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This paper aims to present two-stage network models in the presence of stochastic ratio data.

Black-box, free-link and fix-link techniques are used to apply the internal relations of the two-stage network. A deterministic linear programming model is derived from a stochastic two-stage network data envelopment analysis (DEA) model by assuming that some basic stochastic elements are related to the inputs, outputs and intermediate products. The linkages between the overall process and the two subprocesses are proposed. The authors obtain the relation between the efficiency scores obtained from the stochastic two stage network DEA-ratio considering three different strategies involving black box, free-link and fix-link. The authors applied their proposed approach to 11 airlines in Iran.

In most of the scenarios, when alpha in particular takes any value between 0.1 and 0.4, three models from Charnes, Cooper, and Rhodes (1978), free-link and fix-link generate similar efficiency scores for the decision-making units (DMUs), While a relatively higher degree of variations in efficiency scores among the DMUs is generated when the alpha takes the value of 0.5. Comparing the results when the alpha takes the value of 0.1–0.4, the DMUs have the same ranking in terms of their efficiency scores.

The authors innovatively propose a deterministic linear programming model, and to the best of the authors’ knowledge, for the first time, the internal relationships of a two-stage network are analyzed by different techniques. The comparison of the results would be able to provide insights from both the policy perspective as well as the methodological perspective.

Each production unit is responsible for the protection of the environment. The restricted undesirable production effects lower environmental damage. This paper emphasizes a proportional reduction of the undesirable outputs, and it supports the growth of desirable outputs as much as possible as well. The two-stage proposed model not only considers the viewpoint of the managers to follow the environmental regulations but also it assigns some bounds on producing undesirable factors according to international environmental protocols. Additionally, the restricted bounds on the undesirable outputs, in both stages, enhance the discriminatory ability of the model.

Two-stage network structure based on Data Envelopment Analysis (DEA) is applied as the main methodology for this paper. The advantages of the proposed model are appointed to assess the environmental units.

Comparing with the existing models, the proposed approach presents a new two-stage model to deal with the environmental issues. Furthermore, the discriminatory ability of the efficiency scores is improved. The distribution of this model is greater than the existing ones.

This paper is fully written, submitted and revised during limitations caused by coronavirus .

The proposed method is employed in two different cases. The efficiency scores of 25 power plants and 13 poultry farms are determined. In fact, the undesirable outputs never meet zero in the process of production but they can be reduced. The results of this research support the effect of the undesirable factors' restriction on the reduction scenario. Both of the examples show that imposing the upper bounds for the undesirable products provide low-efficiency results in comparison with the existing model. On the other hand, the results cover the arguments of sustainability in the evaluation of environmental efficiency.

In the production process, desirable outputs and undesirable factors are produced jointly so undesirable factors never meet zero. This paper develops a new two-stage method to reduce the undesirable outputs at each stage. First, the model confirms the reduction of undesirable outputs. Second, this model imposes restrictions on intermediate and final undesirable outputs according to environmental rights and the concerns of the managers. The model increases the discrimination of the efficiency assessment of real-life two-stage environmental systems as well. Then it focuses on the production of desirable outputs. The new objective function is defined according to the aim of the proposed model that not only declares better efficiency decomposition to the individual system but also the efficiency score is evaluated for each stage.

A Nash bargaining game data envelopment analysis (NBG-DEA) model is proposed to measure the efficiency of dynamic multi-period network structures. This paper aims to propose NBG-DEA model to measure the performance of decision-making units with complicated network structures.

As the proposed NBG-DEA model is a non-linear mathematical programming, finding its global optimum solution is hard. Therefore, meta-heuristic algorithms are used to solve non-linear optimization problems. Fortunately, the NBG-DEA model optimizes the well-formed problem, so that it can be solved by different non-linear methods including meta-heuristic algorithms. Hence, a meta-heuristic algorithm, called particle swarm optimization (PSO) is proposed to solve the NBG-DEA model in this paper. The case study is Industrial Management Institute (IMI), which is a leading organization in providing consulting management, publication and educational services in Iran. The sub-processes of IMI are considered as players where their pay-off is defined as the efficiency of sub-processes. The network structure of IMI is studied during multiple periods.

