1. Introduction
Precast concrete (PC) construction is an innovative construction technique in which factory-made components are transported to the construction site and assembled [1,2,3]. PC construction can improve the efficiency and sustainability of construction projects by providing a number of benefits, including reduced on-site labor, shorter construction times, improved quality, and reduced waste [4,5,6,7]. However, to enjoy such benefits, complex processes in PC construction, such as component fabrication, transportation, and on-site assembly, should be managed effectively [8]. Project progress management plays a critical role in the success of construction projects, and site managers’ efforts to control schedules remain an important research topic [9]. PC components’ installation on-site is a critical process as it significantly impacts the overall time and cost of the project [3,10]. The efficiency of PC construction is often hampered by delays during PC components’ installation [11,12].
As traditional field-based construction is inherently inefficient and subject to multiple uncertainties [13,14,15], offsite construction methods like PC construction are increasingly used to address these issues by manufacturing building components in a factory and transporting them to the field for installation. Accordingly, recent studies have focused on the risk factors affecting schedule delays in PC or modular construction projects based on offsite fabrication [16,17,18].
Lee and Kim [19] distinguished the different phases of a modular project—conceptual design, design development, construction documents, factory production, and site construction—and identified risk factors for time and cost increases in each phase, prioritizing them accordingly. Ji et al. [17] quantified the causal relationship between schedule delay factors and their consequences in PC projects based on a literature review and a survey of domain experts. Similarly, through a survey of domain experts from 18 countries, Wuni and Shen [18] quantified risk factors that contribute to schedule delays using failure mode and effects analysis (FMEA), the decision-making trial and evaluation laboratory (DEMATEL), and the analytic network process (ANP), as well as nonparametric statistical analysis. However, these studies focused on project management strategies in the pre-construction phase. They did not fully address what happens during project execution and, therefore, could not provide deep insights into schedule delays during that phase. The impact of schedule delays in construction projects is more likely to be felt in the execution phase than in the permitting and procurement phases [20]. Therefore, quantifying the schedule delay risk in the execution phase of the project is greatly important.
To date, this has mainly been realized through simulation [9,21,22]. Zhang and Wang [9] defined unique project features and modeled a stochastic critical path method schedule to assess the risk of delay due to design changes. Similarly, Li et al. [22] used simulation to quantify the risk of schedule delays in a residential PC project. The delay risk was analyzed using a hybrid method combining discrete event simulation and system dynamics. These studies simulated the project execution phase and predicted delays according to the project situation, but they usually dealt with PC component installation as one chunk of the simulation process. Although delays in PC installation were recognized as critical to the overall schedule of PC project execution, these studies did not provide detailed information about the factor–delay relationship in the daily work of PC installation.
One of the main causes of delays in the PC installation process is the practice of relying on field managers’ experience and intuition to guide them in scheduling component installation on many projects. Field managers often refer to past process sheets or drawings to establish installation schedules. However, this traditional approach often results in installation delays as it fails to address the complex project-specific interaction of various factors such as climate, component characteristics, and site conditions [10,11]. These factors may affect the installation process simultaneously and, in certain conditions, cause significant delays to the installation. The installation process in PC construction is subject to the complex interaction of multiple delay factors, which can lead to severe schedule disruptions when occurring simultaneously [16,23].
Although there have been research efforts to shed light on the relationship between the contributing factors and delays in PC installation, few studies have addressed the simultaneous effects of multiple delay factors or explored what combination of factors will lead to severe schedule disruptions in PC installation. Najafi and Kong [24] developed regression models for estimating the PC installation time, which assumed that different factors affect the installation time in an additive manner. Leung et al. [25] and Tam et al. [26] utilized machine learning algorithms for the same purpose, as did Najafi and Kong [27]. Li et al. [28] developed a simulation model for schedule risks in prefabrication housing, while Zhang and Wang [9] used a data-driven approach with BIM to quantify delay risks. These algorithms take multiple delay factors at a set of inputs, but their black box approach means they cannot be used to identify severe schedule disruptions given a combination of delay factors. In addition, different steps in PC installation (e.g., rigging, lifting, and fixing) are affected significantly by different delay factors [11]. Therefore, there is a need to develop new models that take a set of delay factors as inputs and identify severe schedule disruption (i.e., severe schedule disruptions) situations a field manager may encounter in PC installation management.
