Explainable Machine Learning-Based Estimation of Labor Productivity in Rebar-Fixing Tasks

Abstract

Efficient labor productivity forecasting is a critical challenge in construction engineering, directly influencing scheduling, cost control, and resource allocation. In reinforced concrete projects, accurate prediction of rebar-fixing productivity enables managers to optimize workforce deployment and mitigate delays. This study proposes a machine learning-based framework to forecast rebar-fixing labor productivity under varying site and environmental conditions. Four regression algorithms—Random Forest (RF), Extreme Gradient Boosting (XGBoost), Support Vector Regression (SVR), and k-Nearest Neighbors (KNN)—were trained, tuned, and validated using grid search with k-fold cross-validation. RF achieved the highest accuracy, with an $R^2$ of 0.901 and RMSE of 19.94 on the training set and an $R^2$ of 0.877 and RMSE of 22.47 on the test set, indicating strong generalization. Model interpretability was provided through SHapley Additive exPlanations (SHAP), revealing that larger quantities of M32 and M25 rebars increased productivity, while higher temperatures reduced it, likely due to lower labor efficiency. Humidity, wind speed, and precipitation showed minimal influence. The integration of accurate predictive modeling with explainable machine learning offers practical insights for project managers, supporting data-driven decisions to enhance reinforcement task efficiency in diverse construction environments.

1. Introduction

In both developed and developing nations, the construction sector plays a vital role in economic development since it contributes significantly to the gross domestic product (GDP) [1,2,3]. Enhancing productivity in this sector not only attracts greater investment but also strengthens industry competitiveness and creates employment opportunities [4]. As a labor-intensive industry, labor costs typically represent 30% to 60% of total project expenditures [5,6]. Consequently, improving labor productivity is critical to overall project performance. Despite its importance, the construction industry continues to struggle with stagnant or declining productivity growth [7]. Site productivity has a significant impact on the total productivity of construction projects during the construction phase. Nonetheless, forecasting it remains challenging for construction managers due to its dependence on factors such as site size and the specific location of measurement [8]. Additionally, numerous variables can influence productivity, including the complexity of sequential tasks, labor skill levels, the availability of tools and materials, and site-specific conditions [9]. These factors can vary significantly between projects, complicating productivity estimation.

Effectively modeling construction labor productivity requires quantifying and understanding the interrelationships among key influencing factors. Traditional approaches to estimating productivity often rely on the judgment of estimators, published industry benchmarks, or historical data from previous projects. However, estimator-based predictions can be influenced by personal bias and changes in personnel, while published productivity rates typically represent industry-wide averages rather than the specific performance of a given contractor [10]. In contrast, historical project data tend to provide more accurate and reliable estimates [1]. Therefore, adopting robust modeling techniques for construction labor productivity helps eliminate the subjectivity and limitations of conventional methods.

Recent advancements in computational modeling offer alternative pathways to capturing productivity dynamics more precisely. These models account for variability in productivity based on input parameters, enabling more effective scheduling and planning of construction projects [11,12]. Artificial intelligence (AI) can be utilized to create inference models that provide more accurate productivity estimates by avoiding the subjectivity and limitations associated with traditional methods. AI mimics human learning by drawing from past experiences and applying that knowledge to generate rapid responses to new data or analogy-based solutions to unfamiliar problems [13,14]. As a powerful tool, AI has the potential to improve construction efficiency and effectively address complex engineering challenges through advanced computational systems [15,16,17].

Statistical techniques to detect patterns and extract insights from collected data were the main methods that researchers relied on in the early stages of the data utilization era. However, these techniques are limited in their ability to fully leverage the vast datasets now available in the construction industry [18]. With the rapid growth of data volume in this sector [19], machine learning (ML) methods are increasingly being applied to model, estimate, and optimize challenges across the entire lifecycle of complex projects [20,21]. By drawing inferences from diverse historical data sources, ML techniques help uncover predictive patterns and identify both nonlinear and linear relationships [22,23]. Various approaches, including Support Vector Machines (SVMs), artificial neural networks (ANNs), and ensemble models, are frequently used and compared for their predictive accuracy [24]. SVM constructs optimal hyperplanes in high-dimensional spaces to arrive at global solutions. ANNs, inspired by biological neural systems, replicate human learning through interconnected networks of neurons. Ensemble learning methods—such as Random Forests, Adaptive Boosting, and Extreme Gradient Boosting—combine the outputs of multiple weak learners to produce the most accurate predictions through aggregation or voting.

