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Systematic Review

Measuring Circular Economy with Data Envelopment Analysis: A Systematic Literature Review

by
Svetlana V. Ratner
1,2,3,*,
Andrey V. Lychev
3,
Elisaveta D. Muravleva
3 and
Daniil M. Muravlev
3
1
Department of Economic and Mathematical Modelling, Peoples’ Friendship University of Russia, 6 Miklukho-Maklaya St., 117198 Moscow, Russia
2
Laboratory for Scientometric Analysis and International Rankings, Armenian State University of Economics, Nalbandyan 128, Yerevan 0025, Armenia
3
College of Computer Sciences, National University of Science and Technology “MISIS”, 4 Leninsky Ave., Bldg. 1, 119049 Moscow, Russia
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2025, 30(5), 102; https://doi.org/10.3390/mca30050102
Submission received: 27 June 2025 / Revised: 7 September 2025 / Accepted: 15 September 2025 / Published: 17 September 2025
(This article belongs to the Special Issue Feature Papers in Mathematical and Computational Applications 2025)
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Abstract

This article presents a systematic literature review of data envelopment analysis (DEA) models used to evaluate circular economy (CE) practices. The review is based on 151 peer-reviewed articles published between 2015 and 2024. By analyzing this collection, this review categorizes different DEA models and their levels of application, discusses the data sources utilized, and identifies the prevailing methodologies and evaluation criteria used to measure the CE performance. Despite the extensive literature on measuring the circular economy using DEA, a critical evaluation of existing DEA approaches that highlights their strengths and weaknesses is still missing. Our analysis shows that DEA models provide valuable insights when assessing circular strategies, namely, R2—Reduce, R8—Recycling, and R9—Recovering. Over 40% of the surveyed literature focuses on China, with nearly 20% on the European Union. Other regions are sparsely represented within our sample, highlighting a potential gap in the current research landscape.
Keywords:
circular economy; data envelopment analysis; literature review; recycling; sustainable development
MSC:
91B74; 90B30; 90C05
JEL Classification:
Q53; Q58; C61; C67

1. Introduction

Measuring the circular economy (CE) presents a number of significant challenges, as highlighted in the existing literature [1,2,3,4]. This is largely due to the differing interpretations of the CE concept, often simplifying it to merely material recirculation. Most existing metrics, such as waste generation, material footprint, recycling rates, and others, fail to adequately represent the complexities of multifunctionality and the consequences of material downcycling. While the fundamental principles and overarching vision of CE are well-articulated and widely understood, translating these into measurable progress presents a significant hurdle. Consequently, there is currently no universally adopted monitoring framework or standardized metrics to robustly evaluate its implementation and impact [5,6]. This difficulty in quantification stems from various inherent complexities. The various ‘R’ principles (3Rs, 6Rs, etc.) used in the literature also differ [2]. Starting as a set of hierarchical strategies aimed at optimizing resource efficiency, minimizing waste generation, and reducing environmental impact throughout a product’s life cycle (Reduce, Reuse, Recycle), they later evolved into more comprehensive frameworks (such as 6R, 9R, 10R, and 12R), integrating strategies that intervene at earlier stages of the product life cycle.
Therefore, a wide range of measurement approaches exists that cover different aspects and are seemingly unrelated to each other. The research landscape related to the CE transition is characterized as fragmented and granular [5]. Defining efficiency indicators in a circular economy is highly complex [7]. Researchers find it challenging to develop indicators that accurately measure CE performance levels, particularly with regard to waste reduction, reuse, and recycling. These difficulties include uncertainty of system boundaries, the necessity to measure counterfactual parameters (i.e., estimating the amount of waste that would have been generated without CE strategies), and the tendency to ignore hidden trade-offs (e.g., the high energy consumption involved in recycling processes). The definition and establishment of these indicators are challenging.
Currently, there is no widely accepted monitoring framework or standardized metrics for evaluating progress toward a CE [5,6]. The CE concept is not clearly defined, and there is no commonly accepted definition. This makes it difficult to determine which elements should be measured. Furthermore, the various ‘R’ principles (3Rs, 6Rs, etc.) used in the literature also vary [2]. A wide range of measurement approaches exists that cover different aspects and are seemingly unrelated to each other. The research landscape related to the CE transition is characterized as fragmented and granular [5]. Defining efficiency indicators in a circular economy is highly complex [7]. Researchers find it difficult to develop indicators that accurately measure CE performance levels, particularly with regard to waste reduction, reuse, and recycling. The definition and establishment of these indicators are challenging.
Current measurements of resource productivity and efficiency are considered unsatisfactory in the context of the circular economy [8]. These metrics often fail to fulfill the circular economy’s primary objective of preserving the value of products, components, and materials for as long as possible [9]. Moreover, only a few CE metrics assess features related to maintaining value [5]. The lack of necessary data is also a significant limitation. Without adequate data, it is difficult to define indicators, which requires companies to invest considerable time and economic resources. Data collection can be challenging, partly due to a lack of information exchange between researchers and company managers, potentially due to confidentiality issues [10]. Efforts are often hindered by discrepancies, gaps, and contrasts in data [6]. Moreover, the measurement and assessment of circular performance is not yet a common practice in companies. Indicators struggle to directly influence business practice. There may also be low stakeholder participation in the design of indicators [11].
Another challenge is the apparent lack of interest in analyzing the middle-of-life (MoL) phase of a product’s life cycle [1]. Existing methodologies tend to focus more on the stages from production to disposal than on the initial development phase (BoL). Furthermore, while environmental and economic factors are frequently considered, social equity is less often incorporated into CE indicators that combine the 3Rs principles [12].
These challenges highlight the ongoing need for further research, as well as the development of common methods and strategies, to enable the systematic and practical measurement and assessment of the degree of circularity across different systems and levels.
In recent years, data envelopment analysis (DEA) has become a popular methodological approach for measuring the performance, efficiency, and dynamic evolution of various aspects of CE [13,14,15]. One reason for its popularity is that the CE inherently involves undesirable outputs such as pollution and waste. DEA models can incorporate these factors by treating them as inputs to be minimized or as specific outputs, often using methods such as the slacks-based measure (SBM) or directional distance function (DDF) [13,16,17,18]. Furthermore, the DEA can decompose systems to evaluate the efficiency of internal subsystems (e.g., industrial production, environmental treatment, recycling, and wastewater treatment) and individual factors (inputs and outputs) within them [14,15].
In many recent studies, network DEA models have been widely used to recognize that CE systems have internal structures and interconnected stages. These models break down the system into stages (e.g., production, treatment, and recycling) and analyze the efficiency of each stage and of the system as a whole. This approach moves beyond the ‘black box’ view of traditional DEA [19,20,21]. In summary, the DEA provides a flexible and objective framework for evaluating the complex, multi-input, multi-output systems inherent in the circular economy. Over the last five years, various extensions such as network, dynamic, game-theoretic, and fuzzy DEA models have been developed to address the specific structural, temporal, and data characteristics of CE performance evaluation.
However, prior to applying the DEA, there is a challenge in properly defining and selecting the key criteria, as well as the appropriate inputs and outputs, for evaluating urban or industrial circular economies. Existing indicator systems are sometimes criticized for being too general, lacking management or potential indicators, or for not fully capturing the circular loop and its link to sustainable development [15]. Furthermore, as there are many different types of DEA models, selecting the most suitable model structure, orientation (input vs. output), and assumptions (e.g., constant or variable returns to scale, CCR/CRS vs. BCC/VRS) for a particular CE context necessitates careful consideration and expertise [22,23].
This study aims to conduct a systematic literature review of work published between 2015 and 2024 on measuring the circular economy (or certain aspects of it) using DEA. The specific research questions for this review are as follows:
RQ1: To reveal the state of the art by identifying the strengths and weaknesses of existing DEA approaches for measuring the multifaceted circular economy.
RQ2: To identify specific knowledge gaps and methodological challenges and inform future research aimed at providing more accurate, dynamic, and actionable insights to promote CE development.

