A DEA model for two-stage systems with Fuzzy data

An efficiency measurement model of a university faculty is proposed with additional new sub-functions that produce new output variables, based on the network Data Envelopment Analysis (DEA) model for systems with a hierarchical structure.For production systems composed of hierarchical processes, the system efficiency is well represented as the aggregated performance of the components involved in the system. It is identified that the conventional DEA model ignores internal process activities in a university. Therefore, an improved DEA model based on a network structure that accounts for more activities in a university is proposed to measure its overall efficiency. The impact of major functions of a university are taken into account to represent the output variables in assessing the efficiency. Currently, collaboration activities have been given more attention, so, this variable is suggested as a new output for the hierarchical production system. In order to show the practicality of the model, a hypothetical set of data of 14 faculties has been used as a numerical example. The results show that none of the faculties is relatively efficient since its functions were found to be inefficient. The proposed model enables to help the management of university faculties to identify weaknesses of each function and thus to plan for suitable actions on improving the overall performance of the university.

Data envelopment analysis (DEA) is a tool for measuring the relative efficiency of decision-making units (DMUs) that perform similar tasks. One of the uses of the DEA is the establishment of benchmarks for inefficient DMUs. These benchmarks play the role of target for inefficient DMUs. However, traditional DEA (TDEA) models fail to rank the efficient DMUs, and as a result, they cannot determine a benchmark for the inefficient DMUs. To overcome this shortcoming, this paper proposes virtual network DEA (NDEA) approach. The proposed method not only ranks the whole inefficient and efficient DMUs but also establishes a virtual benchmark called ideal DMU. The case study demonstrates the applicability of the proposed model.

The rapid development of the aviation industry has brought about the deterioration of the climate, which makes airline efficiency become a hot issue of social concern. As an important nonparametric method, Data Envelopment Analysis (DEA), has been widely applied in efficiency evaluation. This paper examines 130 papers published in the period of 1993–2020 to summarize the literature involving the special application of DEA models in airline efficiency. The paper begins with an overall review of the existing literature, and then the radial DEA, nonradial DEA, network DEA, dynamic DEA, and DEA models with undesirable outputs applied in airline efficiency are introduced. The main advantages and disadvantages of the above models are summarized, and the drivers of airline efficiency are analyzed. Finally, the literature review ends up with future research directions and conclusions.

When the number of Decision-Making Units (DMUs) is not large enough compared to the total number of input parameters and outputs, traditional Data Envelopment Analysis (DEA) and Network Data Envelopment Analysis (NDEA) models often produce solutions that identify many DMUs as efficient, in addition to obtaining unrealistic weight distributions. In fact, this poor discrimination power and unrealistic weight distribution presented by DEA and NDEA models remain a major challenge, leading to the development of models to improve this performance. Thus, this paper proposes a Multiple Criteria Network Data Envelopment Analysis (MCNDEA), based on relational NDEA models. The idea of this model is to be used in network structures. To test the MCNDEA model, one a real instance linked to an evaluation problem of academic departments of a public university was used. Other instances were also used to validate the proposed MCNDEA, and these tests are included in the supplementary files. Finally, it should be noted that, in summary, the model proposed in this article had greater discrimination power of the analyzed DMUs, being able to identify the most efficient departments in each of the considered stages, besides pointing out to the University Management points of improvement regarding the best use of its resources for each department.

Combining ranking scales and selecting variables in the DEA context: The case of industrial branches

This study explores the intellectual landscape and methodological evolution of Data Envelopment Analysis (DEA) in the context of renewable energy and carbon emission efficiency. Using bibliometric techniques and data extracted from the Web of Science Core Collection (2389 publications from 2000 to 2024), the research identifies influential authors, institutions, and thematic clusters shaping the field. The results reveal that DEA has evolved from a traditional efficiency assessment tool into a comprehensive analytical framework supporting sustainable energy transition and carbon mitigation policies. Six major research clusters were identified, encompassing carbon emission measurement, efficiency benchmarking, methodological innovations, industrial applications, circular economy perspectives, and international productivity comparisons. Notably, Asian scholars, particularly from China and Taiwan, dominate the research landscape, reflecting strong regional leadership in empirical and methodological advancements. The findings demonstrate that recent studies increasingly adopt advanced models such as network DEA, dynamic DEA, DEA–Malmquist, and hybrid DEA–machine learning approaches to address complex energy systems. Comparative insights highlight DEA’s advantages over Stochastic Frontier Analysis (SFA) in handling multi-dimensional, non-parametric data, while emphasizing the need for hybrid frameworks to improve robustness. This study contributes to the ongoing discourse on energy sustainability by mapping knowledge structures, revealing methodological trajectories, and providing guidance for future research on efficiency and carbon reduction strategies.

Data envelopment analysis (DEA) is one of the most appropriate methods for a data-oriented approach to evaluate the performance of a set of entities called decision making units (DMUs). This study aims at evaluating the efficiency of Iranian regional power companies using data envelopment analysis (DEA), under the uncertainty conditions in the fuzzy necessity scheme. In this study, we determine the total efficiency as well as the efficiency of each stage including the production, transmission and distribution using fuzzy network DEA (FNDEA). Since the Iranian power industries have a network structure, the network DEA process has been used for evaluating the efficiency of the processes of companies. Sixteen Iranian regional power companies were selected and analysed based on the performance of the production, transferring, and distribution.

