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<title-group><article-title>From Theory to Practice: Leveraging DEA and MCDA for Robust Composite Indicator Frameworks in Sustainable Development</article-title></title-group>
<contrib-group>
<contrib contrib-type="author"><name><surname>Nejatpour</surname><given-names>Davoud</given-names></name><xref ref-type="aff" rid="aff1"/></contrib>
<contrib contrib-type="author"><name><surname>Hadi Vencheh</surname><given-names>Abdollah</given-names></name><xref ref-type="aff" rid="aff1"/></contrib>
<contrib contrib-type="author"><name><surname>Jamshidi</surname><given-names>Ali</given-names></name><xref ref-type="aff" rid="aff1"/></contrib>
<aff id="aff1">Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran.</aff>
</contrib-group>
<abstract><p>This study elucidates a novel methodological framework that synergizes Data Envelopment Analysis (DEA) with Multi-Criteria Decision Analysis (MCDA) to critically assess and enhance composite indicator systems in the realm of sustainable development. Through meticulous application to two pivotal sectors in Iran water resource management and renewable energy utilization we demonstrate the framework’s capacity to generate empirical insights that inform policy-making and strategic resource allocation. Utilizing DEA, we quantitatively evaluate the relative efficiencies of these sectors across various provinces, highlighting significant discrepancies in performance outcomes. The results indicate that Tehran attains the foremost efficiency score in renewable energy utilization, underscoring its effective harnessing of resources relative to other provinces. This research not only advances the theoretical discourse surrounding DEA and MCDA integration but also provides a pragmatic template for evaluating sustainability initiatives. By fostering a deeper understanding of operational efficiencies and inefficiencies, the framework developed herein has the potential to guide effective decision-making processes aimed at achieving Sustainable Development Goals (SDGs) in Iran and analogous contexts worldwide.</p></abstract>
<kwd-group kwd-group-type="author"><kwd>Data envelopment analysis</kwd><kwd>Multi-criteria decision analysis</kwd><kwd>Composite indicator</kwd><kwd>Sustainability</kwd></kwd-group>
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<body>
<sec id="sec-1"><label>1</label><title>Introduction</title>
<p>The quest for sustainable development is increasingly recognized as a critical global challenge, necessitating integrated, multidimensional approaches to assessment and policymaking. As traditional economic indicators often fail to encapsulate the complex interplay between economic growth, social equity, and environmental protection, the development of composite indicators has emerged as a compelling solution. Composite indicators aggregate multiple dimensions of performance into a single metric, thus facilitating more informed comparisons across different entities be they countries, regions, or organizations <xref ref-type="bibr" rid="ref-1">[1]</xref>–<xref ref-type="bibr" rid="ref-3">[3]</xref>. However, their construction remains fraught with methodological challenges, including selection bias, weighting issues, and aggregation methodologies, which can significantly affect the interpretability and robustness of the indicators <xref ref-type="bibr" rid="ref-4">[4]</xref>, <xref ref-type="bibr" rid="ref-5">[5]</xref>.</p>
<p>Data Envelopment Analysis (DEA) provides a robust framework for constructing composite indicators, enabling researchers and policymakers to measure the relative efficiency of Decision-Making Units (DMUs) in converting multiple inputs into multiple outputs <xref ref-type="bibr" rid="ref-6">[6]</xref>. As a non-parametric method of frontier analysis, DEA accounts for the possibility that DMUs may operate under different conditions, thus offering a more nuanced evaluation of performance compared to traditional parametric approaches <xref ref-type="bibr" rid="ref-7">[7]</xref>–<xref ref-type="bibr" rid="ref-9">[9]</xref>. The adaptability of DEA to handle various types of input and output variables has led to its application across diverse sectors, including healthcare, education, and environmental management <xref ref-type="bibr" rid="ref-10">[10]</xref>–<xref ref-type="bibr" rid="ref-13">[12]</xref>. Moreover, the robustness of DEA has been enhanced through the incorporation of sensitivity analyses, which allow practitioners to evaluate the stability of efficiency scores against changes in data inputs <xref ref-type="bibr" rid="ref-14">[13]</xref>.</p>