2. Methodology

To answer these research questions, we perform a systematic literature review using the PRISMA protocol. This review was registered at Open Science Framework (OSF) and publicly available at https://osf.io/y4dxe (accessed on 1 July 2025).
The systematic review was conducted using journal articles retrieved from both Google Scholar and Scopus. In the Scopus database, the search query
TITLE-ABS-KEY: {(“DEA” OR “data envelopment analysis”) AND “circular economy”}
was applied, yielding a total of 117 articles. Given the limited number of results obtained from Scopus, the review was supplemented with publications from Google Scholar, which offers a broader scope of sources. Due to the constraints of Google Scholar’s search functionality, relevant publications were collected for each year from 2015 to 2024 using the Publish or Perish software, version 8.17.4863.9118.
As a result of data extraction, a total of 6684 records were obtained. The flowchart of the selection procedure according to the PRISMA protocol is presented in Figure 1. After the eligibility evaluation, 1431 papers were excluded based on the exclusion criteria described in Table 1. Next, a full-text search was conducted on the articles to identify the occurrence of the keywords “data envelopment analysis” and “circular economy”. As a result, 3574 articles were excluded because they did not contain these keywords. The remaining 1323 publications were analyzed by two researchers, who are the authors of this paper, based on an agreement on several inclusion and exclusion criteria (see Table 1). If the article does not present calculations based on the DEA model, incorporating variables that include indicators related to the circular economy, it is excluded.
The two researchers applied these criteria independently in order to decrease bias. According to [24,25], this method is considered to be a best practice for literature review. Finally, 151 articles were included in the literature review. Based on this corpus, we conducted bibliometric and content analyses to identify underlying models and reveal emerging trends in the application of DEA to the circular economy.