Performance evaluation of bus routes: A provider and passenger perspective

Revenue management (RM) deals with selling the right product to the right customer at the right time at the right price through the right channel to maximise revenue. The innovation of RM lies in the way decisions are made. The performance of revenue management approaches can be evalu- ated against several criteria. Both discrete and continuous multicriteria models can be used to analyse RM. The performance pyramid is a comprehensive, fully integrated per- performance system that captures multiple perspectives such as internal, financial, customer and innovation. The assessment is based on a combina- tion of Analytic Hierarchy Process (AHP), Analytic Network Process (ANP) and Data Envelopment Analysis (DEA) approaches. Customer behavior modeling is gaining increasing attention in revenue management. Customer choice models can be extended with more inputs and more outputs. Evaluation of alternatives can be performed using DEA- based evaluation methods. The search for an efficient frontier in a DEA model can be formulated as a multiobjective linear programming problem. We propose to use an Aspiration Level Oriented Procedure (ALOP) to solve the problem. Keywords: revenue management, performance measurement, multiple criteria, Analytic Hierarchy Process (AHP), Analytic Network Process (ANP), Data Envelopment Analysis (DEA), customer behavior, efficient frontier, Aspiration Level Oriented Procedure (ALOP)

Food security is a global challenge. With rising world population and demand for food being compounded by resource and arable land constraints, raising the efficiency of food production and use has become increasingly important. While much of the research on food security is focused on farm efficiency and productivity, most neglect post-harvest (PH) handling which is critical in determining the availability of food. In this study, we employ the network Data Envelopment Analysis (DEA) model to evaluate the PH efficiency of milling, using data from Kenya’s rice processing industry. The results show lower efficiency scores when using a network DEA model, which reflects its greater discriminatory power when compared to the standard DEA approach. The study also quantified sources of productive efficiency using a fractional regression model and identified storage space and distance to market as having an impact on drying efficiency; while experience, age of mill, servicing and energy type influenced milling efficiency. The results suggest that policy makers should focus on investing in drying technologies and storage facilities to improve drying efficiency. To improve milling efficiency, policy recommendations include enhancing millers’ access to better technologies, investing in reliable sources of energy and providing PH handling workshops to reduce PH losses.

Energy efficiency of China's industry sector: An adjusted network DEA (data envelopment analysis)-based decomposition analysis

In this paper, we present for the first time the on-field production process of soccer teams as a mixed (serial and parallel) structure two-stage network system. According to this, the first stage consists of two distinct sub-processes (offense and defense) that operate in parallel. These respectively use players’ offensive and defensive actions as inputs to produce two different intermediate measures, namely, goals scored and prevention of goals conceded. These, in turn, are the inputs of the second stage (points’ accumulation sub-process) that produces accumulated points. Furthermore, based on a two-stage network Data Envelopment Analysis (DEA) model, we estimate the offensive, defensive, and athletic efficiency of soccer teams during a league season. According to our proposed framework, these three different efficiency scores are provided (for each soccer team under evaluation) by a single linear programming problem. For this purpose, aggregate-over-games statistics from the 2013–14 Greek premier soccer league are used.

In order to measure the efficiency of systems composed of several processes more appropriately, various network data envelopment analysis (DEA) models have been developed. One type of the model, which is able to calculate the system and process efficiencies at the same time, is relational. This paper discusses the relationship between the system and process efficiencies measured from this model, and derives five properties. The first is general to all types of network structure, which states that the efficiency slack of the system is the sum of those of the component processes. This implies that a system is efficient if and only if all its component processes are. The second to fourth correspond to three types of structure, series, parallel, and dynamic. The last states that any unstructured system can be transformed into a series of parallel structures for efficiency decomposition. Numerical examples are used to help explain the idea of each type of decomposition. Efficiency decomposition enables decision makers to identify the processes that cause the inefficiency of a system, and thus to make effective changes to it.KeywordsData envelopment analysisNetworkEfficiency decompositionRelational model

Sensitivity analysis of network DEA: NSBM versus NRAM

In a two-stage system with two divisions connected in series, fairly setting the target outputs for the first stage or equivalently the target inputs for the second stage is critical, in order to ensure that the two stages have incentives to collaborate with each other to achieve the best performance of the whole system. Data envelopment analysis (DEA) as a non-parametric approach for efficiency evaluation of multi-input, multi-output systems has drawn a lot of attention. Recently, many two-stage DEA models were developed for studying the internal structures of two-stage systems. However, there was no work studying the fair setting of the target intermediate products (or intermediate measures) although unreasonable setting will result in unfairness to the two stages because setting higher (fewer) intermediate measures means that the first (second) stage must make more efforts to achieve the overall production plan. In this chapter, a new DEA model taking account of fairness in the setting of the intermediate products is proposed, where the fairness is interpreted based on the Nash bargaining game model, in which the two stages negotiate their target efficiencies in the two-stage system based on their individual efficiencies. This approach is illustrated by an empirical application to insurance companies.