to a financial services situation.

유입량의 변동성을 고려한 Fuzzy DEA 기반의 댐 군 연계운영 가중치 대안 평가

The multi-reservoir operation problem for efficient utilization of water resources involves conflicting objec-tives, and the problem can be solved by varying weight coefficient on objective functions. Accordingly, decision makers need to choose appropriate weight coefficients balancing the trade-offs among multiple objectives. Although the appropriateness of the weight coefficients may depend on the total amount of water inflow, reservoir operating policy may not be changed to a certain degree for different hydrological conditions on inflow. Therefore, we propose to use fuzzy Data Envelopment Analysis (DEA) to rank the weight coefficients in consideration of the inflow variation. In this approach, we generate a set of Pareto- optimal solutions by applying different weight coefficients on Coordinated Multi-reservoir Operating Model. Then, we rank the Pareto-optimal solutions or the corresponding weight coefficients by using Fuzzy DEA model. With the proposed approach, we can suggest the best weight coefficients that can produce the appropriate Pareto-optimal solution considering the uncertainty of inflow, whereas the general DEA model cannot pinpoint the best weight coefficients.