3. Bibliometric and Content Analysis

In this section, we present a bibliometric analysis of 151 selected papers on measuring the circular economy with DEA from 2015 to 2024. A comprehensive summary of the selected papers can be found in Supplementary Materials (Tables S1 and S2).
Figure 2 shows the annual number of publications from 2015 to 2024. The data reveal a substantial increase in research activity concerning the application of DEA models to evaluate the efficiency of the circular economy over the past decade. Between 2015 and 2018, an average of approximately three articles were published each year. However, starting in 2019, there has been a significant increase in the volume of publications, with a tenfold increase in recent years. The average annual growth rate of 50% indicates a high level of interest and demonstrates increasing academic engagement in this field. It is expected that the number of studies related to the circular economy will continue to rise annually. The exponential trend line fitted to the number of publications aligns closely with observed data, reinforcing the expectation that the utilization of DEA models in assessing circular economy initiatives will experience sustained growth.
Figure 3 presents a pie chart illustrating how publications are distributed across different publishers. Elsevier is the dominant publisher, contributing around half of all articles examining the application of DEA models to measure the efficiency of the circular economy. MDPI and Springer are the second largest, collectively representing around 25% of the total publications. Wiley and IOP publishers follow with shares of 6% and 2.6% respectively. Due to Elsevier’s leading position, this analysis provides a further breakdown of its publications by journal. This analysis reveals that most of the relevant articles have been published in the Journal of Cleaner Production and Waste Management, emphasizing the practical focus of the analyzed studies.
Figure 4 shows how keywords were used in the 151 papers selected for the systematic review. The figure illustrates the annual evolution and emergence of top research keywords. Most of the keywords depicted in the chart have emerged since 2019 due to an increase in the volume of publications during this period. The presence of the keywords ‘DEA’ and ‘circular economy’ among the top-ranked terms can be attributed to the specific search criteria used to select the relevant publications. Overall, the frequency of keywords remains relatively stable over the analyzed period. Certain terms such as ‘waste management’, ‘municipal waste management’, and ‘Malmquist index’ exhibit an upward trend, indicating increasing scholarly interest in the assessment of waste management systems and evaluating productivity change over time. Conversely, the usage of terms like ‘recycling efficiency’ demonstrates a declining pattern, suggesting a potential shift in the research focus of DEA models.
Table 2 presents the most significant studies identified within the analyzed corpus. It comprises ten highly cited publications focused on measuring the circular economy with DEA, published between 2015 and 2024. It is noteworthy that the majority of these influential works—seven out of ten—were published during 2019–2020, suggesting that recent research has been based particularly on methodologies developed during that period and built upon findings established then. This concentration underscores the pivotal role of studies from these years in shaping current approaches within the field. It is interesting to note that nine out of ten articles were published in journals from Elsevier, and one article in a journal from Wiley.
The most cited article [26] explores the impact of economic openness and R&D investment on green economic growth in the context of the circular economy. For this purpose, the authors use econometric models, explicitly incorporating pure technical efficiency as one of the factors. Wu et al. [27] applied a two-stage DEA model with additive and non-cooperative efficiency measures to assess the efficiency of industrial production processes across provincial regions in China. In this model, input resources are shared between the first and second stages. Undesirable intermediate outputs generated during the production stage are considered as waste products that are processed in the disposal stage, resulting in recovered resources, which are subsequently reused as inputs within the first stage. Halkos and Petrou [28] analyzed waste generation efficiency in EU countries. A comparative analysis was conducted, examining the DEA results in conjunction with the recycling rates for each country during the study period. This analysis demonstrated a relationship between countries’ DEA efficiency scores and their recycling rates. Giannakitsidou et al. [29] used DEA models to measure the performance of EU countries in managing and exploiting their MSW. Expósito and Velasco [30] conducted an analysis of MSW recycling across regions in Spain. Mavi and Mavi [31] conducted an assessment of the energy efficiency across OECD countries. To ensure comparability, a common set of weights in the DEA model is employed to evaluate all OECD nations uniformly. Additionally, the Malmquist productivity index is utilized to analyze temporal changes in efficiency over the specified period. Pagotto and Halog [32] integrated material flow analysis (MFA) and DEA to evaluate resource efficiency and assess the potential for enhancing competitiveness within the Australian agri-food sector. Fan and Fang [33] evaluated the levels of CE development across regions in China and proposed strategic recommendations to promote CE initiatives, thus facilitating the country’s transition toward a more sustainable development paradigm. Liu et al. [34] evaluated the eco-efficiency of a circular economy system in China’s coal mining regions, utilizing emergy theory combined with DEA to provide a comprehensive assessment. Jiang et al. [35] proposed a data-driven methodology that integrates R clustering, DEA, and gray relational analysis (GRA) to evaluate the ecological performance of remanufacturing processes, thereby facilitating the development of more effective strategic solutions.
Table 2. Top 10 highly cited papers published from 2015 to 2024.
Table 2. Top 10 highly cited papers published from 2015 to 2024.
AuthorsTitleYearCitationsCites per Year
Song, X.; Zhou, Y.; Jia, W. [26]How do economic openness and R&D investment affect green economic growth?—evidence from China201918428.68
Wu, J.; Zhu, Q.; Ji, X.; Chu, J.; Liang, L. [27]Two-stage network processes with shared resources and resources recovered from undesirable outputs201614315.19
Halkos, G.; Petrou, K.N. [28]Assessing 28 EU member states’ environmental efficiency in national waste generation with DEA201913821.51
Mavi, N.K.; Mavi, R.K. [31]Energy and environmental efficiency of OECD countries in the context of the circular economy: Common weight analysis for Malmquist productivity index201913320.73
Pagotto, M.; Halog, A. [32]Towards a Circular Economy in Australian Agri-food Industry: An Application of Input-Output Oriented Approaches for Analyzing Resource Efficiency and Competitiveness Potential201613113.91
Fan, Y.; Fang, C. [33]Circular economy development in China-current situation, evaluation and policy implications202013024.00
Liu, X.; Guo, P.; Guo, S. [34]Assessing the eco-efficiency of a circular economy system in China’s coal mining areas: Emergy and data envelopment analysis201910916.99
Giannakitsidou, O.; Giannikos, I.; Chondrou, A. [29]Ranking European countries on the basis of their environmental and circular economy performance: A DEA application in MSW202010719.75
Expósito, A.; Velasco, F. [30]Municipal solid-waste recycling market and the European 2020 Horizon Strategy: A regional efficiency analysis in Spain201810414.02
Jiang, Z.; Ding, Z.; Zhang, H.; Cai, W.; Liu, Y. [35]Data-driven ecological performance evaluation for remanufacturing process201910115.74
Note: The total number of citations was obtained from Scopus in May 2025.
An important aspect of content analysis is examining the geographical distribution of research objects. This offers insights into the level of global interest and engagement with the DEA applications in the circular economy domain. In the analyzed papers, international research was conducted across four regions—the EU, EEA, OECD, and V4 countries. The remaining studies encompassed a total of 20 countries, of which approximately 50% are situated in Europe.