<p>Despite its strengths, DEA does not inherently address the subjective nature of indicator weighting, which is critical in the context of sustainable development, where priorities may differ among stakeholders <xref ref-type="bibr" rid="ref-15">[14]</xref>. This is where Multi-Criteria Decision Analysis (MCDA) plays a complementary role. MCDA encompasses a variety of decision-making frameworks designed to evaluate multiple conflicting criteria in a systematic manner <xref ref-type="bibr" rid="ref-16">[15]</xref>– <xref ref-type="bibr" rid="ref-19">[18]</xref>. Techniques such as the Analytic Hierarchy Process (AHP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) provide structured methodologies for prioritizing criteria and integrating stakeholder preferences into the decision-making process <xref ref-type="bibr" rid="ref-20">[19]</xref>. The combination of DEA and MCDA offers a pathway towards more transparent, participatory, and robust assessments of sustainability performance by allowing for quantitative efficiency analysis alongside qualitative stakeholder input.</p>
<p>Recent studies have begun to illuminate the potential of integrating DEA and MCDA methodologies to enhance the construction of composite indicators. For instance, Shao et al. <xref ref-type="bibr" rid="ref-21">[20]</xref> developed a hybrid model that combines DEA for efficiency measurement with AHP for weighting selection, resulting in a composite indicator framework applicable to urban sustainability assessments. Similarly, Arabi et al. <xref ref-type="bibr" rid="ref-22">[21]</xref> demonstrated the efficacy of employing DEA alongside TOPSIS for evaluating the sustainable performance of renewable energy projects, highlighting the versatility of an integrated approach. Such advancements underscore the necessity for a shift towards methodological pluralism in sustainability assessments, whereby the strengths of various analytical frameworks are harnessed to create more reliable and actionable indicators.</p>
<p>Despite the promising developments in integrating DEA and MCDA, numerous gaps remain in the literature. The absence of standardized protocols for integrating these methodologies can lead to inconsistencies in application and interpretation <xref ref-type="bibr" rid="ref-23">[22]</xref>. Furthermore, the dynamic and often contentious nature of sustainability objectives necessitates continuous engagement with stakeholders to ensure that the composite indicators reflect evolving priorities and values <xref ref-type="bibr" rid="ref-24">[23]</xref>. This article aims to bridge the existing gap by offering a comprehensive review of the theoretical foundations and practical implications of leveraging DEA and MCDA for the development of robust composite indicator frameworks in sustainable development. The objective is to provide a detailed roadmap that can guide future research and practice in constructing resilient and context-sensitive indicators that can withstand scrutiny and foster sustainable outcomes.</p>
</sec>
<sec id="sec-2"><label>2</label><title>Methodology</title>
<p>Combining DEA and MCDA for robust composite indicator frameworks in sustainable development is an intriguing and complex process. Below is a structured methodology that relies on both approaches to create a unified framework for evaluating sustainable development indicators.</p>
<sec id="sec-3"><label>2.1</label><title>Methodology Overview</title>
<sec id="sec-4"><title>Problem definition and objectives</title>
<p>I. Define the specific Sustainable Development Goals (SDGs) to be assessed <xref ref-type="bibr" rid="ref-25">[24]</xref>.</p>
<p>II. Identify Key Performance Indicators (KPIs) relevant to the chosen SDGs <xref ref-type="bibr" rid="ref-26">[25]</xref>.</p>
</sec>
<sec id="sec-5"><title>Data collection</title>
<p>I. Gather quantitative data for the KPIs from credible sources. Ensure data is normalized for comparability (e.g., scaling between 0 and 1).</p>
<p>II. Collect qualitative data through surveys or expert consultations to assess intangible indicators.</p>
</sec>
<sec id="sec-6"><title>Preliminary analysis</title>
<p>I. Use statistical techniques (e.g., correlation matrix) to determine the relationships between selected KPIs. II. Identify any multicollinearity issues and eliminate or combine indicators as necessary.</p>
</sec>
<sec id="sec-7"><title>DEA</title>
<p>I. Model choice: choose a DEA model (CCR or BCC) depending on whether you are assuming constant or variable returns to scale.</p>