Although many studies apply AI to construction productivity modeling, they differ in the types of tasks, algorithms, input features, and geographic contexts analyzed. Numerous studies have been developed in recent years to estimate productivity within the field of construction management. For example, the study [25] developed and tested three neural networks trained on expert survey data to estimate productivity for formwork, steel fixing, and concrete pouring in developing countries, demonstrating strong generalization and effective sensitivity analysis of influencing factors. Also, another study [26] develops and tests a Deep Neural Network model to estimate excavator productivity on HS2 sites, showing adequate predictive accuracy. The paper [27] develops a machine learning-based model achieving 99.09% precision to predict the productivity of prefabricated external insulation systems, addressing skilled labor shortages and enabling quick analysis without real data. In addition, the study [28] developed a logistic regression model linking human resource management practices to building project productivity, providing a tool to estimate the probability of achieving high productivity based on HRM implementation levels. Moreover, the paper [9] developed an artificial neural network model using ten factors to predict marble floor finishing productivity in Iraqi projects, achieving 90.9% average accuracy and an 89.55% correlation coefficient. Furthermore, the paper [29] proposes an automated machine learning tool using SVM and Naïve Bayes models to estimate steel structure productivity rates, showing that ML can improve accuracy and efficiency over traditional experience-based methods. Also, the study [30] developed a neural network model to estimate labor production rates for concrete columns, addressing unreliable data and subjective factors often ignored in traditional productivity measurement. Another study [31] developed a multivariable linear regression model using ten factors to predict marble floor finishing productivity in Iraqi projects, achieving 96.3% average accuracy and a 90.6% correlation coefficient. In addition, the study [32] used decision trees and the Apriori algorithm to classify factors affecting Turkish ceramic tiling crew productivity, based on time study data including crew size, age, and experience. Furthermore, the study [33] developed neural network models with Bayesian regularization and early stopping to predict labor productivity in Iranian power plant projects, finding that Bayesian regularization performed better and identifying key influencing factors through sensitivity analysis. In addition, the study [34] compared transformed regression and neural network models for predicting dozer productivity, finding that the ANN better captured complex, nonlinear factors affecting equipment performance. Moreover, the study [35] developed a hybrid Neural Network-Driven Fuzzy Reasoning model optimized by genetic algorithms to accurately predict construction productivity using both crisp and fuzzy data, outperforming traditional methods. Furthermore, the study [1] introduced an engineering approach using artificial neural networks with tanh activation to model carpentry and rebar labor productivity, achieving more accurate predictions than traditional methods and demonstrating integration with construction databases for economic and social benefits. Also, the study [36] proposed using artificial neural network-based prediction intervals instead of single-point estimates to more reliably forecast labor productivity, demonstrating improved accuracy and credibility in a case study. Last but not least, the study [37] compared several neural network techniques to model construction labor productivity, finding that backpropagation neural networks performed best in predicting productivity considering environmental and operational factors.

Although many studies apply AI to construction productivity modeling, they differ in the types of tasks, algorithms, input features, and geographic contexts analyzed. Numerous studies have been developed in recent years to estimate productivity within the field of construction management. For example, the study [25] developed and tested three neural networks trained on expert survey data to estimate productivity for formwork, steel fixing, and concrete pouring in developing countries, demonstrating strong generalization and effective sensitivity analysis of influencing factors. Also, another study [26] develops and tests a Deep Neural Network model to estimate excavator productivity on HS2 sites, showing adequate predictive accuracy. The paper [27] develops a machine learning-based model achieving 99.09% precision to predict the productivity of prefabricated external insulation systems, addressing skilled labor shortages and enabling quick analysis without real data. In addition, the study [28] developed a logistic regression model linking human resource management practices to building project productivity, providing a tool to estimate the probability of achieving high productivity based on HRM implementation levels. Moreover, the paper [9] developed an artificial neural network model using ten factors to predict marble floor finishing productivity in Iraqi projects, achieving 90.9% average accuracy and an 89.55% correlation coefficient. Furthermore, the paper [29] proposes an automated machine learning tool using SVM and Naïve Bayes models to estimate steel structure productivity rates, showing that ML can improve accuracy and efficiency over traditional experience-based methods. Also, the study [30] developed a neural network model to estimate labor production rates for concrete columns, addressing unreliable data and subjective factors often ignored in traditional productivity measurement. Another study [31] developed a multivariable linear regression model using ten factors to predict marble floor finishing productivity in Iraqi projects, achieving 96.3% average accuracy and a 90.6% correlation coefficient. In addition, the study [32] used decision trees and the Apriori algorithm to classify factors affecting Turkish ceramic tiling crew productivity, based on time study data including crew size, age, and experience. Furthermore, the study [33] developed neural network models with Bayesian regularization and early stopping to predict labor productivity in Iranian power plant projects, finding that Bayesian regularization performed better and identifying key influencing factors through sensitivity analysis. In addition, the study [34] compared transformed regression and neural network models for predicting dozer productivity, finding that the ANN better captured complex, nonlinear factors affecting equipment performance. Moreover, the study [35] developed a hybrid Neural Network-Driven Fuzzy Reasoning model optimized by genetic algorithms to accurately predict construction productivity using both crisp and fuzzy data, outperforming traditional methods. Furthermore, the study [1] introduced an engineering approach using artificial neural networks with tanh activation to model carpentry and rebar labor productivity, achieving more accurate predictions than traditional methods and demonstrating integration with construction databases for economic and social benefits. Also, the study [36] proposed using artificial neural network-based prediction intervals instead of single-point estimates to more reliably forecast labor productivity, demonstrating improved accuracy and credibility in a case study. Last but not least, the study [37] compared several neural network techniques to model construction labor productivity, finding that backpropagation neural networks performed best in predicting productivity considering environmental and operational factors.

While there has been considerable research on construction productivity in general, work that looks specifically at rebar-fixing productivity is surprisingly rare. Rebar installation is not only labor-intensive but also a schedule-critical activity, and it is affected by a wide range of factors—from crew size and skill level to site conditions. Yet, most existing studies treat it as part of broader construction operations rather than examining it on its own. Because of this, contractors and planners often lack targeted, data-driven guidance for managing one of the most demanding tasks in reinforced concrete construction.

The ability to accurately predict rebar-fixing productivity is important because planning and scheduling often depend on subjective judgment and incomplete records. Reliable forecasts at the component level allow contractors to anticipate potential delays, refine work plans, allocate resources more effectively, and respond to unforeseen changes during the project.

In response to this need, the present study proposes a data-driven framework for assessing and forecasting rebar-fixing labor productivity. Four machine learning algorithms—Random Forest (RF), Extreme Gradient Boosting (XGBoost), k-Nearest Neighbors (KNN), and Support Vector Regression (SVR)—were developed and optimized through GridSearchCV hyperparameter tuning. Their performance was evaluated using well-established statistical measures.

Because such models often operate as “black boxes,” the SHapley Additive exPlanations (SHAP) method was applied to interpret their predictions. SHAP provides a clear understanding of how each input factor—such as crew size, rebar complexity, and environmental conditions—affects productivity. This improves transparency, strengthens trust in the results, and offers practical insights for decision-makers.