Table 3 presents the distribution of articles by country (or territory) of study. The table indicates that out of 151 articles, approximately 43% are devoted to assessing the efficiency of the circular economy in China. Researchers predominantly apply DEA at the national level, with Chinese provinces serving as the decision-making units (DMUs). The principal data source for such studies is the China Statistical Yearbook, which offers a comprehensive array of statistical information. While it offers a broad quantitative data set, it also includes key statistics related to resource utilization, waste management, recycling, and environmental protection that are essential for evaluating circularity.
The EU countries are next in terms of geographical coverage. The application of the DEA method to the analysis of CE in EU countries was documented in a total of 28 articles, which accounted for 19% of the selected studies. The main data source for these studies was the Eurostat database, which provides a comprehensive collection of data relevant to measuring the efficiency of the circular economy within EU member states. The available data focused on resource use, waste management, recycling, and material flows, enabling the assessment of how effectively economies were transitioning toward circularity.
A total of eight articles focused on research conducted in Italy and Chile, respectively. In both cases, the primary level of analysis was at the national scale, primarily due to the accessibility of data collected by governmental authorities at the provincial level. The datasets were obtained from the database of the Italian Institute for Environmental Protection and Research (ISPRA) and the National System for the Declaration of Waste (SINADER). These databases contained important indicators of the circular economy, particularly in the context of waste management and resource efficiency, and were aggregated at the national level. In contrast, research on the CE in Spain was conducted exclusively at the regional level. A total of seven such studies were identified.
Three studies on the CE within OECD countries were grounded in data obtained from the OECD database. In the cases of Taiwan and Brazil, the analysis was primarily conducted at the national level. Regional data were obtained from the respective databases provided by environmental ministries. The Brazilian SNIS database provided municipal-level information and was administered by the Ministry of Regional Development. Regional environmental data for Taiwan were provided by the Ministry of Environment through an open data platform.
Figure 5 categorizes the selected studies into distinct levels to clarify the scale at which each study operates. It shows that 22 articles were conducted at the local level. These papers primarily examined operational practices or case studies related to resource management and circular economy implementation at the organizational or technological level. A total of 21 papers focused on the regional level, utilizing provincial databases to facilitate comparisons within one or more administrative regions. Additionally, 71 studies were conducted at the national level, representing the largest category within the dataset. This prevalence is primarily attributable to the existence of comprehensive and systematically maintained databases curated by government organizations, which support large-scale national analyses. At the international level, 37 country-specific studies were identified, mainly focusing on research within EU and OECD member countries.
The distribution of studies across these levels reflects both the availability of relevant data sources and the scope of research interests within the field. The observed distribution of papers across different levels of analysis was largely influenced by the availability of data sources. Specifically, the predominance of studies at the national level could be linked to the existence of comprehensive databases that enabled analysis across various regions or provinces. Conversely, the relative scarcity of regional- and local-level studies may have been attributed to challenges related to obtaining datasets at the municipal or organizational level, which often required extensive primary data collection or access to proprietary information. Therefore, the current distribution reflects not only research priorities but also the practical constraints imposed by data availability, highlighting the critical role that existing data sources played in shaping analysis within the CE field.
As illustrated in Figure 6, the majority of researchers demonstrate a preference for well-established, single-stage DEA models for evaluating the efficiency of the circular economy. This preference is primarily driven by the availability of existing software tools that facilitate their calculations. Conversely, network models, as highlighted in [36], have recently begun to gain traction and are gradually becoming more common within the literature. These studies typically employ two-stage models, a choice largely influenced by their simple structure and the relative ease of implementation. The adoption of a more complex network DEA models often require the development of specialized mathematical models adapted to specific problems, which can pose significant methodological challenges. Consequently, such studies constitute a minority within this review, reflecting both the developmental stage of these models and their higher implementation complexity.
Figure 7 represents the distribution of papers by technology type used for constructing the production possibility set of DEA models. Note that the total number of technologies exceeds the total number of articles. This is because papers that proposed multiple DEA models with different RTS assumptions were counted multiple times. The diagram shows that both CRS and VRS types were used with comparable frequency; however, the CRS assumption was utilized slightly more often. The application of other types of technology was exceedingly limited.
Table 4 summarizes the measures of efficiency used in single-stage DEA models. The majority of the studies employed conventional CCR and BCC models with radial measures of efficiency. The slack-based measure was used in 17% of single-stage models, making it the second most frequently used method. However, it is worth noting that SBM was the predominant efficiency assessment method within network DEA models. Compared to SBM, the DDF measure was used less frequently. Benefit of the Doubt, the Russell measure, and other methods for assessing efficiency are generally scarce, and their application by researchers remained irregular. This pattern persisted within circular economy studies, reflecting a narrow application of different efficiency assessment techniques in the field.
Combining DEA with other methods is an important aspect of CE research. This integration allows for the development of new knowledge and improved modeling capabilities. Our analysis reveals that the majority of the examined studies employed DEA as the main metric for evaluating efficiency in the circular economy. Furthermore, approximately half of the analyzed papers relied solely on DEA to calculate performance estimates and draw conclusions based on these results to answer research questions and provide policy recommendations.
Table 5 provides a comprehensive summary of the methods employed in conjunction with DEA. This table illustrates the diversity of approaches used for measuring CE in combination with DEA. A noteworthy trend among the examined papers is the prevalence of second-stage analyses that aim to identify the causes of inefficiency. This approach usually involves statistical methods with respect to exogenous factors and often uses truncated regression (tobit) models. In many papers, DMUs are geographically linked, representing countries, regions, municipalities, or cities. Consequently, specialized geographic regression methods, such as geographically weighted regression, Moran’s I, and spatial migration analysis, are employed to reveal geographical patterns. The Malmquist index and its generalizations, including the Malmquist–Luenberger productivity index, are frequently utilized to assess the dynamic performance of units. Factor analysis is commonly combined with DEA to reduce the number of input and output variables, thereby enhancing the overall efficiency of the analysis. Cluster analysis is typically applied following DEA to identify groups of similar DMUs based on their efficiency scores.