Accordingly, this study aimed to identify and delineate the paths to severe schedule disruptions during the PC component installation process. When equipped with knowledge of the combination of factors that can cause severe delay situations in PC installation, a field manager can recognize these occasions early on and consider countermeasures in a timely manner. To that end, we collected PC component installation data and performed k-means clustering to group delay factors with similar characteristics. We then quantified the influence of each cluster group on the delays of installation work steps using a metric called “delay intensity”. Based on the quantified intensity, we identified the most severe delay paths that could occur with a given cluster group of delay factors. This research is novel in that it focuses on the PC component installation process and reveals the simultaneous impact of delay factors, which can lead to severe delay paths.
2. Experimental Procedure
This study identified and delineated severe delay paths that result from the simultaneous effects of delay factors during the installation of PC components. To that end, we collected 2858 observations of component installation, according to the different work steps, from a logistics center project in Korea from May to July 2022. Then, cluster analysis was conducted for each work step to group the observations according to their characteristics. Clustered groups were assessed and scored based on the time spent on the work step. Finally, quantitative analysis was performed to identify a set of characteristics (i.e., delay factors) that affected the delay in installation throughout the work steps and led to the most severe time delay.
2.1. Data Collection
The unit of analysis for this study was an observation of one of the work steps involved in installing different types of PC components, i.e., columns, beams, and slabs. This study classified the work steps into rigging (attaching ring clutches to the components to ensure safe lifting and the subsequent installation of the PC components), lifting (transporting the ring-clutched PC components to the designated installation location via crane), assembling (fixing PC components in their final location), unrigging (removing the ring clutches once the components have been installed), and returning (moving a crane to its original location for reuse), in accordance with many other studies, such as Jeong et al. [11] (Figure 1). Thus, every observation could be categorized into one of the 15 sets with a specific component type and a specific work step.
To collect the data for analysis, the authors visited a PC construction project site, a 28-story logistics center with a total floor area of 133,327 m2 using two mobile cranes (450-ton and 750-ton capacity) for 25 days from May to July 2022 and video-recorded observations. Drawings, as well as thermometer and anemometer data, were also gathered and used for analysis. Out of 2848 initial observations, 891 were removed due to indiscernible start and end times or video quality issues. Additionally, 76 observations were removed because their durations fell below the 1.5 interquartile range (IQR) below the first quartile or above the 1.5 IQR above the third quartile, i.e., they were outliers. Finally, 1881 observations remained for analysis (Table 1).
Based on previous studies [11,24,28,29] and interviews with three experts (average experience: 12.9 years), for each observation we gathered the following data in order to explore the relationship between delay factors and actual delays in installation:
Component factors: Physical characteristics of PC components can play an important role in shaping the work time required and the necessary equipment and resources. This study measured each component’s weight, area, length, and height. The component type (standard or irregular) and number of lifting inserts were also measured for each observation.
Location factors: Accessibility, safety, and the complexity of the surrounding environment or structure can influence the installation time. Accordingly, this study measured the departure distance (yard/delivery vehicle to crane distance), arrival distance (installation location to crane distance), crane angle between the start and end points, location type (external or internal), and elevation of the installation point.
Human factors: This study measured the number of workers involved during the installation. Other factors, such as personal health conditions and ages, were not included in this study, as video recordings and documents were the primary sources of information.
Environmental factors: Adverse weather represents an environmental factor that can significantly impact installation work’s safety and progress speed. During the data collection period (May–July 2022), the site experienced varied weather conditions typical of Korea’s early summer season. Temperature ranged from 18 °C to 32 °C, and wind speeds varied from 0.5 m/s to 8.5 m/s. While this period does not capture the full annual weather variation, it includes both favorable conditions (light winds, moderate temperatures) and challenging conditions (strong winds, high temperatures) that commonly affect PC installation. Weather data were collected using calibrated thermometers and anemometers at 10-min intervals throughout each workday. Accordingly, this study measured temperature and wind speed during the work.
2.2. Data Preparation
The collected data underwent preprocessing before data analysis. This is essential to enhance data quality and guarantee the reliability of the analysis results [30,31]. Recursive feature elimination with cross-validation (RFECV) was first employed for the clustering analysis to identify the main factors contributing to the delay for each work-step-level observation. This is a technique for evaluating the performance of a model by assessing the relative importance of contributing factors, as achieved by iteratively removing factors that are deemed to be less critical and cross-validating them. Table 2 shows the results of the RFECV.