The contributions of this study can be summarized as follows:

• Addressing a research gap: Introducing a predictive approach tailored specifically to rebar-fixing productivity, an area with limited previous investigation.
• Practical benefits: Providing an objective and accurate tool to support scheduling, resource allocation, and risk management in construction projects.
• Enhanced interpretability: Using SHAP to make model predictions transparent and actionable, encouraging wider adoption of AI-based tools in construction management.

By combining accurate prediction with clear interpretability, the proposed approach offers both a methodological advancement and practical value, contributing to continuous improvement in construction productivity.

2. Materials and Methods

2.1. Research Methodology

The first step of our methodology was to collect a comprehensive database to develop the ML prediction models for labor productivity. The data were collected from rental housing projects in Hong Kong as cited in the study [38]. Four main parts were related to the field study and data collection process. The first part focused on identifying the types of data required to prepare for on-site observations. The second part addressed the basic weather conditions. The third part involved observing the work processes of laborers on-site, and the fourth part documented the work status of each worker. Data for parts one, two, and three were collected by reviewing CAD drawings, inspecting construction components, documenting weather conditions, and directly observing site activities. The information on labor activity was collected using a work sampling method. Two observers watched and recorded each work process in order to minimize operational errors. After the data collection phase, we identified the important features that can be used as input variables, along with the output variable, which is labor productivity for rebar fixing (kg/m-hr). The next step is data splitting, in which the data were divided into training and testing sets using an 80/20 split. This percentage split is widely used and accepted by many researchers [39,40,41,42,43]. The training set was then used to build and optimize the machine learning models. It is very important to note that the performance of these models heavily depends on their parameters, so a hyperparameter tuning methodology was applied at this stage. GridSearchCV was used to find the hyperparameters that deliver the best performance. It is a method that exhaustively tests all possible combinations of parameter values to choose the most effective set for the model. Since the performance of the developed models needed to be tested, several statistical performance metrics were used, including coefficient of determination ($R^2$), root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and absolute difference within the 20% index (A20-index ).These metrics enabled us to evaluate the models’ generalization ability and assess their prediction accuracy. Finally, the black-box machine learning models were interpreted using the SHAP methodology. This approach was used to help decision-makers identify the factors that have the most significant impact on the predictions. It also provides insights into how each feature contributes to the model’s output. The complete methodology for building the machine learning model is illustrated in Figure 1.

2.2. ML Model Theory

2.2.1. Support Vector Regression (SVR)

Support Vector Regression (SVR) is a supervised machine learning algorithm derived from the principles of Support Vector Machines (SVMs), originally proposed by Vapnik and his collaborators [44]. While SVM is primarily designed to classify data by finding an optimal hyperplane that separates classes with a maximum margin, SVR adapts this principle to regression by fitting a function within a specified error margin, enabling accurate prediction of continuous target variables. SVR aims to identify a function that not only captures the underlying trend in the data but also generalizes well to unseen instances by balancing model complexity and prediction error, as shown in Figure 2.

The fundamental idea behind SVR is to construct a predictive function $f\left(x\right)=w^T\varphi \left(x\right)+b$, where $\varphi \left(x\right)$ denotes a nonlinear mapping of the input features into a high-dimensional space, w is the weight vector, and b is the bias term [45]. Unlike traditional regression models that minimize the squared error, SVR introduces an $\epsilon$-insensitive loss function that ignores errors within a certain margin $\epsilon$ around the actual target values. In other words, deviations smaller than $\epsilon$ are not penalized, which leads to a sparse model and improves generalization.

The optimization problem in SVR is formulated as follows [46]:

$$\underset{w,b,\xi ,{\xi }^{*}}{min}{\displaystyle \frac{1}{2}}{\parallel w\parallel }^2+C\sum _{i=1}^n\left({\xi }_i+{\xi }_i^{*}\right)$$

(1)

subject to

$$\left\{\begin{array}{c}{y}_i-w^T\varphi \left(x_i\right)-b\le \epsilon +{\xi }_i,\hfill \\ w^T\varphi \left(x_i\right)+b-y_i\le \epsilon +{\xi }_i^{*},\hfill \\ {\xi }_i\ge 0,{\xi }_i^{*}\ge 0,i=1,\dots ,n.\hfill \end{array}\right.$$

(2)

Here, ${\xi }_i$ and ${\xi }_i^{*}$ are slack variables that allow the model to accommodate prediction errors beyond the $\epsilon$ margin, while $C>0$ is a regularization parameter that controls the trade-off between the model’s flatness and the degree to which deviations larger than $\epsilon$ are tolerated.

To handle nonlinear relationships between the features and the response variable, SVR employs kernel functions that implicitly map the data into a higher-dimensional feature space. Commonly used kernels include the radial basis function (RBF), polynomial, and linear kernels. The RBF kernel, in particular, is favored due to its ability to model complex, nonlinear patterns without requiring explicit specification of the transformation function $\varphi \left(x\right)$.

SVR has been successfully applied in a wide range of engineering and scientific domains due to its capacity to model both linear and nonlinear dependencies, robustness to outliers, and effectiveness with small to medium-sized datasets. Moreover, SVR’s formulation provides control over model complexity through the regularization parameter C and prediction tolerance through the $\epsilon$-insensitive loss function, making it suitable for applications where precision within a predefined threshold is more important than minimizing the absolute error.

2.2.2. Random Forest Regression (RF)

Random Forest Regression (RF) is an ensemble learning method that constructs a large number of individual decision trees during training. The mean value obtained from those trees is used to make the final prediction for regression tasks. Since it aggregates the output of multiple trees, it enhances predictive accuracy and controls overfitting. In the RF algorithm each tree is trained on a random subset of the original dataset sampled with replacement. This methodology is known as bagging (bootstrap aggregating). Additionally, a random subset of features is selected at each node during the construction of each tree, which helps to determine the best split, introduce further randomness, and reduce the correlation between individual trees.