4. Discussion and Policy Implications

To evaluate how DEA models capture the principles of the CE, the existing literature was analyzed through the lens of the R-ladder framework. Several different R-ladders are currently known in the literature, which more or less capture the concept of the circular economy.
The classic 3R principle of the circular economy—Reduce, Reuse, Recycle—originally formed the basis of circular thinking and waste management strategies. It was initially conceived as a waste prevention strategy to promote more efficient resource utilization, mitigate waste generation, and lessen overall environmental impact. The progressive evolution of R-concepts in recent years reflects a more sophisticated understanding of how to optimize resource efficiency and minimize environmental impact throughout a product’s entire life cycle. A guiding principle across these frameworks is the inherent hierarchy—strategies positioned higher in the hierarchy (corresponding to lower R numbers) are generally more desirable as they preserve greater value and have a smaller environmental footprint. The various R frameworks (3R, 6R, 9R, 10R, and 12R) are not merely additive; they build on each other by integrating more nuanced strategies that intervene earlier in the product life cycle, thereby preserving higher material and functional value. Strategies such as ‘Refuse’ and ‘Rethink’ are considered to have the greatest impact, whereas ‘Recycle’ and ‘Recover’ are generally seen as last-resort options within the hierarchy. The growing number of R-terms in the literature reflects the increasing complexity and holistic nature of CE implementation across diverse economic sectors. By implementing these strategies, the circular economy aims to create a more sustainable and resource-efficient system that moves away from the linear ‘take-make-dispose’ model.
In this study, we rely on the popular 9R concept—a set of strategies focused on minimizing waste and maximizing resource utilization. These strategies include Refuse, Rethink, Reduce, Reuse, Repair, Refurbish, Remanufacture, Repurpose, Recycle, and Recover. They are often presented in hierarchical order, with the earlier ‘Rs’ being preferable as they prevent waste at the source (see Table 6).
In each DEA model, the set of inputs and outputs determined which aspect of the circular economy was being measured. Next, frequency analysis was used to determine which R-strategies are most frequently evaluated in the literature using DEA (see Table 7).
Our analysis reveals a significant gap between the hierarchical ideal of the circular economy and the practical application of DEA in measuring it. The literature can be categorized based on the R-strategies that current DEA models are equipped to measure, highlighting a clear bias toward lower-value, end-of-life processes.
The most commonly measured aspect of the CE is the performance of the recycling (or waste management with recycling) system (R8). Both environmental aspects of this efficiency and purely economic aspects, i.e., the efficiency of recycling business models, are measured. In addition, several studies in our sample have focused on comparing the characteristics of several different recycling technologies and several different organizational designs.
Temerbulatova et al. [136] present a typical example of a model measuring recycling efficiency, using 27 EU countries as DMUs. The inputs of the model are X 1 —generation of municipal waste per capita (kg per capita); X 2 —water exploitation index; X 3 —final energy consumption (million tons of oil equivalent); and X 4 —social progress index (SPI). The outputs of the model are Y 1 —circular material use rate (% of total material use) and Y 2 —municipal waste recycling rate (%). According to the model’s logic, efficient countries are those that achieve the highest indicators for waste recycling and the reuse of recovered materials, while minimizing municipal waste generation, water, energy consumption, and social capital input. In essence, efficient countries possess the most effective material recycling systems, which aligns with stage R8 of the circular economy principles.
The second most popular dimension of CE, measured with DEA, is the efficient use of resources, primarily natural resources such as energy and water, but in some cases, financial resources also. Most often, resource efficiency is measured at the sectoral, regional, or even national level. Improving resource efficiency can be attributed to the R2 strategy (Reduce). The same type of strategy was applied to models in which the volume or share of renewable energy produced was taken into account as one of the outputs. In this case, we assumed that the use of RES reduces the use of other nonrenewable natural resources.
A typical example of a DEA model measuring resource efficiency (R2) is presented by Xian et al. [43]. This study evaluates the efficiency of the 10 administrative districts of Shenzhen City, treating them as DMUs, using the following inputs and outputs. The inputs included in the model are: X 1 —energy input (gasoline for production and supply of water + diesel for production and supply of water) (ton of SCE); X 2 —water input (industrial water consumption + residential water consumption) ( m 3 ); X 3 —completed investment in water resource management (Yuan). The following indicators are used as outputs in the model: Y 1 —GDP (Yuan); Y 2 —undesirable output (treated wastewater − reuse of wastewater + discarded wastewater) ( m 3 ). The model has a simple one-stage structure. According to the optimization algorithm’s logic, the most efficient administrative districts are those that achieve maximum economic output (GDP) and minimum wastewater production, with the least possible consumption of energy, water, and investment resources. This implies the most efficient use of water and energy in production processes and effective water resource management. This approach aligns with the R-ladder concept’s R2 stage, which focuses on reducing the use of natural resources.
Next in popularity is the R9 strategy. Typically, it reflects the performance of recycling and waste management systems. It can be distinguished as a separate strategy only by the inputs and outputs of the DEA model, which take into account energy consumption and recovery.
The remaining strategies are difficult to define unambiguously, as different aspects of the circular economy are intertwined in most DEA models. In particular, when using an indicator like the “circular material use rate” (https://ec.europa.eu/eurostat/web/products-manuals-and-guidelines/-/ks-gq-18-013, accessed on 27 June 2025) as an output of the model, a high efficiency score may indicate both the development of a recycling system and the development of higher rungs of the R-ladder, such as R4—Repair, R5—Refurbish, and R6—Remanufacture. When the DEA model is built to evaluate the efficiency of a production system, in our opinion, the use of strategies R7 and R3 is unlikely, as production processes are highly standardized and often do not allow the reuse of equipment, materials, and raw materials. However, when it comes to households and municipalities, the use of the R3 or even R0 strategy is quite likely and can be indirectly detected in the reduction of household waste generation. Therefore, all strategies that relate to product life cycle prolongation are labeled as probable in most of the papers.
