Data envelopment analysis has long provided a rigorous way to compare the efficiency of organizations, systems, and decision-making units that use multiple inputs to generate multiple outputs. However, conventional DEA remains largely static: it evaluates the available observations but cannot readily learn from historical data, predict the efficiency of unseen units, or adapt to rapidly changing environments. Our study began with a fundamental question: Can DEA evolve from a retrospective benchmarking method into a predictive, interpretable, and reproducible decision-support framework through machine learning?

1. Recognizing the limitations of static efficiency analysis

Since its introduction, DEA has been applied across banking, healthcare, manufacturing, agriculture, education, energy, transportation, supply chains, and environmental sustainability. Its appeal lies in its ability to evaluate multiple inputs and outputs without requiring researchers to specify a predefined production function.

Yet this strength is accompanied by important limitations. Classical DEA is deterministic, sensitive to noise and outliers, and unable to generalize beyond the observations used to construct its efficiency frontier. When a new decision-making unit is introduced, the frontier generally needs to be recalculated. In increasingly data-intensive environments, where managers require continuous monitoring, forecasting, and rapid decision support, static efficiency scores alone are no longer sufficient.

Machine learning appeared to offer a promising response. Artificial neural networks, support vector machines, random forests, boosting algorithms, clustering methods, and deep-learning architectures had increasingly been combined with DEA to predict efficiency, classify organizations, identify drivers of poor performance, and process complex or time-dependent data.

However, the literature remained fragmented. Some studies used DEA scores as targets for machine-learning models, others treated them as features, rankings, classes, or benchmarking references. Different research communities were developing related approaches without a unified understanding of how the field was evolving. Existing DEA reviews largely focused on historical models, bibliometric trends, or individual application sectors rather than systematically examining the integration of DEA with machine learning.

This fragmentation motivated us to bring the field together.

2. Mapping a rapidly expanding research landscape

We conducted a systematic review following the PRISMA framework. The search initially identified 521 records. After screening and eligibility assessment, 313 studies were retrieved, from which 210 peer-reviewed articles were systematically and critically analyzed. We also examined 30 additional studies representing emerging learning-based frontier models.

One of the clearest findings was the speed at which the field had expanded. Annual DEA–ML publications increased from fewer than 20 studies per year during much of 2015–2019 to 70 studies in 2025. This growth showed that the combination was no longer an isolated methodological experiment. It had become a recognizable research direction spanning operations research, artificial intelligence, decision sciences, engineering, economics, and management.

Nevertheless, the analysis also revealed that methodological development remained uneven. Classical DEA formulations continued to dominate: the CCR and BCC models appeared in 73 and 71 studies, respectively. These models provide understandable and theoretically established efficiency measures, but their continued dominance also indicates that many researchers still rely on familiar static formulations before adding a separate predictive layer.

On the machine-learning side, artificial neural networks were the most frequently used models, appearing in 91 studies. Support vector regression and random forests followed with 28 and 27 studies, respectively. More recent models, including deep neural networks, long short-term memory networks, convolutional neural networks, gradient-boosting algorithms, and attention-based approaches, were beginning to appear, but their adoption remained limited.

The literature therefore showed a field growing quickly in volume while progressing more cautiously in methodological integration.

3. Discovering two distinct paths of DEA–ML integration

An important outcome of the review was our recognition that the literature contained two fundamentally different research paths.

The first path comprises traditional DEA–ML hybrids. In these studies, DEA is generally applied first to estimate efficiency scores. Machine learning is then used to predict those scores, classify efficient and inefficient units, cluster comparable organizations, or explain the contextual factors associated with performance. This sequential structure extends DEA’s analytical usefulness, but the machine-learning model remains largely separate from the construction of the efficiency frontier.

The second path represents a more fundamental shift toward learning-based frontier models. Approaches such as Efficiency Analysis Trees, Convexified Efficiency Analysis Trees, Dynamic EAT, DEA-Based Machines, Unsupervised DEA, Support Vector Frontier models, convexified and relaxed SVF variants, adaptive regression splines, and boosting-based frontier methods incorporate statistical learning directly into frontier estimation.

These methods do not merely predict efficiency scores produced by a conventional DEA model. Instead, they use mechanisms such as pruning, regularization, cross-validation, constrained optimization, risk minimization, and shape-constrained learning to estimate or refine the frontier itself.

This distinction became central to the study. It allowed us to frame the development of the field not simply as “DEA combined with machine learning,” but as a broader transition:

from using machine learning after efficiency measurement to using statistical learning within efficiency-frontier construction.

