Two-stage Network Data Envelopment Analysis Research Articles

Allocating the fixed cost as a complementary input in two-stage system: A DEA approach

The existing research on fixed cost allocation (FCA) in two-stage system data envelopment analysis (DEA) models typically regards the fixed cost as an additional input for each decision-making unit (DMU). However, these models overlook the prevalent real-world scenario where fixed costs act as complementary inputs in actual production processes. This study proposes a general two-stage network DEA model that incorporates the fixed cost as a complementary input to optimize the allocation scheme. First, we construct a functional relationship between the efficiency scores of DMUs and their allocated fixed costsusing a modified super-efficiency DEA model, which effectively classifies DMUs and solves infeasible solutions within the variable returns to scale (VRS) framework. Then, we propose a fair and unique allocation model based on fairness and efficiency maximization principles. Specifically, we allocate fixed costs based on the operational scale for inelastic DMUs while equitably increasing the efficiency scores for elastic DMUs. Finally, a numerical example and an empirical study on subsidy allocation among 30 provinces demonstrate the rationality and acceptability of our approach.

A performance evaluation system for product eco-design in the fashion supply chain

With the increasing environmental awareness of citizens, sustainable fashion has become a hot topic in industry, academia, and society. The importance of product eco-design (ED) in ensuring the sustainability of organizations and supply chains cannot be overstated. This paper aims to establish an eco-design performance evaluation system and identify the most effective management mechanism. To achieve this goal, a linked two-stage network Data Envelopment Analysis (DEA) model is developed. This model has a well-defined internal structure and potential causal relationships between variables; and the two stages are Internal and Supplier Management (ISM) and Openness and Collaboration (OC). We analyze stage and overall efficiencies using proactive, reactive, and simultaneous approaches. Additionally, we explore the convergence characteristics of the industry's ED efficiency from 2015 to 2018. The results show that the overall ED efficiency of fashion enterprises is significant when considering the interrelatedness of subsystems. However, there is disharmony between the two stages. As the proactive approach, ISM is the optimal strategy to maximize ED efficiency. On the other hand, OC is critical to eco-design performance. This paper contributes to the existing literature by developing an innovative DEA analytical framework for evaluating eco-design performance. It also identifies the most eco-efficient way to achieve better environmental performances, which allows decision-makers to better allocate their design efforts and improve both short- and long-term corporate sustainability.

Congestion: relation between traditional DEA congestion and two-stage processes congestion

Congestion is a kind of inefficiency because it causes the decision-making units (DMUs) to be inefficient and reduces their output. Identifying inefficient DMUs and determining the cause of their inefficiencies has been one of the most important reasons for referring to the internal structure of DMUs and analyzing the effect of intermediate products on subDMUs (or stages) performance. In this paper, to characterize the cause of the DMU’s congestion, we refer to its internal structure as a two-stage network data envelopment analysis (DEA) and decompose the DMU’s congestion into black-box (BB) and two-stage structure congestion. Also, inputs have two separate and simultaneous roles; the black-box’s inputs role and the stage1’s input role, so three congestion types occur. Thus, we sought to analyze the relation between two types of initial inputs congestion, and intermediate products congestion, and express their effects on BB congestion. Finally, we define three congestion definitions and model the relation between two types of input congestion, intermediate products congestion and BB inputs congestion. Finally, a practical example illustrates the proposed method.

Two-stage network data envelopment analysis production games

<abstract> <p>DEA (Data Envelopment Analysis) production games combine DEA theory with cooperation games and assess the benefits to production organizations with single-stage structure. However, in practical production problems, the production organizations are always with network structures. The structure of the production organization not only affects its own benefits, but also relates to the cooperation among organizations. Therefore, it is necessary to study DEA production games with network structures. In this paper, we consider the production organizations with two-stage processes, wherein the organizations are assumed to possess available resources and own technologies. The technology level of each organization is reflected by the observed units based on the network DEA (NDEA) production possibility set. Suppose that the organizations can cooperate through the ways of pooling the initial resources and (or) sharing the technology in each production process. According to the different cooperation styles of each stage in the alliance, seven types of cooperation among organizations are considered. The models of maximizing the revenues of coalitions, namely the NDEA production games, are established corresponding to the seven types, by which the maximal revenue for each coalition can be calculated. We prove that two-stage DEA production games have the super-additive property, and can be expressed as linear programming games. Hence, they are equivalent to the linear production games, and they are totally balanced. Therefore, the proposed cooperative games have a non-empty core, and hence have nucleolus, and the Owen set belongs to the core. In addition, based on the basic conceptions of the nucleolus and the Owen set, the revenue can be allocated among organizations in the alliance. Finally, a numerical example and an empirical application to 17 bank branches of the China Construction Bank in the Anhui Province are presented to illustrate the applicability of the proposed approach, and the relationship between the cooperative manners and the revenue allocation is reflected in analytical results.</p> </abstract>