<p>II. Inputs and outputs: clearly define which indicators are inputs (resources used) and which are outputs (results achieved).</p>
<p>III. Formulation: for a simple DEA model, you would solve the following linear programming problem for each DMU <xref ref-type="bibr" rid="ref-27">[26]</xref>:</p>
<p>∑s j=1 vjyrj</p>
<p>Maximize θ = ∑m . (1)</p>
<p>i=1 uixij</p>
<p>Subject to:</p>
<p>∑s j=1 vjyrj ≤ 1, for all j, ui, vj ≥ 0,</p>
<p>θ = efficiency score.</p>
<p>yrj = output for indicator r of DMU j.</p>
<p>xij = input for indicator i of DMU j.</p>
<p>ui =weight for input i.</p>
<p>vj = weight for output j.</p>
<p>Efficiency scores: calculate efficiency scores for each DMU, which will indicate the performance of each unit in relation to the best performers.</p>
</sec>
<sec id="sec-8"><title>MCDA</title>
<p>I. Weight assignment: assign weights to the KPIs based on stakeholder preferences or expert judgment using techniques II. Synthesis of scores: use an MCDA technique to integrate the efficiency scores from DEA and adjust them based on the weights assigned.</p>
<p>Using a weighted sum model <xref ref-type="bibr" rid="ref-28">[27]</xref>:</p>
<p>Si = ∑n k=1 wk × DEAi, (3)</p>
<p>Si = aggregated score for DMU i, wk = weight of criterion k, DEAi = efficiency score of DMU i.</p>
</sec>
<sec id="sec-9"><title>Assessment of results</title>
<p>I. Rank the DMUs based on the aggregated scores from the MCDA step.</p>
<p>II. Perform sensitivity analysis to see how changes in weights affect rankings and decisions.</p>
</sec>
<sec id="sec-10"><title>Interpretation and policy recommendations</title>
<p>I. Analyze the ranking of DMUs to inform policy decisions, focusing on how less efficient units can improve their performance.</p>
<p>II. Present findings to stakeholders and discuss implications for sustainable development.</p>
<p>To implement the combined DEA and MCDA methodology for a robust composite indicator framework in sustainable development, let&apos;s consider a practical case study focusing on two subjects:</p>
<p>I. Water resource management in Iran.</p>
<p>II. Renewable energy sources in Iran.</p>
<p>These examples will involve identifying KPIs, collecting data, performing DEA, and applying MCDA.</p>
</sec>
</sec>
</sec>
<sec id="sec-11"><label>3</label><title>Case Study 1: Water Resource Management in Iran</title>
<sec id="sec-12"><label>3.1</label><title>Problem Definition and Objectives</title>
<p>The objective is to evaluate the efficiency of various provinces in Iran regarding their water resource management practices, specifically focusing on the sustainable use of water resources.</p>
</sec>
<sec id="sec-13"><label>3.2</label><title>Key Performance Indicators</title>
<p>The following KPIs will be used for the analysis:</p>
<sec id="sec-14"><title>Inputs</title>
<p>I. I1: total water withdrawal (million cubic meters).</p>
<p>II. I2: agricultural water consumption (million cubic meters).</p>
</sec>
<sec id="sec-15"><title>Outputs</title>
<p>I. O1: agricultural production (tonnes).</p>
<p>II. O2: water use efficiency (tonnes per million cubic meters).</p>
</sec>
</sec>
<sec id="sec-16"><label>3.3</label><title>Data Collection</title>
<p>We will now collect hypothetical data for five provinces in Iran. The data is normalized for comparability.</p>
<table-wrap id="tab1"><label>Table 1</label><caption><p>Hypothetical data for five provinces in Iran.</p></caption><graphic content-type="pdf-region" xlink:href="pdf-region:4:65.9,669.7,537.1,757.6"/><p content-type="note">This table is shown in the PDF version of the article.</p></table-wrap>
</sec>
<sec id="sec-17"><label>3.4</label><title>Preliminary Analysis</title>
<p>A correlation matrix can be created to assess relationships between the KPIs. However, for simplicity, we will proceed directly to the DEA analysis.</p>
</sec>
<sec id="sec-18"><label>3.5</label><title>Data Envelopment Analysis</title>
<p>We will use the BCC model, assuming variable returns to scale <xref ref-type="bibr" rid="ref-29">[28]</xref>. The DEA model will be set up for each province and will calculate the efficiency score for each province using the following linear programming formulation:(for each output/input ratio).</p>
<p>yi Maximize θ = , xi (4) i = 1, 2,</p>
<p>y1= output (agricultural production).</p>
<p>x1= input (total water withdrawal).</p>
<p>y2= output (water use efficiency).</p>
<p>x2= input (agricultural water consumption).</p>
<p>Efficiency will be calculated for each province based on the two outputs and two inputs. For each province, the linear programming problem will calculate:</p>
