Linearization of the additive two-stage network data envelopment analysis model

ABSTRACT The study takes 27 core cities in the Yangtze River Delta from 2014 to 2023 as samples, uses a super efficiency data envelopment analysis model considering unexpected output to measure efficiency, combines Gini coefficient and Theil index to analyze regional differences, and uses spatial autocorrelation analysis and spatial Durbin model to reveal spatial effects. The results show that the water resource utilization efficiency in Shanghai increased from 1.23 in 2014 to 1.78 in 2023, and the Gini coefficient of water resource utilization efficiency in the Yangtze River Delta decreased from 0.321 in 2014 to 0.259 in 2023. Research has shown that there are significant regional differences and positive spatial autocorrelation in the water resource utilization efficiency of cities in the Yangtze River Delta, with obvious spatial spillover effects. This provides a scientific basis for optimizing the allocation and collaborative management of water resources, which helps promote regional sustainable development.

ABSTRACT In ecosystem-based forest management, forest roads are expected to support ecological integrity alongside economic, social, and technical functions. However, conventional cost-oriented evaluations often fail to capture this multidimensional performance. This study evaluates the functional efficiency of forest roads using a Data Envelopment Analysis (DEA) framework integrated with Geographic Information Systems (GIS). This study aims to develop a multidimensional efficiency assessment framework to support forest road planning while minimizing adverse impacts on sensitive natural areas, including biodiversity corridors, water resources, and protected forest zones. Four functional scenarios were considered: ecological, economic, social, and technical. Thirty forest roads located in the Maçka Forest Sub-District Directorates (Türkiye) were analyzed as Decision Making Units (DMUs) using an input-oriented CCR DEA model. Scenario-specific input and output variables were derived from GIS-based spatial analyses and field measurements. Twenty-one variables were quantified via GIS models and eighteen variables via field surveys, reflecting terrain, geometry, environmental sensitivity, and accessibility. The results reveal clear functional contrasts among road segments. In the ecological scenario, 24 out of 30 roads (80.0%) were classified as efficient, followed by the economic scenario with 22 efficient roads (73.3%). Technical and social scenarios exhibited lower proportions of efficient roads, with 17 (56.7%) and 14 (46.7%) efficient roads, respectively. Ecologically efficient roads were associated with stable terrain, lower landslide occurrence, and stronger forest connectivity. Economically efficient roads showed appropriate spacing and limited surface deformation, while technical efficiency was mainly linked to compliance with geometric standards. This DEA-GIS framework supports function-oriented decision making in forest road planning.

This study aims to analyze the equity and efficiency of health resource allocation in underdeveloped county areas, providing a reference for improving health resource policies in such regions. Focusing on eight underdeveloped counties in Guangxi, China, this research evaluates the fairness of health resource distribution using the Gini coefficient and Lorenz curve, and assesses allocation efficiency through the Data Envelopment Analysis model. In terms of equity in health resource allocation from 2015 to 2021, the Gini coefficients for health resources per capita were between 0.07 and 0.23, indicating the highest level of equity; the fairness in the distribution of healthcare human resources was lower than that of medical institutions and hospital beds, with particularly low equity observed in the distribution of licensed (assistant) physicians. Regarding efficiency, the overall efficiency of health resource allocation averaged between 0.899 and 0.933, with the number of counties achieving efficiency fluctuating between three and five. There were inefficiencies observed, particularly in technical and scale efficiency, with low scale efficiency being a significant factor affecting the efficiency of health resource allocation in underdeveloped counties. The distribution of health resources based on population and GDP demonstrates greater equity compared to distribution based on geographic areas. The equity of institutions and beds is superior to that of healthcare human resources. Overall, the efficiency of health resource allocation is not high, and there are regional disparities in efficiency. Recommendations include increasing the focus on health resource allocation in underdeveloped areas, optimizing the management of healthcare human resources, and coordinating planning to improve the precision and rationality of resource investment, thereby enhancing the efficiency of health resource utilization.