Measuring the Efficiency of Turkish Research Universities via Two-Stage Network DEA with Shared Inputs Model

The efficiency of universities, which have a network structure of production process, is an essential component of performance measurement in education. However, most previous studies use traditional Data Envelopment Analysis (DEA), which disregards the network structure of the production process in universities. This study adopts a two-stage Network Data Envelopment Analysis (NDEA) with shared inputs model to assess the overall, teaching and research efficiencies of Turkish research universities. The findings show that only 6 out of 23 research universities are efficient, and some universities with lower world rankings are more efficient than those with higher rankings. On the other hand, no significant difference was found between the efficiency levels of regions with a high level of socio-economic development and regions with a relatively low level of socio-economic development. The study also evaluates the effects of different priority scenarios on efficiency and the optimal allocation of shared inputs between sub-processes. This study provides guidance for universities seeking to improve their performance and for the Council of Higher Education (CHE) in determining incentives for research universities. It also promotes the use of multi-stage NDEA with shared inputs model over traditional DEA for accurate efficiency assessment in the field of education.

Assessing environmental and operational efficiencies: a multi-objective optimisation problem in a two-stage network data envelopment analysis

Abstract The environmental efficiency of industries plays an important role in economic development of countries. Accordingly, dividing the internal network structure of industries into two sub-processes, including green and operational stages enables decision-makers to assess both of the efficiencies simultaneously. Such assessment can be implemented using a non-parametric methodology termed data envelopment analysis (DEA). Standard DEA models consider the whole system of decision-making units (DMUs) as a single process (i.e., black-box). The black-box approach ignores modelling of the internal network structure of the assessed DMUs. This issue tackled by network DEA models since it considers the internal network structure of DMUs. In the network DEA, the efficiency evaluation of system stages is essential to identify its overall efficiency, resulting to a multi-objective optimisation problem. Therefore, the network DEA is a widely welcomed methodology proposed for solving multi-objective problems. This paper assesses the operational and environmental efficiencies of a network structure system by converting the multi-objective optimisation problem into a linear single objective function. In this investigation, a technique of tri-objective function problem is proposed. The proposed technique transforms into a single objective function by keeping one objective function and shifting the other two objective functions into the model’s constraints. The applicability and usefulness of the proposed technique have been tested using a data set of 20 industries. The developed approach provides valuable evaluations to decision-makers to rank DMUs by considering their green and operational efficiency simultaneously.

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.

Efficiency assessment of public sector management and culture-led urban regeneration using the enhanced Russell-based directional distance function with stochastic data

Generic data envelopment analysis (DEA) models are based on deterministic input and output. However, input and output vectors are often interrupted by random factors, such as measurement errors and data noise, in real economic situations. This study proposes a new chance-constrained network DEA model based on the modified directional distance function (DDF) and enhanced Russell measure (ERM) model for assessing government management and culture-led urban regeneration. In addition to exploring the randomness of data, this study integrates the advantages of both ERM and DDF and considers the inefficiency level from a non-oriented viewpoint, the direction vector, and each input and output simultaneously. Each input and output of the two production stages can use non-radials to measure efficiency. Results show that the urban-rural gap has gradually widened since 2015. To validate the legitimacy of the model, this study utilizes the bootstrapping method to verify the results of the stochastic network DEA model and the conventional two-stage network DEA approach. This study also considers different alpha values as basis for comparison to confirm whether the results obtained differ by uncertainty level.

Development of the neutrosophic two-stage network data envelopment analysis to measure the performance of the insurance industry

Development of the neutrosophic two-stage network data envelopment analysis to measure the performance of the insurance industry

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.

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.