For a more complex conceptual model, consider the one constructed by Castellano et al. [103], where the DMUs included 54 OECD countries and several other nations. The inputs of this model were X 1 —material footprint and X 2 —hazardous waste per capita. It is important to note that these indicators were not traditional resources; rather, they represented undesirable outputs of the economic system. However, in the DEA, a common practice is to ensure the minimization of such undesirable outputs (like hazardous waste or material footprint) is to treat them as inputs within the model. This approach aligns with DEA’s principle of minimizing inputs to achieve efficiency and was frequently employed in environmental efficiency studies. A wide range of indicators served as outputs of the model, as follows: Y 1 —domestic material consumption, Y 2 —municipal waste recovered, Y 3 —number of companies publishing sustainability reports, Y 4 —sustainable public procurement policies and action plans, Y 5 —global citizenship education and education for sustainable development in curricula, Y 6 —global citizenship education and education for sustainable development in teacher education, Y 7 —global citizenship education and education for sustainable development in national education policies.
In this scenario, the most effective countries are those that generate the smallest environmental footprint and the least hazardous waste per capita. Simultaneously, they achieve the highest rates of waste recycling (R8, R9), prioritize domestic resource consumption (thereby reducing reliance on other resource types, R2), and actively promote R0—Rethink and R1—Refuse through enhanced corporate and civic environmental responsibility. It is important to note that the prevalence of R0—Rethink and R1—Refuse practices is measured indirectly in this model. This exemplifies a key advantage of DEA as a methodology—its capacity to measure latent variables, which are not directly quantifiable, by forming complex combinations of input and output indicators. However, our sample included very few studies that used such an approach
Only one paper considered all rungs of the R-ladder due to the fact that the data were collected by a survey method [102]. This made it possible to determine exactly what strategy is used by the surveyed enterprises.
It is also worth mentioning that, in contemporary literature, DEA is often combined with other methods. Our sample also includes articles where DEA is combined, most often with regression, less often with spatial models [16,39,52,62,111]. However, in these studies, the efficiency indicator of a circular process or system is first calculated using DEA, and then regression is applied to identify the determinants of the already calculated efficiency. That is, nothing changes in the very approach to measuring the efficiency (in this case, circularity) of the studied process or system. Thus, the use of additional methods does not contribute to improving the measurability of circular processes and/or systems.
Therefore, the analysis demonstrates the following critical disconnect: DEA models are most frequently applied to the least desirable circular economy strategies (Recycling and Recovery). It is worth noting that this is not an inherent flaw in the DEA methodology itself, but rather a direct consequence of a systemic lack of clear and specific statistical indicators for higher-order R-strategies. The “measurable” aspects of the CE are those that generate easily quantifiable data (e.g., tons of waste recycled, energy recovered), while the more impactful, preventative strategies (e.g., product redesign, conscious non-consumption) remain statistically invisible.
This creates a significant risk of misinterpretation. Relying on current DEA applications alone could lead to the conclusion that the circular economy is primarily about waste management, rather than a fundamental redesign of our production and consumption systems. The ambiguity of indicators like the “circular material use rate” further compounds this issue, as it conflates low-value recycling with high-value product life extension, preventing a nuanced evaluation of circular progress. Unfortunately, the potential of constructing informative indices reflecting the effectiveness of all circular economy strategies using DEA has not yet been fully realized in practice due to the lack of clear statistical indicators measuring the effectiveness of actions aimed at prolonging the product life cycle. The first steps of the hierarchy of R-strategies could only be determined indirectly from data on the development of innovation, circular economy education, and waste reduction.
Another area in which DEA applications for measuring CE could be improved is that, although methods exist [168], not all CE-related DEA studies include undesirable outputs (e.g., pollution and residual waste), which lead to incomplete assessments. Furthermore, few DEA-based studies translate their results into policy recommendations for accelerating the transition to a circular economy. The link between efficiency scores and actionable strategies is weak.
Drawing upon the analysis presented in this review, several critical and urgent policy implications for the effective transition toward a circular economy emerge. Firstly, statistical agencies must significantly enhance their data infrastructure. This requires the proactive development and implementation of new statistical indicators designed to capture activities at the top of the ‘R-ladder’ hierarchy. Quantifiable metrics relating to product repair rates, refurbishment volumes, the penetration of reuse platforms, and the adoption of genuinely circular business models are essential for accurately assessing CE progress and the effectiveness of related interventions.
Secondly, policymakers must be wary of policy distortion resulting from an undue reliance on existing metrics. Current assessment frameworks often inadvertently prioritize end-of-pipe solutions, such as recycling (R8) and energy recovery (R9), which can create perverse incentives. This can lead to resources being misallocated toward less impactful recovery operations at the expense of critical investments in upstream innovation, such as waste prevention (R0), extended product longevity (R1), and fundamental system-level redesign (R2).
Thirdly, this review highlights the importance of promoting methodological diversity in assessment. Although quantitative tools such as data envelopment analysis (DEA) can provide valuable insights, they should be used alongside a wider range of assessment tools. As existing research has highlighted, survey-based methodologies can be an effective way of capturing the adoption and diffusion of higher-order circular strategies. Integrating qualitative data and detailed case studies is essential to provide a more comprehensive and contextualized understanding of the challenges and successes of CE implementation.
Finally, direct policy support for innovation in measurement and practice is crucial, particularly with regard to ‘Rethink’ and ‘Refuse’ strategies. As these strategies are inherently linked to shifts in design paradigms, consumption patterns, and educational initiatives, they require dedicated funding for research and development. This includes supporting pilot projects that rigorously test new circular business models, as well as investing in comprehensive educational programs that foster sustainable consumption. While the direct impact of these programs may not be quantifiable by traditional efficiency models. Such targeted investments are essential for catalyzing systemic change and ensuring a truly effective circular transition.