The proposed NBG-DEA model is applied to measure the efficiency scores in the IMI case study. The solution found by the PSO algorithm, which is implemented in MATLAB software, is compared with that generated by a classic non-linear method called gradient descent implemented in LINGO software.

The experiments proved that suitable and feasible solutions could be found by solving the NBG-DEA model and shows that PSO algorithm solves this model in reasonable central process unit time.

The purpose of this paper is to examine the development of rice supply chain in the context of the role of rice farmer organizations and cooperative networks in Thailand.

Primary data were solicited from the cooperatives and members of cooperatives for this study through questionnaire administration. The questionnaire containing a five-point Likert scale was posed to respondents to ascertain their problems before and after joining the network (for cooperative) and after joining the cooperative (for members). This study employed the independent two-sample student t-test (two-tailed) to test for significant difference in the means of scores regarding the problems of cooperatives before and after the cooperative network, and also to test for significant difference in the means of scores of the problems of members of the cooperatives before and after joining the cooperative.

The study revealed that key production and marketing problems such as increased transaction costs and market uncertainties confronting the cooperative organizations have been diminished as a result of the networks. Key problems of the members of the cooperatives such as exploitation and opportunistic behavior of traders to whom they sell their products have been reduced as a result of joining the cooperatives.

This paper is not without caveat. The governance structures in relation to leadership, financial arrangements and bargaining power balance have not been analyzed in this study and these are avenues for further research.

To the best of the authors’ knowledge, this study is the first that examined the combined roles of farmer organizations and cooperative networks in developing the rice supply chain in Thailand.

As a transition economy, China is interested in allocating its limited innovation resources economically, reasonably and efficiently to produce as many outputs as possible with its limited financial and human resources. Nonetheless, what is the efficiency of the allocation of innovative resources for civil–military integration enterprises, and what factors hinder its efficiency improvement? The purpose of this paper is to explore these problems.

The improved two-stage network data envelopment analysis (DEA) method is used to measure the overall efficiency and stage efficiency of the innovation resource allocation of 58 Chinese civil–military integration listed companies from 2010 to 2016. Tobit model is used to analyze the influencing factors of resource allocation efficiency.

The results indicate that the overall efficiency and stage efficiency of innovation resource allocation fluctuate in varying degrees during the period. The optimization of overall efficiency is restricted by lower efficiency of innovation achievement transformation. Enterprise scale was found to have a significant negative impact on both overall and two-stage efficiencies. Proportion of research and development (R&D) personnel had a positive effect on the overall and two-stage efficiency. Government support had a significant positive effect on the stage of innovation resource development and overall efficiency.

Previous research studies have used either the DEA or stochastic frontier analysis method to measure the efficiency of innovation activities as a whole and ignored the stage of initial investment to final output in innovation activities. That is, the process in which initial input of R&D resources becomes innovation output, and then becomes economic benefits. Therefore, this paper studies the efficiency of innovation resource allocation of civil–military integration listed companies. The improved two-stage chain network DEA method and Tobit model were used.

The purpose of this paper is to apply data envelopment analysis (DEA) techniques to the collective decision-making environment to appraise two-stage production process under different decision preferences.

The authors propose a novel multi-criteria group decision-making approach that uses consensus-strategic data envelopment analysis (CSDEA) to appraise two-stage production process under two different decision strategies, which are efficiency- and fairness-based group decision preferences.

The authors find that the proposed CSDEA model evaluates the performance of the decision-making units (DMUs) not by diminishing other competitors but rather based on group interests of the entire decision set.

The authors extend Li’s two-stage model to cases that consider both intermediate inputs and outputs. The authors address the issue of incorporating collective managerial strategy into multi-criteria group decision-making and propose a novel CSDEA model that considers not only the individual-level performance of a DMU but also the group-level or collective decision strategies.