Regional Differences and Convergence of Urban Water Use Efficiency in the Yangtze River Economic Belt

This study used a two-stage network data envelopment analysis model to measure the water use efficiency of 108 cities in the Yangtze River Economic Belt in the initial water use and wastewater treatment phases from 2009 to 2019. We divided the urban water use efficiency of six significant urban clusters in the Yangtze River Economic Belt using the Dagum Gini coefficient. We also tested the convergence characteristics of urban water use efficiency in six significant urban clusters in the Yangtze River Economic Belt using convergence and convergence kinds. According to this report, the Yangtze River Economic Zone’s cities often have low levels of water use efficiency, which is primarily due to ineffective wastewater treatment. The 108 cities in the Yangtze River Economic Zone are divided into four types based on the average values of water use efficiency in the initial use and wastewater treatment phases; the highest number of cities are in the double-low category, with low average values of water use efficiency in the initial use and wastewater treatment phases. During the study period, spatial differences in urban water use efficiency in the Yangtze River Economic Zone narrowed, with the differences stemming mainly from hyperdensity, followed by intra- and inter-regional differences. Meanwhile, there is convergence in urban water use efficiency in the Yangtze River Economic Belt, significant β convergence in the urban agglomerations of the Yangtze River Delta, Jianghuai, middle reaches of the Yangtze River, Chengdu–Chongqing, and Central Yunnan, and insignificant β convergence in the Central Qian urban agglomeration. After considering control factors, such as industrial structure, financial development level, environmental regulation, economic development level, and science and education development level, the water use efficiency of the six major urban clusters in the Yangtze River Economic Belt converges faster, but the influence of these control factors on the water use efficiency of each urban cluster is heterogeneous. Research results have reference value for the development of improvement strategies on differentiated urban water use efficiency in the Yangtze River Economic Belt. By measuring the regional differences in water use efficiency of urban agglomerations in the Yangtze River Economic Belt and clarifying their convergence mechanism, it provides a basis for analyzing the spatial pattern of water use efficiency in urban agglomerations and has reference value for formulating differentiated urban water use efficiency improvement strategies in the Yangtze River Economic Belt.

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.

Exploring the Influence of Environmental Investment on Multinational Enterprises’ Performance from the Sustainability and Marketability Efficiency Perspectives

Sustainable development strategies are necessary to ensure sustainable performance even though resources are scarce in a firm. In this study, a two-stage production process is designed to analyze a firm’s performance, including sustainability and marketability, using a two-stage network data envelopment analysis. This process will help managers of a firm understand how to improve sustainability and marketability efficiency. The relationship between environmental investment and firm performance is also investigated using truncated regression. The results show that the environmental innovation score (EIS) and resource use score (RUS) have significant negative relationships with firm performance in the short term due to the fact of additional expenses incurred during the innovative research and development of new products and services. Moreover, the study reveals that the emission score positively affects both sustainability efficiency and marketability efficiency, while EIS and RUS have no effects on the efficiencies. These empirical findings are meant to assist managers in better comprehending the characteristics of business sustainability across industries with varying scales and performance levels, offer better business strategies for resource allocation, and enhance a firm’s performance in the post-pandemic era.

On second order cone programming approach to two-stage network data envelopment analysis

In two recent papers, [Guo, C., Wei, F., & Chen, Y. (2017). A note on second order cone programming approach to two-stage network data envelopment analysis. European Journal of Operational Research, 263(2), 733–735; and Chen, K., & Zhu, J. (2017). Second order cone programming approach to two-stage network data envelopment analysis. European Journal of Operational Research, 262(1), 231238] converted the general multiplicative two-stage DEA (data envelopment analysis) network model into a parametric/single second order conic programming (SOCP) problem. In this paper, we (i) note that the proposed transformation cannot result in an equivalent mathematical program in view of the fact that the general multiplicative two-stage DEA model is basically a nonconvex optimisation problem, possibly with several local and global optimums, whereas a single SOCP is a convex optimisation; (ii) demonstrate that there is a subtle technical error contained in the main transformation process proposed in both papers; (iii) illustrate, by providing a numerical counterexample, that the optimal solution obtained from the resulting single SOCP problem might be substantially different from the original model’s optimum; and (iv) offer some computational remark for solving the multiplicative/additive two-stage DEA model.

Examining operational efficiency with prudent risks of Covid-19: a contextual DEA analysis with an undesirable intermediate measure.