5. Conclusions

This systematic literature review of DEA applications within the CE context reveals a significant growth in scholarly interest in recent years. This increasing attention is accompanied by an evolution in the complexity of DEA models employed, with network and dynamic DEA approaches becoming increasingly prevalent. This methodological sophistication reflects a desire to capture the multifaceted and temporally evolving nature of CE performance.
The observed popularity of DEA stems from its capacity to generate comprehensive performance indices by leveraging readily available statistical data. These indices offer a valuable lens through which to evaluate the development level of various CE dimensions, providing a more holistic understanding than is attainable through the isolated analysis of individual statistical indicators. Specifically, DEA-derived efficiency scores serve as latent variables, effectively synthesizing the complex interplay of factors contributing to CE performance. These scores represent an indirect, but insightful, measure of aspects that are either impossible or excessively time-consuming to quantify directly.
Our analysis indicates that DEA models yield particularly informative insights when evaluating the implementation of circular strategies, i.e., R2—Reduce, R8—Recycling, and R9—Recovering. However, the current capabilities of the DEA appear limited in comprehensively assessing the extent and effectiveness of other circular economic strategies. While opportunities exist to manipulate indicators for indirect reflection of specific aspects, a pressing need remains for further development of the statistical framework employed in measuring the circular economy.
Regarding the geographical distribution of the surveyed literature, a significant proportion, exceeding 40%, focuses on China. The European Union is also prominently represented, accounting for nearly 20% of the studies. Conversely, other geographical regions are sparsely represented within our sample, highlighting a potential gap in the current research landscape.

Supplementary Materials

The following supporting information can be downloaded at https://www.mdpi.com/article/10.3390/mca30050102/s1, Table S1: Summary of selected articles for the systematic literature review, and Table S2: Overview of DEA models used for measuring circular economy performance.

Author Contributions

Conceptualization, S.V.R.; methodology, S.V.R. and A.V.L.; software, E.D.M. and D.M.M.; validation, S.V.R. and A.V.L.; formal analysis, A.V.L., E.D.M. and D.M.M.; investigation, E.D.M. and D.M.M.; resources, S.V.R., E.D.M. and D.M.M.; data curation, E.D.M. and D.M.M.; writing—original draft preparation, S.V.R. and A.V.L.; writing—review and editing, S.V.R. and A.V.L.; visualization, A.V.L., E.D.M. and D.M.M.; supervision, S.V.R.; project administration, S.V.R.; funding acquisition, S.V.R. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Russian Science Foundation (project No. 23-11-00197).

Data Availability Statement

The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding authors.

Acknowledgments

The authors thank the journal editor and anonymous reviewers for their guidance and constructive suggestions.

Conflicts of Interest

The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

Abbreviations

The following abbreviations are used in this manuscript:
BCCBanker, Charnes, Cooper
CCRCharnes, Cooper, Rhodes
CECircular Economy
CRSConstant Returns-to-Scale
DDFDirectional Distance Function
DEAData Envelopment Analysis
DMUDecision Making Unit
EEAEuropean Economic Area
EUEuropean Union
GRAGrey Relational Analysis
MFAMaterial Flow Analysis
OECDOrganization for Economic Co-operation and Development
SBMSlacks-Based Measure
VRSVariable Returns-to-Scale