As seen in Figure 3, given a dataset $\mathcal{D}={\left\{\left(x_i,y_i\right)\right\}}_{i=1}^n$, where $x_i\in {\mathbb{R}}^p$ are the input features and $y_i\in \mathbb{R}$ is the response variable, the Random Forest model constructs T decision trees ${\left\{f_t\left(x\right)\right\}}_{t=1}^T$. The final prediction $\widehat{y}$ is obtained by averaging the outputs of all trees [47]:

$$\widehat{y}={\displaystyle \frac{1}{T}}\sum _{t=1}^T{f}_t\left(x\right).$$

(3)

Because of averaging and not relying heavily on a single tree, RF is robust to noise and multicollinearity while also reducing variance [48,49]. In addition, the importance of the features is a key characteristic of Random Forests. It provides valuable insights for researchers to understand the influence of input variables on the target response. Hyperparameters such as the number of trees (n_estimators), the maximum depth of each tree, and the number of features considered at each split are typically optimized using cross-validation to balance the bias–variance trade-off. Due to its non-parametric nature, RF can model complex nonlinear relationships without requiring assumptions about data distribution, making it suitable for a wide range of regression problems in engineering and science.

2.2.3. K-Nearest Neighbors (KNN)

In 1967 a widely recognized supervised learning technique known as the K-Nearest Neighbors (KNN) algorithm was introduced by Cover and Hart [50]. This algorithm is frequently used for regression tasks in numerous disciplines. The concept of proximity is the core idea that KNN is based on. Based on this concept the algorithm identifies the k closest instances in the training dataset using a chosen distance metric. The value of k determines how many neighbors are taken into account for making a prediction. When a new input is provided, the algorithm measures its distance from all training samples and selects the k closest ones. It then computes the mean of their corresponding target values, which becomes the predicted value for the new input. This approach leverages the surrounding data points to generate accurate and data-driven predictions.

2.2.4. Extreme Gradient Boosting (XGBoost)

Chen and Guestrin presented XGBoost, a state-of-the-art version of the traditional gradient boosting algorithm, designed for greater scalability and accuracy [51]. The difference between Random Forest (RF) and this algorithm is that trees in XGBoost are built sequentially, with each new tree aiming to improve the performance of the existing model by correcting its errors, whereas in RF, trees are built independently and in parallel. XGBoost integrates decision trees and gradient boosting to produce a highly accurate and robust predictive model. It leverages the advantages of various machine learning techniques, creating an ensemble of weak learners (decision trees) and progressively enhancing the model by adding new trees that address the shortcomings of the previous ones. This algorithm stands out due to its ability to handle numerous features and high-dimensional datasets efficiently, in addition to its built-in regularization mechanisms that help reduce overfitting. Furthermore, XGBoost offers a high degree of customization, allowing fine-tuning of its parameters to optimize performance. The mathematical representation of XGBoost is as follows:

Given a training dataset ${\left\{(x_i,y_i)\right\}}_{i=1}^n$, where $x_i$ represents the feature vector and $y_i$ is the corresponding output variable, the objective of the XGBoost algorithm is to learn a predictive function $F\left(x\right)$ that minimizes the following objective function [51]:

$$L\left(F\right)=\sum _{i=1}^n\mathcal{I}\left(y_i,F\left(x_i\right)\right)+\sum _{k=1}^K\mathsf{\Omega }\left(f_k\right)$$

(4)

where $L\left(F\right)$ denotes the total objective function, $\mathcal{I}\left(y_i,F\left(x_i\right)\right)$ is the loss function measuring the difference between the true and predicted values, and $\mathsf{\Omega }\left(f_k\right)$ is a regularization term applied to each individual tree $f_k$ to penalize model complexity. XGBoost selects the loss function based on the nature of the task. For regression problems, it typically employs mean squared error, whereas for classification tasks, it uses cross-entropy loss.

$$\mathsf{\Omega }\left(f_k\right)=\gamma T_k+{\displaystyle \frac{1}{2}}\lambda \sum _{j=1}^T{w}_j^2$$

(5)

where $\gamma$ controls the balance between model complexity and accuracy, $T_k$ is the number of leaves in the $k\mathrm{th}$ decision tree, $\lambda$ is the regularization coefficient that determines the strength of the penalty, and $w_j$ denotes the weight of the $j\mathrm{th}$ leaf node [51]. To mitigate the issue of overfitting, a penalty is incorporated into the gradient boosting methodology through regularization, which is a distinctive characteristic of the XGBoost algorithm. The objective function consists of two components: a loss function, which measures the difference between predicted and actual values, and a regularization term, which penalizes overly complex models to enhance generalization.

The overall prediction process of XGBoost is illustrated in Figure 4. It begins with a single decision tree. The model then calculates the residuals—the errors between the predicted and actual values. A new decision tree is trained on these residuals, with the goal of correcting the mistakes made by the previous tree. This process continues iteratively: each newly added tree focuses on the residuals from the combined predictions of the existing ensemble. The model updates its predictions by aggregating the outputs of all the trees. This iterative process—computing residuals, training new trees, and updating predictions—continues until a stopping criterion is met, such as reaching a maximum number of trees or achieving a predefined performance threshold.