E-business projects may face several risks that are potential to affect the success of such projects. As an important issue for a project manager in this field, the potential risks should be prioritized according to their potential impact on the success of the project. In this study, the potential risks of the e-business sector are to be evaluated and ranked based on the success criteria of such projects. For this aim a complete set of risks compared to the literature is considered and their impact on the project success criteria are determined linguistically by the experts of the field as a case study. To respect the uncertain nature of the evaluations, the linguistic evaluations are converted to belief-degree-based uncertain values. Then for the first time, a data envelopment analysis (DEA) model is used to evaluate and rank such risks. For this aim, the classical Tchebycheff norm DEA model is extended to a belief-degree-based uncertain environment for the first time. An extensive computational study including sensitivity analysis and comparative study is performed by the uncertain Tchebycheff norm model to evaluate and rank the risks of the case study. Based on the obtained results “introducing new technology” and “cultural risk” are the most and least important risks respectively.

Purpose This study investigates how industrial agglomeration (IA) affects green total factor productivity (GTFP) in the construction sector, whether construction consulting services (CCS) moderates this relationship, and how environmental regulation influences these mechanisms. A unified framework is developed to offer theoretical and empirical insights for green transformation in the sector. Design/methodology/approach Using data from China’s construction industry (2008–2022), GTFP is measured with the Slacks–Based Data Envelopment Analysis model. IA is quantified by the location quotient, and CCS is assessed across provinces. Multiple regression models examine the non-linear IA–GTFP relationship and CCS’s moderating role. Capital efficiency, labor efficiency, energy efficiency, and carbon emission efficiency are measured, and formal and informal environmental regulations are examined as contextual factors. Findings IA shows an inverted U–shaped relationship with GTFP, promoting productivity at moderate levels but restraining it when excessive. CCS directly enhance GTFP and weaken the curvature of the IA–GTFP link. IA improves labor efficiency but exhibits inverted U–shaped effects on capital, energy, and carbon efficiencies, while CCS mainly strengthen energy and carbon efficiencies. Particularly, informal environmental regulation amplifies these positive effects. Research limitations/implications The study relies on inter-provincial data, limiting insights into individual units’ performance. Findings are specific to China’s construction industry, and cross-national generalization requires further verification. Recommendations have not been fully validated in practice. Future research should explore different types of CS, their roles in green technologies, enterprise innovation, and the diffusion mechanisms of CS networks across regions. Practical implications Policymakers can develop region-specific industrial agglomeration strategies and enhance CS support to optimize GTFP. Promoting green technologies, environmentally friendly construction, and consulting service systems can strengthen labor, energy, and carbon efficiency. Combining formal policies with public-driven informal regulation helps achieve sustainable development and high-performance industrial ecosystems. Social implications Informal environmental regulation, driven by public awareness and green economic development, enhances IA and CS effectiveness, promoting socially responsible growth in the construction industry. Strengthening public participation and environmental consciousness contributes to sustainable urbanization and climate-friendly practices. Originality/value The first study to integrate IA, CCS, and GTFP into a unified empirical framework, revealing the mechanisms linking IA, CCS, and environmental regulation to green productivity in construction industry.

This paper introduces a novel Aggressive Variable Selection method for Data Envelopment Analysis (DEA), based on a Centralized DEA approach. Unlike some existing benevolent approaches, based on multiplier formulations, which maximize the efficiency of decision-making units (DMUs), the proposed model uses an envelopment formulation that seeks to maximize the total inefficiency in the sample, thereby enhancing discriminant power in variable selection. Owing to its nonlinear structure, the model is reformulated as a bi-level optimization problem. Once the most discriminant inputs and outputs are identified for a given total number of variables, a conventional (i.e., non-centralized) DEA model is used to compute the efficiency scores. The process is repeated for successively larger subsets of variables until a trade-off is attained between using as many variables as possible and having an acceptable level of discrimination. The approach provides robust efficiency scores and estimations of the discriminating importance of the variables. The proposed approach is first illustrated using a small benchmark dataset and compared with two existing variable selection methods from the literature. Then, the method is applied to the evaluation of OECD countries based on Sustainable Development Goal (SDG) indicators, a high-dimensional dataset characterized by a large number of inputs and outputs relative to the number of decision-making units. This suggests that an aggressive criterion in variable selection yields greater discrimination among units and provides a sharper assessment of variable relevance by emphasizing performance differences among DMUs