The purpose of this paper is to provide an effective and simple technique to structural damage identification, particularly to identify a crack in a structure. Artificial neural networks approach is an alternative to identify the extent and location of the damage over the classical methods. Radial basis function (RBF) networks are good at function mapping and generalization ability among the various neural network approaches. RBF neural networks are chosen for the present study of crack identification.

Analyzing the vibration response of a structure is an effective way to monitor its health and even to detect the damage. A novel two‐stage improved radial basis function (IRBF) neural network methodology with conventional RBF in the first stage and a reduced search space moving technique in the second stage is proposed to identify the crack in a cantilever beam structure in the frequency domain. Latin hypercube sampling (LHS) technique is used in both stages to sample the frequency modal patterns to train the proposed network. Study is also conducted with and without addition of 5% white noise to the input patterns to simulate the experimental errors.

The results show a significant improvement in identifying the location and magnitude of a crack by the proposed IRBF method, in comparison with conventional RBF method and other classical methods. In case of crack location in a beam, the average identification error over 12 test cases was 0.69 per cent by IRBF network compared to 4.88 per cent by conventional RBF. Similar improvements are reported when compared to hybrid CPN BPN networks. It also requires much less computational effort as compared to other hybrid neural network approaches and classical methods.

The proposed novel IRBF crack identification technique is unique in originality and not reported elsewhere. It can identify the crack location and crack depth with very good accuracy, less computational effort and ease of implementation.

Competition 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.

In 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”.

The 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.

Grey 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.

Compared 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.

The purpose of this paper is to examine the industrial production efficiency, pollution treatment efficiency, total factor energy efficiency and water efficiency in China with the consideration of technological innovation. This study also explores the distribution proportion of technological innovation between industrial production substage and pollution treatment substage.

A nonparametric method, data envelopment analysis (DEA), is used as the model foundation of this study. Specifically, a novel two-stage range-adjusted measure (RAM-DEA) with shared inputs is constructed to analyze the China’s industrial system. In this study, the panel data of 30 provinces from 2008 to 2015 are used.

This study found that although the current environmental regulation reduced the efficiency of industrial production, it could significantly improve the pollution treatment level. However, the lack of pollution treatment capacity was still an obstacle for development of China's industrial system. Compared with the total factor energy efficiency, the total factor water efficiency had more room for improvement. The optimal distribution of technological innovation in the two substages performed little change and the distribution roughly followed the “three-seven principle”.

More attention should be paid to improve the pollution treatment level and total factor water efficiency. And more R&D expenditure should be used in the industrial production substage in the eastern coastal areas, while in the inland areas, more R&D expenditure should be used in the pollution treatment substage.

This study proposed a model to environmental efficiency score with considering interval data under two-stage evaluation structure, which could strengthen the theory and expand the application scope of DEA approach.

This paper aims to investigate efficiency in the UK hotel industry and further evaluate the impacts of hotel characteristics and industry environment on efficiency.

The network data envelopment (DEA) weak link approach is used for the efficiency analysis, while the determinants of efficiency are evaluated by bootstrapped truncated regression.

The findings show that the UK hotel industry is very inefficient. The results of overall efficiency deconstruction show that the second-stage production process experiences an even lower level of efficiency than that of the first stage. The second-phase analysis shows that both the hotel-specific characteristics and the industry-specific characteristics are significantly related to UK hotel efficiency.

The robustness of the results is affected because a single set of input-intermediate product-outputs and a single DEA method were used. Therefore, further studies can use alternate inputs, intermediate measures and outputs in the efficiency analysis. In addition, the robustness of the efficiency score can be checked using alternate parametric or non-parametric methods.

Hotels in the UK should focus on cost reduction, business diversification, improvement in the capital level and labor productivity, while at industry and macroeconomic level, discounts are recommended to be provided to international tourism and the tourism industry should be further opened.

The weak-link approach has been applied to estimate the efficiency level, as this provides more robust and accurate results compared to other non-parametric methods in the existing empirical studies and unique hotel-specific and industry-specific determinants of efficiency are considered in the second-stage analysis.