We then normalized the data using MinMaxScaler to compare delay factors with varying units and scales, such as weight, size, and departure and arrival distances. MinMaxScaler is a method that transforms the values of each feature into a range between 0 and 1 using the minimum and maximum values. We then compared PCA with t-SNE and UMAP for dimensionality reduction of the normalized data. While t-SNE (78.3%) and UMAP (81.5%) showed lower performance, PCA provided superior results by extracts principal components by orienting them in the direction where the variance of the data is maximized, thereby transforming high-dimensional data into a lower dimension. Through PCA, two principal components were extracted from a total of 13 factors, which accounted for 86.8% of the total variance. This indicates that PCA, in this case, effectively reduced the complexity of the data while preserving the essential information.
2.3. Data Clustering
This study conducted a cluster analysis of the data collected during the PC components’ installation. Clustering is a machine learning technique used to identify and categorize groups with similar characteristics within a dataset, which has proven useful in discovering inherent patterns and structures [32]. This research elicited clusters using k-means clustering with the silhouette coefficient.
After evaluating several clustering methods including DBSCAN and hierarchical clustering, this study employed k-means clustering due to its superior performance (silhouette coefficient: 0.87, compared to DBSCAN: 0.78 and hierarchical: 0.81). K-means clustering is an algorithm that divides data into k clusters, assigning each data point to the nearest cluster center and repeatedly updating the cluster centers until convergence is achieved [33,34]. While various distance metrics can be used for clustering, this study employed Euclidean distance based on comparative analyses showing consistent results with Manhattan and Mahalanobis distances. Clustering utilizes the Euclidean distance for the initial updates of cluster centers. Subsequent recalculations of the centers for each data point within a cluster are then updated based on the mean location, and this process is repeated until no changes are detected or a specified number of iterations is reached.
The elbow method determines the optimal number of clusters by observing the changes in the sum of squared errors (SSE) as the number of clusters increases [35,36]. In this study, the elbow method was applied after reducing the data’s dimensionality to two through PCA. The number of clusters increased from one to ten incrementally while performing k-means clustering. The point where the sharp decrease in SSE ceased was identified as the optimal number of clusters.
Additionally, to assess the quality of the derived clusters, this study utilized the silhouette coefficient, which measures the fit of the clustering results by calculating the difference between the average distance of each data point to other points in the same cluster and the average distance to points in the nearest cluster. The range of the silhouette coefficient is from minus (−) one to one, with values closer to one indicating more appropriate clustering results.
2.4. Data Analysis
Clustering analysis resulted in clustered groups representing 15 sets with different component types and work steps. We assessed each of the groups on the degree to which it deviated from the normal situation and was delayed. While more granular measurement approaches like z-scores could potentially capture subtler variations, our decile-based assessment effectively captures key factor interactions by evaluating how combinations of components, locations, labor, and environmental conditions collectively impact delays. For this assessment, we first calculated deciles of the observations according to the duration for each set, where the fifth decile represented the median of the observations. For example, when factors like large components and strong winds occur simultaneously, their combined effect is reflected in the delay intensity value, rather than simply adding individual factor effects. The average of every clustered group was calculated and assigned a positive value as the delay intensity when larger than the fifth decile, and vice versa. For example, if a particular group’s average was between the fifth and the sixth deciles, its delay intensity value was one. The delay intensity was two if it was between the sixth and the seventh deciles. Thus, the delay intensity values could range from minus five (−5—very fast) to five (5—very slow).
After delay intensity values were assigned to all clustered groups with specific characteristics, the authors identified a set of delay factors that simultaneously affected the PC installation work throughout the work steps and caused severe schedule disruptions. Their delay paths were delineated with the summed delay intensity values and discussed with regard to how the factors could have affected the delay, causing severe schedule disruption.
To reinforce this study’s findings, we also conducted a focus group interview to gain an in-depth understanding of experts’ perspectives on the delays in PC components’ installation and potential improvements that may be made. The interview involved six participants (average experience: 20.4 years), who were site managers, designers, and construction experts in the PC construction industry. The interview results were used to derive practical recommendations for improving the PC component installation process.
3. Results
3.1. Clustered Groups by Component Types and Work Steps
3.1.1. Clustering of the Installation Duration Data
As described in the previous section, this study utilized PCA to reduce the dimensionality of the multi-dimensional data collected during the PC component installation process. Before conducting k-means clustering, the elbow method was applied to determine the optimal number of clusters. The sum of squared errors (SSE) was significantly reduced at four clusters, as shown in Figure 2, and this was established as the elbow point, i.e., the optimal number of clusters.
Figure 3 shows the results of the clustering analysis. The centroids of the clustered groups were centrally located within their respective regions, indicating that the algorithm effectively distinguished data points with similar characteristics. An analysis of the characteristics of the four derived clusters revealed that each reflected a different kind of delay factor during the installation: components, location, labor, and environmental conditions.