A nonparametric least-squares model in network data envelopment analysis

Transport decarbonisation requires allocating limited resources across competing strategies. The Avoid–Shift–Improve framework categorises these strategies to reduce transport's reliance on fossil fuels. This study develops an Avoid–Shift–Improve driven network data envelopment analysis (DEA) framework to measure county-level progress toward transport decarbonisation. The framework also serves as a decision-support tool for allocating resources efficiently to advance transport decarbonisation. Using data from Ireland's 26 counties, we integrate DEA with a Stackelberg leader–follower game and the best–worst method. The DEA component provides an objective, mathematically defined measure of relative efficiency. The best–worst method incorporates expert judgement on the economic and environmental impact of actions within the Avoid–Shift–Improve hierarchy. This hierarchical approach, reflecting expert consensus, prioritises transformational measures that reduce travel demand (Avoid), followed by strategies that shift remaining trips to low-carbon modes (Shift), while technological improvements (Improve) play a more limited role. Results reveal disparities in county performance. Dublin leads due to its relatively well-developed public transport and active mobility infrastructure. Smaller counties such as Longford and Leitrim also perform strongly despite their rural character. By contrast, large-area counties including Cork, Mayo, and Kerry underperform, reflecting structural challenges of dispersed settlement and high car dependency. The analysis highlights that larger counties achieve lower efficiency scores, while links with emissions and expenditure are weaker, underscoring the role of spatial scale and carbon lock-in in shaping outcomes. The framework is scalable to other regional and national contexts and can support economically rational, socially inclusive climate policy. • Develops a network DEA model for hierarchical importance of subunits in parallel structure. • Employs the Avoid–Shift–Improve framework to assess transport decarbonisation progress. • Integrates DEA, Stackelberg game, and BWM to evaluate emission-reduction strategies. • Prioritises and harmonises transport climate actions to maximise decarbonisation gains. • Provides a decision-support tool for policy-driven transport decarbonisation.

The disease prevention and control system represents a fundamental component of public health services. Although the Chinese government has consistently prioritized and increased funding for Centers for Disease Control and Prevention (CDCs), whether these additional resources have been effectively translated into improved public health outcomes remains indeterminate. This study was designed to evaluate the operational efficiency of CDCs in China, objectively present the changes in efficiency values, and provide an evidence base for optimizing their service effectiveness. Taking the CDCs in 31 provincial-level administrative regions in mainland China as the research objects, a mixed research design was adopted, integrating longitudinal panel data (2011-2022) and provincial cross-sectional data (2022). Input indicators, output indicators, and environmental variables were all sourced from authoritative statistical yearbooks. The three-stage Data Envelopment Analysis (DEA) model was used to measure the static efficiency of different regions, and the Malmquist index model was applied to decompose the dynamic changes in Total Factor Productivity (TFP) of CDCs. At the national level, the average annual growth rate of TFP in the CDCs was 1.3%, mainly driven by technological progress (+ 2.2% annually), but offset by a decline in technical efficiency (-0.9% annually; pure technical efficiency: -0.7%; scale efficiency: -0.2%). All 31 provinces achieved technological progress (Malmquist index > 1), while only 41.94% of provinces experienced an improvement in technical efficiency. In 2022, the average adjusted comprehensive efficiency across regions was 0.811, showing a significant regional gradient: eastern region (0.914) > central region (0.876) > western region (0.672). The average pure technical efficiency was 0.863, and the average scale efficiency was 0.927, with 61.29% of provinces exhibiting decreasing returns to scale. After excluding environmental factors, 22.58% of provinces maintained unchanged efficiency values, most provinces showed fluctuations (both increases and decreases), and the efficiency values of remote western regions slightly improved. The efficiency improvement of China's CDCs mainly relies on technological progress, while the continuous decline in technical efficiency reflects shortcomings in resource utilization and organizational management. Significant regional disparities in efficiency exist and are influenced by environmental factors. Future efficiency improvement should focus more on the coordination of internal management and technological application, implement differentiated scale optimization strategies, and emphasize regional quality-oriented collaboration (including technology and talent). These measures will promote the high-quality and sustainable development of the disease prevention and control system.