<table-wrap id="tab2"><label>Table 2</label><caption><p>Efficiency scores for each province.</p></caption><graphic content-type="pdf-region" xlink:href="pdf-region:4:66,247.6,537.1,324.2"/><p content-type="note">This table is shown in the PDF version of the article.</p></table-wrap>
</sec>
<sec id="sec-19"><label>3.6</label><title>Multi-Criteria Decision Analysis</title>
<sec id="sec-20"><title>Weight assignment</title>
<p>Let&apos;s assign weights to the KPIs based on expert judgment:</p>
<p>I. Weight for agricultural production (O1): 0.6.</p>
<p>II. Weight for water use efficiency (O2): 0.4.</p>
</sec>
<sec id="sec-21"><title>Synthesis of scores</title>
<p>Now, we will apply the weighted sum model to integrate the efficiency scores from DEA.</p>
<p>Calculate aggregated scores:</p>
<p>Si = w1 × θi + w2 × θi, (5) where:</p>
<p>Si = aggregated score for province i.</p>
<p>w1 = weight for O1.</p>
<p>w2 = weight for O2.</p>
<table-wrap id="tab3"><label>Table 3</label><caption><p>Aggregated scores.</p></caption><graphic content-type="pdf-region" xlink:href="pdf-region:5:66,581.3,537.1,658"/><p content-type="note">This table is shown in the PDF version of the article.</p></table-wrap>
<p>From the aggregated scores, we can rank the provinces:</p>
<p>I. Isfahan: 2.39 (best performance).</p>
<p>II. Tehran: 2.22.</p>
<p>III. Khorasan (R): 2.12.</p>
<p>IV. Khuzestan: 1.93.</p>
<p>V. Fars: 1.84 (worst performance).</p>
<p>Isfahan shows the best efficiency in water resource management, suggesting effective practices that could be studied and replicated in other provinces.</p>
<p>Fars has the lowest efficiency score, indicating a need for improved water management strategies, possibly through better irrigation techniques or technology adoption.</p>
</sec>
</sec>
</sec>
<sec id="sec-22"><label>4</label><title>Case Study 2: Renewable Energy Utilization in Iran</title>
<p>The objective is to assess the efficiency of different provinces in Iran regarding their renewable energy utilization, with a focus on solar and wind energy. The analysis will help identify best practices and areas for improvement.</p>
<sec id="sec-23"><label>4.1</label><title>Key Performance Indicators</title>
<p>The following KPIs will be used in the analysis:</p>
<sec id="sec-24"><title>Inputs</title>
<p>I1: total renewable energy investment (million USD).</p>
<p>I2: total area for renewable energy projects (hectares).</p>
</sec>
<sec id="sec-25"><title>Output</title>
<p>O1: total renewable energy generated (GWh).</p>
<p>O2: renewable energy utilization efficiency (GWh per million USD investment).</p>
</sec>
</sec>
<sec id="sec-26"><label>4.2</label><title>Data Collection</title>
<p>We will collect data for ten provinces in Iran. The data will include information on renewable energy investments, areas dedicated to projects, energy generation, and utilization efficiency. Here’s the hypothetical dataset:</p>
<table-wrap id="tab4"><label>Table 4</label><caption><p>Data on renewable energy utilization.</p></caption><graphic content-type="pdf-region" xlink:href="pdf-region:6:56.4,613.5,537.8,757.6"/><p content-type="note">This table is shown in the PDF version of the article.</p></table-wrap>
</sec>
<sec id="sec-27"><label>4.3</label><title>Preliminary Analysis</title>
<p>A correlation analysis will help us understand the relationships between the KPIs. However, we will proceed directly to the DEA analysis.</p>
</sec>
<sec id="sec-28"><label>4.4</label><title>Data Envelopment Analysis</title>
<p>The BCC model assumes variable returns to scale <xref ref-type="bibr" rid="ref-29">[28]</xref>.</p>
<sec id="sec-29"><label>4.4.1</label><title>Efficiency calculation</title>
<p>We will calculate the efficiency scores for each province based on the two outputs and two inputs. The following formulation is used for each province&apos;s efficiency:</p>
<p>αO1i+βO2i</p>
<p>Maximize θi = I1 +I2 , (6)</p>
<p>where:</p>
<p>i = number of provinces.</p>
<p>O1i= total renewable energy generated (GWh).</p>
<p>O2i= renewable energy utilization efficiency (GWh per million USD investment) I1i= total renewable investment (million USD).</p>
<p>I2i= total area for projects (hectares).</p>
<p>α , β are weights assigned to outputs, assumed to be 0.5 each here for simplicity.</p>
<table-wrap id="tab5"><label>Table 5</label><caption><p>Efficiency scores.</p></caption><graphic content-type="pdf-region" xlink:href="pdf-region:6:66,117.4,537.1,250.3"/><p content-type="note">This table is shown in the PDF version of the article.</p></table-wrap>
</sec>
</sec>
<sec id="sec-30"><label>4.5</label><title>Multi-Criteria Decision Analysis</title>