2.3. Performance Measures

After the model is constructed, its performance is assessed using the testing error. Models with lower testing errors indicate stronger predictive abilities. In this study, well-known performance metrics were used, including $R^2$, RMSE, MAE, MAPE, and the A20-index. The definitions of these metrics are as follows:

$$R^2={\displaystyle \frac{{\sum }_{i=1}^n{\left(x_i-{\widehat{p}}_i\right)}^2-{\sum }_{i=1}^n{\left(x_i-y_i\right)}^2}{{\sum }_{i=1}^n{\left(x_i-{\mu }_i\right)}^2}}$$

(6)

$$\mathrm{RMSE}=\sqrt{{\displaystyle \frac{1}{n}}\sum _{i=1}^n{\left(x_i-y_i\right)}^2}$$

(7)

$$\mathrm{MAE}={\displaystyle \frac{1}{n}}\sum _{i=1}^n\left|x_i-y_i\right|$$

(8)

$$\mathrm{MAPE}={\displaystyle \frac{1}{n}}\sum _{i=1}^n\left|{\displaystyle \frac{x_i-y_i}{x_i}}\right|\times 100\%$$

(9)

$$\mathrm{A}20-\mathrm{index}={\displaystyle \frac{m_{20}}{n}}$$

(10)

$R^2$ measures how well the predicted values align with the observed results, indicating the goodness of fit. The A20-index evaluates the engineering and practical significance of the predictions. RMSE and MAE represent the average magnitude of measurement errors, with MAE applying a uniform (linear) penalty across error sizes and RMSE assigning greater weight to larger errors. Models that yield lower RMSE and MAE values, along with higher $R^2$ and A20-index values, demonstrate higher prediction accuracy.

2.4. SHAP Interpretation of the Developed Model

The model’s interpretations can be easily performed using a well-known theory known as SHAP [52]. It is based on the concept of Shapley values, which are derived from cooperative game theory by calculating the marginal contribution of each feature. Every feature influences the model’s output, and each is assigned a corresponding SHAP value. These values enable a quantitative assessment of how each feature affects the predictions. Because SHAP values are additive, they also allow combinations of features to be interpreted, helping researchers analyze nonlinear interactions among variables.

Each feature has a Shapley value that measures its specific contribution to the model’s prediction. To find the total importance of a single feature j, we calculate a weighted sum of the Shapley values from all subsets of features [52]:

$${\varphi }_j=\sum _{S\subseteq \{x_1,\dots ,x_p\}\setminus \left\{x_j\right\}}{\displaystyle \frac{\left|S\right|!\left(p-\left|S\right|-1\right)!}{p!}}\left[f\left(S\cup \left\{x_j\right\}\right)-f\left(S\right)\right]$$

(11)

where S is a subset of features not including feature $x_j$, p is the total number of features, $f\left(S\right)$ is the model prediction when using only the features in subset S, and $f\left(S\cup \left\{x_j\right\}\right)$ is the model prediction when adding feature $x_j$ to subset S.

SHAP interprets model predictions by representing them as a sum of additive feature contributions, calculated using Shapley values. This interpretation is specified as [52]

$$g\left(z^{\prime }\right)={\varphi }_0+\sum _{j=1}^M{\varphi }_j{z}_j^{\prime }$$

(12)

In this equation, g is the explanation model that operates on M simplified input features. To represent different combinations of these features, we use $z^{\prime }$, a binary vector where each entry indicates if a feature is included. Finally, ${\varphi }_j$ is the resulting Shapley value, which measures the unique contribution of feature j.

3. Database Used

This study utilizes data obtained [38], which focuses on labor productivity within public rental housing projects in Hong Kong, with a particular focus on assessing the productivity of rebar-fixing activities. Data were collected through real-time observations and work sampling methods conducted on an active public housing site. Labor productivity was measured as the amount of work completed per unit of worker time. Observations were carried out over a six-month period, capturing a wide range of weather conditions. The study specifically examined structural framing activities on typical floors between the 14th and 33rd levels. Various influencing factors, including weather conditions, buildability, and project-specific characteristics, were taken into account, with the corresponding parameter values recorded for each observation. The feature variables used in this study were selected based on their documented relevance in previous literature, where similar parameters have been identified as significant predictors of productivity (e.g., [53,54,55]). This ensured that the model incorporated factors with established influence on the target variable. For data preprocessing, standard scaling was applied to normalize the features, a widely adopted technique in machine learning that ensures all variables contribute equally to the model training process and improves optimization convergence. In total, 326 datasets were compiled and used to train predictive models. Labor productivity served as the dependent variable, while 12 independent variables—identified through a comprehensive literature review—were selected based on their presumed influence on on-site labor performance, such as work type and environmental conditions. These variables include temperature ($\mathrm{TP}$), humidity ($\mathrm{HM}$), wind speed ($\mathrm{WS}$), precipitation ($\mathrm{PT}$), quantity of 16 mm diameter rebar ($M_{16}$), 20 mm rebar ($M_{20}$), 25 mm rebar ($M_{25}$), 32 mm rebar ($M_{32}$), 40 mm rebar ($M_{40}$), (H_1.5) quantity of hoop rebar (length = 1.5), (H_1.2) quantity of hoop rebar (length = 1.2), and work type ($\mathrm{WT}$).

A correlation map is presented in Figure 5 to visualize the relationships among the features in which Pearson’s correlation coefficient (r) is used to assess the degree of dependency between variables [56]. The coefficient r offers insight into multicollinearity and interdependence between variables [57]. Its values range from −1 to +1, where −1 indicates a strong negative correlation, +1 signifies a strong positive correlation, and 0 implies no correlation [58]. The bottom row of the Pearson correlation matrix illustrates the correlation between the output variable (LP) and each input feature. Since multicollinearity can negatively impact ML models [59,60], it is generally recommended that the absolute value of r between any two variables remains below 0.8 to mitigate this issue [61,62]. As shown in Figure 5, all r-values, whether positive or negative, are below this threshold, which indicates that the likelihood of multicollinearity affecting the LP prediction models is minimal.

Additionally,

Table 1. Statistical summary for variables in the database.