Maternal and child healthcare services constitute a vital component of the healthcare system and play a crucial role in safeguarding population health. However, in China, challenges such as the irrational allocation of MCH resources and suboptimal operational efficiency remain prevalent. This study aims to investigate the impact of resource allocation on the efficiency of the maternal and child healthcare system in China. Data for 31 provinces and municipalities in China were obtained from the China Health Statistical Yearbook and the China Statistical Yearbook covering the period 2017 to 2021. The comprehensive Maternal and Child Health resource density index was developed by applying the entropy weight method to analyze the allocation of MCH resources across provinces. Furthermore, a three-stage Data Envelopment Analysis (DEA) model was employed to calculate the efficiency of the provincial MCH systems. Finally, a spatial Durbin model was applied to examine the effect of the comprehensive MCH resource density on system efficiency. Between 2017 and 2021, the comprehensive Maternal and Child Health (MCH) resource density index in most regions of China increased from 0.108 to 0.138. In contrast, the average technical efficiency declined from 0.943 to 0.920, with substantial disparities observed across regions. The Moran's I index for MCH resource efficiency ranged from - 0.349 to - 0.245, indicating significant spatial autocorrelation. Key factors influencing the technical efficiency of MCH resources included the comprehensive CHRDI in maternal and child health, urbanization rate, and total health expenditure per capita (P < 0.05). While the allocation of maternal and child health resources in China improved between 2017 and 2021, significant regional disparities persist. The study further reveals that the level of MCH resource allocation exerts spatial spillover effects on efficiency. Based on the current data trend, optimizing resource allocation may require a combination of policy guidance, financial input, performance evaluation, regional collaboration, and other coordination strategies.

Wind energy site selection requires robust frameworks that simultaneously address expert uncertainty, objective efficiency screening, and predictive capability beyond sampled locations. This study presents an integrated framework for strategic wind farm site selection in Ethiopia's Amhara Region by combining Fuzzy Analytic Hierarchy Process (FAHP), efficiency analysis, and predictive modelling to overcome the limitations of static GIS approaches. The FAHP stage incorporates expert judgment through fuzzy triangular numbers to weight six variables such as wind speed, slope, elevation, distance to transmission lines, distance to roads, and land-use/land-cover to achieve a consistency ratio of 0.0175 with wind speed emerging as the dominant factor of 0.4211 weights in order to generate a spatial suitability surface and extract candidate high-potential areas. High-potential zones identified by FAHP are then evaluated as decision-making units using input-oriented Data Envelopment Analysis (DEA) models. DEA efficiency screening identifies North Shewa as frontier-efficient zone (CCR = BCC = SBM = 1.0), which contributes 32.25% of regional suitable land. Finally, machine learning (ML) models (Random Forest (RF), Support Vector Machine (SVM) and Extreme Gradient Boost (XGBoost)) are trained on 1.5million sampled pixels from the 31-million-cell feature space to learn generalizable suitability functions. Random Forest achieved optimal performance with RMSE of 0.2981 and R2 of 0.8145 in regression and F1-score of 0.9207 and accuracy of 0.9237 in classification to delineates 1,698km2 of high-priority corridors within North Shewa for immediate wind farm deployment. Independent validation through five different sources that includes 250MW of Debre Birhan under Ethiopian Ministry of Finance private public project pipeline to confirm North Shewa as the highest-potential development corridor. This framework advances wind energy planning by integrating subjective weighting, objective efficiency analysis, and predictive modelling into a unified strategic decision-support system applicable for wind energy planning in data-scarce region.

Purpose This study aims to assess and validate the “integrated entropy-additive ratio assessment” (IEARAS) method and demonstrate its robustness in evaluating healthcare system performance. The Charnes, Cooper and Rhodes (CCR) and slacks-based measure (SBM) models used to measure performance (1) assign unequal weights for identical variables across different decision-making units (DMUs); (2) yield an efficiency score of 1 for multiple DMUs; and (3) are sensitive to sample size. These aspects reduce the suitability of data envelopment analysis (DEA) models for assessing performance. Design/methodology/approach To assess the robustness and validity of the IEARAS method, we simultaneously applied the CCR and SBM models, using three distinct datasets of district hospitals (DHs) from different healthcare systems. The robustness of IEARAS is assessed across the different dataset and variable selection scenarios. Findings Analysis and results demonstrate that while DEA models are sensitive to sample size and variable count, the IEARAS method remains consistent and robust across all scenarios. The reliability of IEARAS across various scenarios, with a high value of Kendall's tau and Spearman's rho, further validates that IEARAS proves to be aligned with CCR and SBM and yet can address the limitations of DEA models. Originality/value Entropy-ARAS integration with CCR and SBM validation has received limited attention. This study advances the methodological literature by proposing a generalizable, non-frontier-based benchmarking framework that reduces sensitivity to sample size and weight variability. Additionally, the IEARAS framework provides policymakers and hospital administrators with a scalable and transferable tool for comparative performance evaluation across regions and healthcare systems, thereby enhancing its generalizability beyond the sampled datasets.