In the wake of the losses of human lives and disruption to the world economy caused by the spread of the COVID-19 pandemic, it has become imperative to assess the effectiveness of containment strategies adopted by countries. The success of any containment strategy of achieving low mortality and high recovery rate depends on the efficient utilization of available but limited resources, such as number of hospital beds and healthcare workers. While the spreading pattern of the pandemic has been researched heavily, there is limited research that comprehensively focuses on the efficient utilization of available resources to achieve the desired aims of low mortality and high recovery. In order to close this research gap, we employ a two-stage network data envelopment analysis (DEA) to identify the inefficiency in the process and resolve the resource constraints by considering medical and non-medical (administrative) interventions as two serial stages. The number of infected people is treated as the intermediate product, which is an undesirable output of the first stage and subsequently enters the second stage as an input. This network DEA model successfully addresses the conflict between the two stages over the handling of infected people and assesses the vulnerabilities of the countries against the transmission rates of the disease in the respective countries. Thus, the objective of this study is to develop a well-coordinated plan for different government agencies to jointly mitigate the risk under constrained resources. The findings reveal that almost of the Organization for Economic Cooperation and Development (OECD) countries have used their resources suboptimally and are producing, on average, almost half the amount of the maximum possible outputs. As a sizeable amount of inefficiency can be explained by varying economic and demographic factors, such as health expenditure and the proportion of the aged population, the efficiency evaluation has been revisited with adjustments for unfavorable externalities. The analysis and its implications can help policymakers formulate optimal resource plans and identify potential areas for improvement.

Design of humanitarian supply chain system by applying the general two-stage network DEA model

PurposeThe recent COVID-19 outbreak and severe natural disasters make the design of the humanitarian supply chain network (HSCN) a crucial strategic issue in a pre-disaster scenario. The HSCN design problem deals with the location/allocation of emergency response facilities (ERFs). This paper aims to propose and demonstrate how to design an efficient HSCN configuration under the risk of ERF disruptions.Design/methodology/approachThis paper considers four performance measures simultaneously for the HSCN design by formulating a weighted goal programming (WGP) model. Solving the WGP model with different weight values assigned to each performance measure generates various HSCN configurations. This paper transforms a single-stage network into a general two-stage network, treating each HSCN configuration as a decision-making unit with two inputs and two outputs. Then a two-stage network data envelopment analysis (DEA) approach is applied to evaluate the HSCN schemes for consistently identifying the most efficient network configurations.FindingsAmong various network configurations generated by the WGP, the single-stage DEA model does not consistently identify the top-ranked HSCN schemes. In contrast, the proposed transformation approach identifies efficient HSCN configurations more consistently than the single-stage DEA model. A case study demonstrates that the proposed transformation method could provide a more robust and consistent evaluation for designing efficient HSCN systems. The proposed approach can be an essential tool for federal and local disaster response officials to plan a strategic design of HSCN.Originality/valueThis study presents how to transform a single-stage process into a two-stage network process to apply the general two-stage network DEA model for evaluating various HSCN configurations. The proposed transformation procedure could be extended for designing some supply chain systems with conflicting performance metrics more effectively and efficiently.

Cross-efficiency evaluation and improvement in two-stage network data envelopment analysis

Cross-efficiency evaluation and improvement in two-stage network data envelopment analysis

Coordination efficiency for general two-stage network system

Two-stage network data envelopment analysis (DEA) is widely used to evaluate efficiency of different organizations with multiple operations processes or hierarchical structures. Although existing two-stage network DEA assumes two-stage systems resolve the inherent conflicts between two stages, the coordination effect between the two stages is usually ignored. Recently, the relation of two-stage network DEA to traditional “black box” DEA has been studied from the perspective of system coordination. A coordination efficiency was defined and measured by a DEA-based approach based on simple two-stage network systems. In this paper, we propose an extended DEA-based approach for measuring the coordination efficiency for general two-stage network systems. The paper shows that the coordination efficiency based on the multiplier DEA and envelopment DEA approaches is equivalent to each other under both constant returns to scale (CRS) and variable returns to scale (VRS) assumptions. The proposed approach is verified via two numerical examples finally.

글로벌 금융위기와 유럽 금융위기 기간의 항공사 효율성 분석 연구

The global financial crisis and economic recession lead to a decline in airline returns and deterioration in the business environment. In this regard, we compared and analyzed the efficiency of airlines during the global financial crisis and the European financial crisis by using the two-stage Network Data Envelopment Analysis (DEA) model. Network DEA can complement the shortcomings of the traditional DEA model and explain the transformation process hidden in the intermediate process and compare the relationship between efficiency. For the analysis, 16 airlines in Europe and related countries were selected and the period from 2007 to 2016, when the financial crisis occurred, was used. As variables, ‘operating costs’ and the ‘number of employees’ were used as input, and