Variable	Mode	Kurtosis	Min	Max	Mean	Median	Skewness	Range	Std Dev	Std Error
WT	1.00	−1.79	1.00	2.00	1.39	1.00	0.46	1.00	0.49	0.03
TP	20.40	−1.01	12.90	29.80	22.90	22.90	−0.08	16.90	4.29	0.24
HM	84.00	−0.34	61.00	94.00	81.11	83.00	−0.71	33.00	8.52	0.47
WS	14.60	0.36	4.30	23.90	11.36	10.90	0.82	19.60	4.25	0.24
PT	0.00	7.67	0.00	31.30	2.99	0.00	2.95	31.30	7.34	0.41
M_16	0.00	−0.45	0.00	10.00	2.26	0.00	1.21	10.00	3.97	0.22
M_20	0.00	1.69	0.00	8.00	1.29	0.00	1.79	8.00	2.62	0.15
M_25	0.00	−0.72	0.00	12.00	3.09	0.00	0.84	12.00	4.04	0.22
M_32	0.00	1.57	0.00	6.00	0.86	0.00	1.79	6.00	1.82	0.10
M_40	0.00	8.09	0.00	6.00	0.39	0.00	3.08	6.00	1.26	0.07
H_1.2	0.00	−1.32	0.00	33.00	10.70	0.00	0.41	33.00	11.76	0.65
H_1.5	0.00	2.54	0.00	15.00	2.03	0.00	2.13	15.00	5.14	0.29
LP	119.19	0.40	56.66	360.60	164.75	159.16	0.74	303.94	63.71	3.53

presents some important statistical characteristics of the collected dataset. Presenting the distribution of input data is crucial for developing a generalized prediction model [59]. The table includes measures of central tendency such as median, mean, and mode as well as the data range, represented by maximum and minimum values. Furthermore, skewness and kurtosis are reported to describe the symmetry and shape (peakedness or flatness) of the data distribution. These two metrics can assume positive, negative, or, in rare cases, undefined values [63]. According to the literature, acceptable ranges for skewness and kurtosis are from −3 to +3 and −10 to +10, respectively [64]. As shown in Table 1, all input features fall within these recommended thresholds, suggesting that the data distribution is statistically sound. As we mentioned previously, the dataset comprised 326 samples, of which 261 (80%) were allocated to the training set and 65 (20%) to the testing set using a stratified random split with a random state of 42 to ensure reproducibility. To verify that the training and testing sets were representative of the original dataset, we compared the distributions of all input variables in both subsets. Stacked histograms (Figure 6) demonstrate that the variable distributions in the training and testing sets are consistent, indicating that no significant sampling bias was introduced during the split.

4. Model Results

4.1. Optimal Model Results

Tuning the hyperparameters is an essential step in improving the generalization and accuracy of each algorithm used in this study. This can be accomplished by applying grid search combined with five-fold cross-validation to identify the optimal hyperparameter settings for each model. First, one needs to assign an objective function for the GridSearchCV methodology to optimize. In our study, this objective function is designed to identify the parameters that result in the lowest RMSE metric. Exhaustive search for parameter optimization requires defining a specific range (upper/lower bounds) and step size for each parameter. However, this method becomes impractical as the number of parameters grows. With algorithms having anywhere from a few to over a dozen parameters, each with a wide potential range, the number of combinations to test can become computationally prohibitive. To address this, the study focuses on the most important parameters that have the greatest impact on model performance. At the start, a search over a wide range with large steps was carried out to find an approximate optimal interval. Then, a narrower search with smaller steps was performed within this interval to determine the most precise values. This approach helps reduce the time and computational effort required for tuning.

The final values selected through grid search, along with the hyperparameter search ranges, are presented in

Table 2. Hyperparameter settings and selected values for machine learning models.

Model	Hyperparameter	Grid Search Range	Selected Value
Random Forest	$n\_estimators$	(50, 100)	100
	$max\_depth$	(None, 10, 20)	10
XGBoost	$n\_estimators$	(50, 100)	50
	$learning\_rate$	(0.01, 0.1, 0.2)	0.1
	$max\_depth$	(3, 6, 10)	3
SVR	$kernel$	{rbf, linear}	linear
	C	(0.1, 1, 10)	10
	$ϵ$	(0.01, 0.1, 0.5)	0.5
KNN	$n\_neighbors$	(3, 5, 7)	3
	$weights$	{uniform, distance}	uniform
	$metric$	{minkowski, euclidean, manhattan}	minkowski

. In this process, five-fold cross-validation is applied by dividing the training data into five subsets. Each subset serves as a validation set once, producing five sets of prediction results. The RMSE is used as the evaluation metric to identify the optimal combination of hyperparameters within the search space. This cross-validation approach improves the reliability of the results.

4.2. Regression Slope Analysis

This section details the comparison between actual and model-estimated values, as depicted in the provided Figure 7. The figure presents the actual versus model values, including the respective fitting lines for both training and testing datasets. A regression slope exceeding 0.8 is generally indicative of a strong correlation between the observed and predicted values. For the Random Forest (RF) model, the regression slope for the testing dataset was 0.92, while for the training dataset, it was 0.87. Similarly, the XGBoost model demonstrated regression slopes of 0.82 for testing and 0.75 for training. The Support Vector Regression (SVR) model yielded regression slopes of 0.86 for the testing phase and 0.72 for the training phase. The K-Nearest Neighbors (KNN) model showed regression slope values of 0.93 for testing and 0.81 for training. Notably, the regression slopes for the testing datasets across all four models (RF: 0.92, XGBoost: 0.82, SVR: 0.86, KNN: 0.93) surpassed the 0.8 benchmark, signifying a robust agreement between the model estimations and the actual values for previously unseen data. The training data slopes for the RF (0.87) and KNN (0.81) models also met this criterion. While the training slopes for XGBoost (0.75) and SVR (0.72) were slightly below this 0.8 threshold, the overall proximity of the fitting lines for both training and testing sets to the ideal y = x line suggests that the developed models achieved comparable performance across both data subsets. The KNN and RF models, in particular, displayed a very close alignment of their test data fit lines with the ideal prediction line.