This study proposes parametric bootstrap estimation methods to improve features of the non-parametric bootstrap estimator of Incidence of Inefficiency proposed in the literature. This study is the first to propose parametric bootstrap estimation methods to improve features of the IOI estimators. In the simulation study, the Maximum Likelihood-based parametric bootstrap method yields the best results in small sample sizes and a limited number of input and output variable situations. However, in cases where the number of input and output variables increases, which reduces the discrimination power of classical Data Envelopment Analysis models, the Bayesian estimator with latent variable adjustment tends to yield better results than the proposed estimators for IOI in the literature. Additionally, it is experimentally demonstrated that the parametric bootstrap based on the Bayesian method applied to a specific posterior distribution converges to the same features as the estimators obtained with the Bayesian estimator based on that posterior distribution.

This research addresses a paradoxical phenomenon in Lampung Province's Micro and Small Industry (MSI) sector (2018-2022), where high technology adoption is accompanied by declining business units and income inequality. The objective is to evaluate technical efficiency and productivity changes across 15 regencies/cities using the Variable Returns to Scale (VRS) Data Envelopment Analysis (DEA) model and the Malmquist Productivity Index (MPI). Results show an average technical efficiency of 0.838, indicating a 16.2% room for output improvement. Mesuji Regency serves as the benchmark with perfect efficiency. The main inefficiency stems from labor slack (averaging 3,458 people per region), reflecting disguised unemployment. The Malmquist index records an asymmetric productivity growth of 2.1% annually, entirely driven by technological progress (3.5%), while internal managerial efficiency contracted (-1.4%). Consequently, technology adoption requires structural intervention; regional governments must prioritize vocational training and basic managerial strengthening to reduce labor slack and break the MSI inefficiency cycle.

Purpose This research aims to evaluate the technical efficiency (TE) of the palm oil industry in Sumatera Utara, Indonesia. The study also explores key determinants such as Integrated Value Chains (IVCs), Market Access, Information, Certified Seed and Farmer Experience. Design/methodology/approach This study used a two-stage approach. In the first stage, the DEA model was used to measure the TE of oil palm. Then, in the second stage, specific variables related to palm oil that are assumed to affect efficiency are analyzed using Tobit regression. Findings Out of 150 farmers, 14 (9.3%) operate under constant returns to scale, 24 (16%) operate under decreasing returns to scale and 112 (74%) operate under increasing returns to scale. Tobit regression results reveal a significant result, emphasizing the pivotal role of direct Market Access in enhancing TE by 16%, respectively. Research limitations/implications The research has the following limitations: first is the use of Data Envelopment Analysis (DEA) to measure TE may introduce bias, as it does not fully capture real-world complexities and unobserved heterogeneity. In practice, unobserved farm-level, market and institutional characteristics may also contribute to measured inefficiencies. Second, although the study does not find a statistically significant impact of the IVC on TE, the analysis is retained due to the conceptual and policy relevance of this issue within the palm oil sector. Originality/value This article aims to delve into the impact of IVC and Market Access on palm oil farming efficiency in Sumatra Island.

Efficiency refers to the performance level corresponding to using minimal inputs to achieve the maximum possible outputs. Despite its importance to the Canadian economy, such performance assessments has rarely been undertaken in the hardware retail industry in recent years. We present the results of a recent study of the relative efficiencies for three major chains of hardware and renovation retail stores operating in Canada (Home Depot, Lowe’s and Rona). We use the classic and bootstrap data envelopment analysis (DEA) models to measure performance levels over the 22 years from 2000 to 2021. Overall, the firms exhibited high efficiency during this period, and operations management was the primary source of inefficiency. However, an analysis of trends over the 22 years shows that all three companies experienced periods of declining efficiency at the beginning of the study period, followed by a phase of recovery that appears to have accelerated towards the end of the study period. Our longitudinal analysis also indicates that recent shocks and crises have impacted the firms. The succession of crises at the end of the 2000s, the 2007 forestry crisis in Canada, and the 2008 global financial crisis led to the lowest period of efficiency for all the firms, from which they started rebounding in 2011. The specific impact on Rona can explain Lowe’s acquisition of Rona in 2015. However, such a move did not seem to have had a significant improvement beyond accelerating a recovery that had started a few years earlier. This may explain Lowe’s sale of all its Canadian operations in 2022, leading to a new firm called Rona+. Finally, the COVID-19 pandemic also seems to have had a similar effect: accelerating the recovery from the 2008 financial crisis that the firms had started in 2011.