This research also assessed the validity of the clustering results using two approaches. First, the clustering stability was evaluated with our dataset of 1881 observations distributed across 15 sets (average 125.4 observations per set). Bootstrap resampling with 1000 iterations showed highly consistent cluster formations with average Rand indices of 0.78–0.88 across the sets, where values above 0.8 indicate excellent stability. Second, the clustering quality was assessed using the silhouette coefficient. The average silhouette coefficient for the clusters was 0.87, significantly exceeding the generally accepted threshold of 0.5. This high score strongly supports the reliability of our clustering results, indicating well-separated and cohesive clusters (Figure 4). These findings indicate that this study has successfully grouped clusters that are different from each other and internally consistent.
3.1.2. Delay Intensity of the Clustered Groups
The authors assessed each clustered group to assign the metric delay intensity. Delay intensity measured the degree to which the group deviated from the normal situation, i.e., the median of the installation duration values. The minimum value was minus five, which meant that the duration was very short compared to the median duration, while the maximum was five, which meant the duration was very long and delayed.
Table 3, Table 4 and Table 5 show the results of the assessment for PC columns, beams, and slabs, respectively. For each group, the average duration and resulting delay intensity are shown. The worst group’s delay intensity was four, while the best group’s was minus two. For rigging work, the duration seemed to be significantly affected by irregularity, the size of the components, and the number of workers. For lifting work, the distance to the installation location and weather conditions (windy or not) affected the work’s duration more than other factors. Assembling work was affected by more factors than the other work steps. Component factors (irregularity, size), installation location factors (distance, altitude, internal or external position), labor factors (number of workers), and environmental factors (wind condition) affected the assembly duration simultaneously. The component size, irregularity, and wind conditions affected the duration of unrigging work. Finally, the distance and wind conditions were the factors with an influence when returning the crane.
3.2. Severe Delay Paths in the PC Component Installation
Based on the assessment of grouped clusters for each component type and work step, this study identified the most severe delay paths during the installation of PC components. In doing so, this study found that a severe delay can occur during the installation process due to simultaneous and collective effects of a set of delay factors. For example, when a PC column is irregular and large-sized, these factors can impede the rigging work. Additionally, if the column is to be installed at height, this factor works together with the component factors to impede the unrigging work. Accordingly, this study analyzed how a combination of delay factors can affect the sequential work steps throughout the installation process in order to identify the most severe delay paths, comprising the work steps with the largest delay intensity value in total, and the second most severe ones.
To confirm the results, we asked six domain experts how much they agreed with the delay paths using a Likert five-point scale (one: strongly disagree, five: strongly agree). This survey was conducted as part of the focus group interview, as described in a later section.
3.2.1. Delay Paths of PC Column Installation
Figure 5 delineates the risk factors and mechanisms of delay paths C1 and C2 for PC column installation. Path C1 is formed by a combination of factors, including a large component, strong wind, small number of workers, and low and external installation positions at a distance. Path C1’s total delay intensity was calculated as 13 (CR1(+4), CL1(+3), CA1(+3), CU3(−1), and CRT1(+4)), making it the most severe delay path. The average duration is high, at 1409.6 s. The delay occurs in most work steps, excluding unrigging. The experts rated the delay risk of this path highly, with an average score of 4.7. Following that, path C2 is formed from the factors of an irregular and large-sized component, strong wind, and high and external installation position at a distance. The summed delay intensity of this path is 12 (CR2(+1), CL2(+2), CA2(+2), CU1(+3), and CRT1(+4)), and the average duration is 1345.4 s, which is 64.2 s faster than path C1. The experts rated the delay risk of this path highly, at 4.3.
In path C1, during rigging work, the use of large-sized components increases the travel distance for workers, causing delays. When the installation proceeds to lifting, windy weather increases the risk of collisions between structures and equipment and slows the work. Wind also impedes the assembly work, along with a limited number of workers available to oversee installations. On a windy day, if the installation location is at the edge of the structure, the situation can worsen because the workers and equipment struggle to access the location. When the crane is returned after assembling and unrigging, strong wind further exacerbates delays due to the risk of equipment collisions at low altitudes and when in proximity.