An assessment of the developed models’ predictive performance was conducted, with key error metrics and distributions detailed in Figure 8. The Random Forest (RF) model exhibited average, minimum, and maximum errors of 13.23, 0.07, and 100.122 kg/m-h, respectively. For the RF model, 59.38% of prediction errors were within the 0–10 range, 28.00% of errors fell between 10 and 30, and 12.62% of errors were above the 30 threshold. In the case of the XGBoost model, the average, minimum, and maximum errors recorded were 18.315, 0.034, and 132.909 kg/m-h, respectively. The error analysis for the XGBoost model showed that 39.81% of its errors were in the 0–10 range, 40.74% were between 10 and 30, and 19.44% exceeded 30. Furthermore, KNN model presented average, minimum, and maximum error values of 18.11, 0.05, and 176.292 kg/m-h, respectively. The error distribution for the KNN model revealed that 46.77% of errors were in the 0–10 range, 33.23% ranged from 10 to 30, and 20.00% were greater than 30%. Lastly, the SVR model yielded average, minimum, and maximum errors of 25.221, 0.06, and 176.295 kg/m-h, respectively. For the SVR model, error analysis indicated that 31.79% of predictions had errors in the 0–10 range, 37.65% were between 10 and 30, and 30.56% of errors surpassed the 30 mark. This quantitative comparison underscores the superior performance of the Random Forest model, which demonstrated the lowest average and maximum errors and the highest proportion of predictions within the most accurate 0–10% error band. Conversely, the SVR model showed the least favorable performance, with the highest average and maximum errors and the largest percentage of predictions in the >30% error category.

4.3. Statistical Analysis

The predictive efficiencies of the developed models were assessed using several statistical performance indicators, and the corresponding values are provided in

Table 3. Performance comparison of ML models for labor productivity prediction.

Indicator	RF	XGBoost	SVR	KNN
Training
MAE	12.494	18.538	26.073	17.928
RMSE	19.943	26.881	37.355	26.265
$R^2$	0.901	0.821	0.654	0.829
MAPE	9.12%	13.96%	18.37%	13.81%
A20-index	0.8615	0.7769	0.7000	0.8192
Testing
MAE	16.654	17.422	21.814	18.840
RMSE	22.260	22.472	28.706	24.938
$R^2$	0.874	0.872	0.791	0.842
MAPE	10.98%	11.68%	13.57%	12.11%
A20-index	0.8308	0.8308	0.7692	0.8000

and Figure 9. A model that demonstrates a higher coefficient of determination ($R^2$) and lower error metrics (i.e., MAE, RMSE, MAPE) is generally considered more reliable and accurate. Additionally, the A20-index was used to assess the proportion of predictions within a ±20% error margin, with higher values indicating better generalization ability.

In the training phase, the Random Forest model demonstrated the best performance, achieving the highest $R^2$ value (0.901), the lowest MAE (12.494), RMSE (19.943), and MAPE (9.12%), as well as the highest A20-index (86.15%). This indicates that the Random Forest model provided robust learning and was able to capture the underlying patterns in the data effectively. The KNN model followed closely, with $R^2=0.829$, reasonable error metrics (MAE = 17.928, RMSE = 26.265, MAPE = 13.81%), and a competitive A20-index of 81.92%. On the other hand, the SVR model showed the lowest predictive capability in the training set with $R^2=0.654$ and the highest error values, particularly RMSE = 37.355 and MAPE = 18.37%.

During the testing phase, both the Random Forest and XGBoost models achieved the highest $R^2$ values (0.874 and 0.872, respectively), with RF slightly outperforming in terms of RMSE (22.260 vs. 22.472) and MAPE (10.98% vs. 11.68% ). However, they both maintained a slightly higher A20-index (83.08% vs. 83.08%), suggesting it produced a greater proportion of predictions within the acceptable error threshold. The KNN model also exhibited stable and favorable results ($R^2=0.842$, MAE = 18.840, A20-index = 80.00%), further validating its generalization ability. Conversely, the SVR model yielded the weakest generalization ($R^2=0.791$, MAPE = 13.57%, A20-index = 76.92%), though it still maintained acceptable accuracy.

Overall, the Random Forest models consistently provided superior prediction accuracy across both training and testing phases, supported by high $R^2$ scores and low error metrics, as well as favorable A20-index values. These results affirm its effectiveness in modeling the underlying relationship in the data and its ability to generalize well to unseen instances.

4.4. Comparison with Traditional ML Models

Table 4. Performance comparison of ML models on the testing set.

Indicator	Lasso	Decision Tree	Random Forest
MAE	22.557	21.237	16.696
RMSE	28.233	28.019	22.501
$R^2$	0.798	0.801	0.872

presents the evaluation results for the test set using Lasso, decision tree, and Random Forest regression models for the testing set. It can be observed that the Random Forest model outperforms both Lasso and decision tree in terms of predictive accuracy. On the test set, Random Forest achieved the lowest RMSE (22.50), the highest $R^2$ (0.8715), and the lowest MAE (16.70). Compared to Lasso, Random Forest reduced RMSE by 20.3% and increased $R^2$ by 9.2%, while also reducing MAE by 26.0%. When compared to the decision tree, Random Forest reduced RMSE by 20.2%, increased $R^2$ by 8.8%, and lowered MAE by 21.4%.

Overall, Random Forest demonstrates a substantial improvement over both traditional linear modeling (Lasso) and single-tree approaches (decision tree). This highlights the benefit of ensemble learning, where multiple weak learners are combined to enhance prediction accuracy and reduce error, leading to more reliable performance for the given dataset.

4.5. Feature Importance Analysis

The SHapley Additive exPlanations (SHAP) method is used in this study to determine the influence of input features on the predicted labor productivity. SHAP analysis provides two important insights regarding the interaction between input variables and the output. First, the vertical spread (y-axis) illustrates the importance of each feature, showing their influence ranked from most to least, and second, the effect of the actual feature values on the prediction, represented by the horizontal distribution (x-axis) and the color gradient of the data points. Red points correspond to higher input values, which typically contribute positively to the prediction, whereas blue points denote lower values, often associated with a negative influence. The results of this analysis are illustrated in Figure 10.