Importantly, our findings do not suggest that learning-based models should replace classical DEA. Their current evidence base remains concentrated in simulations, computational experiments, and selected empirical applications. Rather, they should be viewed as an emerging complement that can improve generalization, reduce overfitting, accommodate noise, and retain important production-theory assumptions.

4. Looking beyond predictive accuracy

As we examined the literature, it became clear that the central challenge was no longer whether DEA and machine learning could technically be combined. Many studies had already demonstrated that they could.

The more important question was whether these combinations could produce results that were reliable, interpretable, reproducible, and practically usable.

Small datasets remain a persistent problem. Many DEA applications contain only a few hundred decision-making units, yet researchers frequently apply data-intensive neural networks without sufficient external validation. Under such conditions, strong reported performance may reflect overfitting rather than genuine predictive ability.

Interpretability is another concern. DEA is often valued because its efficiency scores and benchmarks have managerial meaning. When these outputs are transferred into opaque machine-learning models, the resulting system may provide more accurate predictions but less useful explanations. Tools such as SHAP, feature-importance analysis, and interpretable tree-based models offer promising solutions, although they remain inconsistently adopted.

Reproducibility also emerged as a major weakness. Only 152 of the 210 reviewed studies explicitly reported their software environments. MATLAB was the most frequently reported platform, appearing in 50 studies, while R and Python each appeared in 35. Many studies depended on several disconnected tools: one platform for DEA estimation, another for machine-learning training, and sometimes a third for visualization or statistical analysis.

Such workflows create opportunities for manual errors and make it difficult to determine precisely how DEA scores were generated, transferred, validated, and used. Small differences in input–output definitions, model orientation, returns-to-scale assumptions, solver settings, preprocessing, train–test splitting, cross-validation, or hyperparameter tuning can materially change the reported results.

Therefore, opening a dataset or sharing isolated code is not enough. Meaningful reproducibility requires transparent documentation of the complete analytical pipeline.

5. Building a pathway toward end-to-end efficiency intelligence

Based on these findings, we proposed a forward-looking implementation pathway in which DEA and machine learning are treated as components of a unified efficiency-analytics system.

Such a pipeline should integrate four stages:

1. DEA formulation and efficiency estimation;
2. machine-learning training and validation;
3. explainability and efficiency-driver analysis; and
4. visualization, reporting, and deployment.

Python offers a particularly suitable foundation because optimization libraries can be combined with data-processing, machine-learning, explainability, and deployment frameworks in one environment. Linear-programming-based DEA formulations can be implemented through tools such as PuLP and connected directly to libraries including Pandas, Scikit-learn, TensorFlow, PyTorch, and SHAP.

However, the goal is not simply to promote one programming language. The wider requirement is to develop standardized, modular, and reusable workflows. Future tools should allow researchers to define decision-making units, select DEA assumptions, estimate efficiency, train predictive models, conduct cross-validation, explain performance drivers, and export reproducibility reports without repeatedly rebuilding the complete workflow.

The development of shared benchmark datasets is equally important. Because data in sectors such as finance, healthcare, and public administration are frequently confidential, future repositories may need to include anonymized, aggregated, synthetic, or controlled-access datasets. Without common benchmarks, it will remain difficult to determine whether apparent improvements arise from superior methods or merely from differences in data, assumptions, and validation procedures.

6. Looking beyond this review

The broader message of our work is that DEA is undergoing a conceptual transformation. It is moving from a method that evaluates the relative efficiency of observed units toward a framework capable of prediction, adaptation, explanation, and potentially real-time decision support.

This transition must nevertheless be approached carefully. Higher predictive accuracy alone does not guarantee better efficiency analysis. Machine-learning models must respect the production assumptions underlying DEA, be validated on appropriate data, and provide explanations that decision-makers can understand and act upon.

Future research should therefore focus not only on developing more complex algorithms, but also on external validation, uncertainty quantification, interpretable learning, dynamic and streaming data, standardized benchmarking, open-source software, and deployment-oriented design. Learning-based frontier models also require broader testing across industries before their practical advantages over classical DEA and traditional hybrids can be firmly established.

Our study was ultimately guided by a simple principle: machine learning should not remove the theoretical discipline that makes DEA valuable. It should help DEA learn, generalize, explain, and respond more effectively to changing environments.

The future of efficiency analysis lies neither in static optimization alone nor in unconstrained predictive modeling. It lies in bringing production theory, optimization, statistical learning, and transparent software together to create efficiency-intelligence systems that are scalable, interpretable, reproducible, and useful in real decision-making.