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Mca 30 00102 g001
Figure 1. PRISMA flowchart of the selection procedure.
Figure 1. PRISMA flowchart of the selection procedure.
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Figure 2. Annual number of publications on measuring the circular economy with DEA from 2015 to 2024 (left) retrieved from Google Scholar and Scopus, and (right) selected for analysis.
Figure 2. Annual number of publications on measuring the circular economy with DEA from 2015 to 2024 (left) retrieved from Google Scholar and Scopus, and (right) selected for analysis.
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Figure 3. Distribution of articles by publishers.
Figure 3. Distribution of articles by publishers.
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Figure 4. Timeline of the most frequently used keywords.
Figure 4. Timeline of the most frequently used keywords.
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Figure 5. Number of papers by the level of analysis.
Figure 5. Number of papers by the level of analysis.
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Figure 6. Network structure of DEA models.
Figure 6. Network structure of DEA models.
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Figure 7. Number of articles by DEA technology type.
Figure 7. Number of articles by DEA technology type.
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Table 1. Selection criteria.
Table 1. Selection criteria.
CriteriaInclusion CriteriaExclusion Criteria
Type of articlePeer-reviewed scholarly journal articles (full papers)Theses or dissertations, books, chapters in edited books, reviews, retracted articles, conference papers (if they are not published in journals), abstracts, books of abstracts, editorials, preprints, working papers, reports (science and policy, technical, study, annual), bibliographies, literature listings, newsletters, resumes, seminars, indexes in journals, datasets, presentations, handbooks
KeywordsThe article contains keywords “data envelopment analysis” and “circular economy”The article does not contain keywords; keywords are mentioned only in tables or references
TimePublished in 2015–2024Published before 2015; published in 2025; available online, but not published
LanguageWritten in the English languagePublished in non-English languages
Knowledge domainEconomics, Business, Management, Sustainable Development, Environmental ManagementOthers
ScopeMeasurements, DEA models, efficiency scoreOthers
MethodologyOriginal theoretical and experimental studiesBibliometric analysis, Systematic literature reviews, Meta-analysis of experimental studies
Table 3. Geographical scope.
Table 3. Geographical scope.
Country/TerritoryNumber of StudiesPrimary Level of AnalysisPrimary Data Source
China65NationalChina Statistical Yearbook
EU28InternationalEurostat database
Italy8NationalThe Italian Institute for Environmental Protection and Research (ISPRA)
Chile8NationalNational System for the Declaration of Waste (SINADER)
Spain7RegionalRegional databases of autonomous communities
OECD3InternationalOECD database
Taiwan3NationalDatabase of Taiwan Environmental Protection Administration
Brazil2NationalNational Sanitation Information System (SNIS) database
Table 4. Measure of efficiency in single-stage DEA models.
Table 4. Measure of efficiency in single-stage DEA models.
Measure of EfficiencyPublicationsPercentage (%)
Radial6963.30
Slack-based1816.51
DDF1110.09
Benefit of the Doubt32.75
Russell21.84
Other65.51
Total109100.00
Table 5. Combination of DEA with other methods.
Table 5. Combination of DEA with other methods.
CategoryMethods, Publications
Statistical analysisConvergence analysis [14,37,38,39,40], OLS [30,41,42,43,44,45], Tobit model [16,30,39,46,47,48,49,50,51,52,53], other regression analysis [26,54,55,56,57], Panel regression [45,58,59], Non-parametric regression [60], Kernel density estimation [17,61], Kruskal–Wallis test [42,59,61,62,63,64,65,66,67], Mann–Whitney test [61,63,68], Kolmogorov–Smirnov test [42,46,61], Wilcoxon test [69,70]
Factor analysisPrincipal component analysis [71,72,73,74,75,76]
Cluster analysis[35,47,74,77,78]
Network analysisGravitational model [79], Social network analysis [76,79], Augmented gravity model [80]
Spatial analysisMoran’s I [16,79,81,82,83], Geographically weighted regression [79,84], Spatial Durbin model [79,81,83], Exploratory spatial data analysis [79], Geographic detector [84], Spatial migration analysis [17], Spatial lag model [81], Spatial error model [81]
Temporal analysisMalmquist productivity index [31,38,45,48,54,85,86,87,88,89,90,91,92], Malmquist–Luenberger productivity index [66,86,93]
OtherMultiple-criteria decision analysis [37,82,94], Analytic hierarchy process [72,95], Grey relational analysis [35,96], Coupling coordination degree analysis [82,97], Material flow analysis [32,98], Decoupling index [99], Exploratory data analysis [23], Improved fruit fly optimization algorithm [96], Artificial neural networks [100], Net present value calculation [101]
Table 6. R-strategies of the circular economy.
Table 6. R-strategies of the circular economy.
R-StrategyExplanation
R0 RefuseActively choosing not to consume or use products that are unsustainable or unnecessary.
R1 RethinkA fundamental rethinking of products and systems to find more sustainable alternatives.
R2 ReduceMinimizing resource consumption and waste generation through efficient production processes and mindful consumption.
R3 ReuseUsing items for other uses.
R4 RepairFixing broken products to extend their lifespan and prevent them from being discarded.
R5 RefurbishRenovating or upgrading products to make them functional again, often with updated features.
R6 RemanufactureCreating new products from used components, often with the same functionality as the original product.
R7 RepurposeFinding new and creative uses for discarded items, giving them a new life.
R8 RecycleProcessing used materials into new products, closing the loop on material life cycles.
R9 RecoverRecovering energy or materials from waste that cannot be recycled or reused.
Table 7. The frequency of measuring CE according to the characteristics of the R-strategy.
Table 7. The frequency of measuring CE according to the characteristics of the R-strategy.
R-StrategyPublicationsPercentage (%)
R0 Refuse[28,102,103]1.40
R1 Rethink[102,103]0.93
R2 Reduce[14,15,16,23,26,28,31,32,34,39,42,43,45,53,57,59,69,70,71,78,79,82,83,84,88,98,99,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125]23.72
R3 Reuse[28,29,33,102]1.86
R4 Repair[28,29,96,102]1.86
R5 Refurbish[29,56,74,76,87,89,102,126]3.72
R6 Remanufacture[29,35,56,74,76,87,89,102,126]4.19
R7 Repurpose[21,29,102,127]1.86
R8 Recycle[13,14,16,17,18,20,21,22,23,27,29,30,37,38,39,40,41,44,45,47,48,49,50,51,52,54,55,56,57,58,60,61,62,63,64,65,66,67,68,72,73,74,75,76,77,79,80,81,83,85,86,87,88,89,90,91,92,93,94,95,96,97,99,100,101,102,103,115,117,118,119,122,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167]53.02
R9 Recover[20,21,22,37,40,46,47,52,73,89,90,102,129,145,148,149]7.44
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Ratner, S.V.; Lychev, A.V.; Muravleva, E.D.; Muravlev, D.M. Measuring Circular Economy with Data Envelopment Analysis: A Systematic Literature Review. Math. Comput. Appl. 2025, 30, 102. https://doi.org/10.3390/mca30050102

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Ratner SV, Lychev AV, Muravleva ED, Muravlev DM. Measuring Circular Economy with Data Envelopment Analysis: A Systematic Literature Review. Mathematical and Computational Applications. 2025; 30(5):102. https://doi.org/10.3390/mca30050102

Chicago/Turabian Style

Ratner, Svetlana V., Andrey V. Lychev, Elisaveta D. Muravleva, and Daniil M. Muravlev. 2025. "Measuring Circular Economy with Data Envelopment Analysis: A Systematic Literature Review" Mathematical and Computational Applications 30, no. 5: 102. https://doi.org/10.3390/mca30050102

APA Style

Ratner, S. V., Lychev, A. V., Muravleva, E. D., & Muravlev, D. M. (2025). Measuring Circular Economy with Data Envelopment Analysis: A Systematic Literature Review. Mathematical and Computational Applications, 30(5), 102. https://doi.org/10.3390/mca30050102

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