As we can see from Figure 10, temperature is the most significant factor in the model output. This is noticeable through the substantial spread of its SHAP values. Notably, higher temperatures (represented by red points) are consistently associated with negative SHAP values, indicating a substantial negative impact on labor productivity. This suggests that elevated temperatures reduce efficiency on construction sites. Workers’ productivity in outdoor heat exposure may decline as individuals instinctively reduce their physical activity to avoid excessive heat buildup in their bodies [65]. Moreover, high temperatures can lead to adverse effects such as irritability, delays, restlessness, and diminished motivation in daily tasks [66]. The study [53] aimed to help industry practitioners understand how high temperatures affect construction labor productivity, supporting the prevention of heat-stress injuries and improving worker safety and comfort. Their productivity models revealed that a 1 °C increase in WBGT (Wet Bulb Globe Temperature) reduced direct work time by 0.57% and increased idle time by 0.74%. The quantity of 32 mm bars is the second most significant factor in predicting labor productivity and has a positive impact. This is evident from the cluster of red dots on the right side of the SHAP plot. The study [55] explained this pattern clearly by noting that using larger bar diameters for a given quantity of reinforcement reduces the number of reinforcement bars to be placed. This results in less labor effort and improved productivity. Since the fixing process mainly involves placing and tying the reinforcement, and because tying bars requires a similar amount of time regardless of their diameter, fewer but thicker bars mean more reinforcement can be installed with the same labor input. As a result, labor productivity increases. However, this behavior is only effective up to a certain point. Increasing the diameter leads to an increase in the weight of the rebar, and this increase can become challenging for workers to lift and maneuver the bars for prolonged periods. In such situations, the added physical strain may offset the productivity gains, potentially leading to reduced efficiency.

5. Practical Application of Research

The practical application of this research in construction management lies in its ability to accurately forecast rebar-fixing labor productivity under varying site conditions, enabling more precise scheduling and resource allocation. The developed AI-driven framework can be integrated into project planning software and real-time decision-support systems, allowing construction managers to make informed adjustments to workforce deployment without relying solely on historical averages or trial-and-error approaches. By incorporating explainable AI methods such as SHAP, the system not only predicts productivity with high accuracy but also clarifies the influence of key factors—such as rebar quantity and ambient temperature—on performance, empowering managers to implement targeted interventions. This approach enhances operational efficiency by minimizing idle time, optimizing crew sizes, and reducing delays caused by unfavorable working conditions. Furthermore, integrating the predictive framework with IoT-enabled monitoring systems and on-site data collection tools can facilitate continuous model updates, ensuring that predictions remain relevant as new data becomes available. In large-scale infrastructure projects, these insights can be used to align labor strategies with project timelines, cost constraints, and safety requirements. Ultimately, the application of this research supports a shift toward data-driven labor management, improving productivity outcomes while enabling proactive responses to changing environmental and operational conditions.

6. Limitations and Future Research

This study is limited by the fact that the developed machine learning models perform optimally within the specific range of data provided for training, and their predictive accuracy may decline when applied to conditions or variable ranges not represented in the dataset. Future research should address this limitation by expanding the dataset to encompass a wider variety of project types, geographical regions, and seasonal conditions to improve model robustness and generalizability. In addition, additional variables, such as crew experience level, shift duration, and site accessibility in future studies can help to capture further nuances influencing labor productivity. Furthermore, exploring advanced optimization strategies, including hybrid metaheuristics and deep learning architectures, could enhance predictive accuracy and reduce computational time. Integrating real-time data streams from IoT-enabled monitoring systems and wearable sensors would allow for continuous model validation and dynamic productivity forecasting in live construction environments. Assessing the economic implications of AI-driven scheduling adjustments and conducting sensitivity analyses under varying environmental scenarios can provide actionable guidance for project managers. Furthermore, extending the framework to predict productivity across other construction trades will broaden its applicability and support holistic workforce planning. Collaboration with contractors, technology providers, and policy-makers will be essential to ensure that AI-based productivity tools are practical, scalable, and aligned with industry standards.

7. Conclusions

Prior studies on construction labor productivity have mainly relied on traditional statistical methods or focused on limited sets of influencing factors. Few have systematically compared multiple machine learning algorithms for rebar-fixing labor productivity prediction, and even fewer have applied explainable AI methods to interpret model outputs in this context. This gap has hindered both predictive accuracy and the ability to understand the role of specific variables in productivity performance.

The main purpose of our research was to evaluate and compare the predictive abilities of four machine learning models, which were Random Forest (RF), XGBoost, Support Vector Regression (SVR), and K-Nearest Neighbors (KNN) in forecasting rebar-fixing labor productivity. Model performance was assessed through MAE, RMSE, $R^2$, MAPE, and the A20-index for both training and testing sets, complemented by visual analysis. The RF model had the best accuracy compared to other models, with an $R^2$ of 0.874, a testing MAPE of 10.98%, and a scatter plot slope close to the ideal 45-degree line between actual and predicted values. Also, when compared with single-learner Lasso and decision tree models, the RF model improved RMSE and MAE by approximately 20%, demonstrating its superior generalization capability.

This study is among the innovative works employing ensemble learning with SHAP to explain predictions for labor productivity in rebar fixing. The analysis identified the quantities of large-diameter rebar (M32 and M25) and ambient temperature as key factors influencing labor performance. Furthermore, it highlighted the superior performance of ensemble methods over individual models, offering a novel strategy and empirical evidence supporting RF as an effective method for predicting construction productivity.

Future research should expand the dataset to include projects of varying scales, structural types, and climatic conditions to improve generalizability. Moreover, incorporating advanced optimization algorithms for automated hyperparameter tuning could further enhance model performance while extending the explainable AI framework to capture temporal productivity variations over the project lifecycle.