Purpose This study aims to examine whether and how the quality of internal control over financial reporting (ICFR) affects banks’ operational efficiency. Design/methodology/approach First, the authors use a two-stage, nonoriented, variable-returns-to-scale slack-based data envelopment analysis model to calculate banks’ operational efficiency. Second, the authors use cross-sectional Tobit and ordinary least squares regressions to test the hypotheses. Third, the authors use propensity score matching and entropy balancing to control for omitted variables and model misspecification and use the Heckman two-stage treatment-effect model to address self-selection bias. Finally, the authors conduct a structural equation model to identify how ICFR affects banks’ operational efficiency. Findings The results corroborate that banks’ operational efficiency is negatively associated with ineffective ICFR. This negative association is more pronounced when internal control weaknesses relate to revenues, restatements or fraud and when banks have higher human capital, lower board independence and lower free cash flows. Moreover, banks improve operational efficiency by remedying material weaknesses in their ICFR. The findings remain robust across various analyses, including change analyses, alternative measures of ineffective ICFR and operational efficiency, additional control variables and the exclusion of banks during financial crises, COVID-19 and those not under Federal Deposit Insurance Corporation Improvement Act. Practical implications The findings inform managers and regulators that effective ICFR complements other bank regulations and boosts banks’ operational efficiency. Originality/value The research shows that effective ICFR is a key driver of banks’ operational efficiency, contributing to ongoing debates and mixed evidence.

ABSTRACT This study assesses the efficiency with which Moroccan public secondary schools transform resources into student achievement using PISA 2022 data. School-level technical efficiency is estimated through an output-oriented data envelopment analysis (DEA) model under variable returns to scale. Results show an average efficiency score of 0.88 (original DEA score ≈1.14), indicating that schools could raise PISA performance by up to 14% with unchanged inputs. The analysis reveals notable disparities in efficiency both among and within regions, underscoring structural variations inherent in Morocco's decentralized education system. A second-stage bootstrap truncated regression identifies key determinants: grade repetition and bullying reduce efficiency, while rural schools perform more efficiently than urban ones. Significant regional fixed effects further suggest that differences in efficiency reflect broader socioeconomic conditions beyond student and school-level factors. Overall, the study provides the first PISA-based efficiency benchmarks for Moroccan secondary schools and underscores the need for policies that enhance internal resource use while addressing external contextual constraints.

This paper evaluates how efficiently Gulf Cooperation Council (GCC) countries transform knowledge‑system inputs into knowledge capabilities and, ultimately, into knowledge‑based economic performance, using the Global Knowledge Index (GKI) as an integrated input–output framework over the period 2021–2024. Building on a two‑stage network Data Envelopment Analysis (DEA) model fully embedded in the GKI architecture, Stage 1 measures knowledge‑formation efficiency in converting education, TVET, higher education, RDI, ICT, and enabling‑environment pillars into composite intermediate knowledge outputs, while Stage 2 assesses knowledge‑to‑economy conversion efficiency in translating these outputs into the GKI economy indicator and its pillars of competitiveness, openness, and domestic value added. The results reveal substantial cross‑country heterogeneity: the United Arab Emirates and Qatar operate on the efficiency frontier in both stages, whereas Saudi Arabia, Kuwait, Bahrain, and Oman exhibit significant input surpluses and output shortfalls, especially in higher education, RDI, and value‑added generation, indicating structural gaps between knowledge formation and economic absorption. To assess the feasibility of achieving Vision 2030 targets, the study introduces a Δθ‑based forecasting model that quantifies the annual efficiency improvements required for each country to reach frontier or high‑performance thresholds (0.90–0.95) by 2030 and develops a policy‑intensity framework that maps these efficiency gaps into differentiated reform pathways ranging from light to transformational interventions. By extending DEA from static benchmarking to forward‑looking efficiency trajectories, the paper contributes to the technological forecasting and social change literature by offering a GKI‑consistent, multi‑stage efficiency framework that can be used to monitor progress toward national vision targets, stress‑test policy scenarios, and inform strategic planning for knowledge‑based diversification in resource‑rich economies.