<p>We assign weights to the KPIs based on stakeholder preferences or expert judgment.</p>
<p>I. Weight for total renewable energy generated (O1): 0.6.</p>
<p>II. Weight for renewable energy utilization efficiency (O2): 0.4.</p>
<p>Using the weighted sum model to integrate the efficiency scores from DEA.</p>
<table-wrap id="tab6"><label>Table 6</label><caption><p>Aggregated scores.</p></caption><graphic content-type="pdf-region" xlink:href="pdf-region:7:66,563.9,537.1,696.8"/><p content-type="note">This table is shown in the PDF version of the article.</p></table-wrap>
<p>Tehran shows excellent performance in renewable energy utilization, indicating effective policies and investments in place. This province could share best practices with others. Golestan has the lowest score, suggesting a need for strategic improvements in renewable energy projects and investments.</p>
</sec>
</sec>
<sec id="sec-31"><label>5</label><title>Discussion</title>
<p>The integration of DEA and MCDA has been demonstrated as a robust framework for the evaluation of efficiency in sustainable resource management initiatives within Iran. The analysis of water resource management and renewable energy utilization has revealed significant performance disparities among provinces, highlighting the need for targeted interventions in areas displaying inefficiencies.</p>
<p>The results indicate that Tehran has achieved the highest efficiency score in renewable energy utilization. This result suggests that factors such as resource allocation, infrastructure investment, and policy support may contribute to the superior performance observed in this province. By identifying both high-performing and underperforming provinces, a clearer understanding of operational dynamics has been established, thereby guiding the development of tailored strategies aimed at optimizing resource use and fostering equitable access to sustainable energy solutions.</p>
<p>Moreover, the application of the integrated framework has facilitated a comprehensive analysis of the interplay between various sustainability indicators. The simultaneous evaluation of multiple criteria allows for the identification of synergies and trade-offs, thereby empowering decision-makers to make informed choices that align with the overarching goals of sustainable development.</p>
<p>While the findings are promising, additional research is warranted to explore the application of DEA in other contexts. The potential for MCDA to prioritize sustainability criteria tailored to local realities also warrants further investigation. As the complexity of sustainability challenges intensifies, the enhancement of analytical frameworks becomes essential for policy formulation, implementation, and evaluation.</p>
</sec>
<sec id="sec-32"><label>6</label><title>Conclusion</title>
<p>In conclusion, a successful demonstration of the practical application of an integrated DEA and MCDA framework has been provided to assess sustainability in crucial sectors in Iran. Actionable insights into the efficiencies and inefficiencies of water resource management and renewable energy utilization have been generated, contributing to the discourse on effective, sustainable development practices.</p>
<p>The findings advocate for a strategic approach to resource management, emphasizing the importance of evidence-based interventions designed to improve performance across provinces. As Iran and similar contexts pursue their sustainability goals, the adoption of this integrated framework is expected to facilitate a nuanced understanding of resource dynamics, ultimately fostering decision-making that aligns with global sustainability imperatives.</p>
</sec>
<sec id="sec-33"><title>Acknowledgments</title>
<p>The authors would like to express their sincere gratitude to the Department of Mathematics at the Isfahan (Khorasgan) Branch, Islamic Azad University, for their continuous support and valuable resources that facilitated this research. Special thanks are also extended to all experts and stakeholders who provided insightful feedback and contributions during the data collection and evaluation processes.</p>
</sec>
<sec id="sec-34"><title>Funding</title>
<p>This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.</p>
</sec>
<sec id="sec-35"><title>Data Availability</title>
<p>The data that support the findings of this study are available from the corresponding author upon reasonable request. Hypothetical datasets used for demonstration purposes in the case studies are included within the article.</p>
</sec>
</body>
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