Path C2 is characterized by increased work and access difficulties due to the irregularity of large-sized components and the need to work at high installation positions on windy days. During the rigging work, irregular shapes of components increase the complexity of tasks. The combination of complex axis control and strong wind during the lifting work tends to lead to delays. Assembling and unrigging work is complicated by the irregular shapes of the large-sized components and the characteristics of the high-rise column work on the edge of the structure. Such combinatorial conditions reduce the workspace and necessitate additional equipment, such as aerial work platforms, leading to delays. Finally, the distance and strong wind affect the crane’s return from the installation location at a height.
3.2.2. Delay Paths of PC Beam Installation
This section explains the risk factors and mechanisms of delay paths B1 and B2 for PC beam installation (Figure 6). Certain sets of risk factors encountered at the beam installation site critically influenced the formation of these distinct paths. Path B1 is formed through the interaction of delay factors, including the use of an irregular and large-sized component, strong wind, many workers, and high and external installation locations at a distance. The total delay intensity value is high, at 15 (BR1(+2), BL1(+4), BA1(+3), BU1(+2), and BRT1(+4)), indicating a considerably high level of delay risk. The average duration is 1187.5 s. The experts rated the delay risk of this path very high, with an average score of 4.8. Path B2 is similar to B1 except that this path is characterized by a standard and regular component instead of an irregular one. The total delay intensity score of this path is 8 (BR2(+1), BL2(+2), BA3(−1), BU2(+2), and BRT1(+4)), and the average duration is 1010.1 s, a decrease of approximately 117.4 s compared to B1. Using a standard component instead of an irregular one can reduce the duration of rigging, lifting, assembling, and unrigging work steps. The experts rated this path 4.5 out of 5.
Path B1 exhibits significant delay-related risk factors. Rigging a large component with an irregular shape requires many clutches and makes safety bar installation difficult, causing delays. A distance involved and windy conditions, in combination with the irregularity of the component, add difficulties to control efforts during the lifting work. Such component factors and windy conditions continue to affect the assembling and unrigging work, and the installation of the component at the edge of the structure introduces additional difficulties in assembly due to access issues and the fall risk.
For path B2, strong wind, a large component, and a high and external installation position at a distance are the main delay factors. The distance to the location and windy conditions affect the duration of the lifting work simultaneously, while the size of the component and windy conditions affect the duration of the unrigging work. The conditions of crane return on this path are the same as in B1, where distant locations and windy conditions cause delays.
3.2.3. Delay Paths of PC Slab Installation
Figure 7 delineates the risk factors and mechanisms of delay paths S1 and S2 for PC slab installation. Path S1 is formed through the interaction of factors, including the use of a large component, a small number of workers, installation in high and external locations at a distance, and strong wind. Path S2 is similar to S1, but the component size is smaller than that of S1. The total delay intensity score is 12 for both paths, while the average duration is 524.0 s for S1 and 521.6 s for S2. Delay path S1 (SR2(+3), SL1(+3), SA1(+2), SU1(+1), and SRT1(+3)) takes longer in assembling but a shorter time is required in rigging compared to S2 (SR1(+4), SL2(+3), SA2(+1), SU2(+1), and SRT1(+3)). The experts agreed on the risks, with an average score of 4.6 for path S1 and 4.3 for path S2.
In path S1, handling a large-sized component increases the movement required of workers during the rigging work, which can be a major cause of an increased work time. For instance, on days when there are not enough workers to do the job efficiently, the scenario arises where a single worker may need to attach the ring clutches on both sides, significantly increasing their travel distance and workload and reducing their work speed. When the installation process proceeds to the lifting work, it is not easy to handle the large component, especially in windy conditions. Such conditions also affect the assembly work negatively, in tandem with distant, external, and high locations of installation points, as they entail fall risks, increase workers’ mental load, and reduce work efficiency. In addition, an increased distance from the crane also extends the time required for return work after assembly.
Meanwhile, path S2 represents the case of installing a small-sized component with adverse weather and location conditions and with a limited number of workers. The delay time is not much different from in path S1. When fewer workers than necessary are deployed during rigging work, the work can be delayed due to difficulties in attaching ring clutches. Small components are easily shaken by strong wind during the lifting phase and require special attention to ensure worker safety. The high altitude and strong wind during the assembly work, especially at height, can also cause a significant delay.
3.3. Focus Group Interview Results
As mentioned, this study conducted a focus group interview with six experts (average experience: 20.4 years) to confirm the appropriateness of the identified delay paths and discuss the practical impact of the delay paths on the PC component installation process. Focus group interviews are a qualitative research method effective for obtaining in-depth insights from participants with specialized knowledge [37]. The experts affirmed that the research findings align with delay patterns occurring in actual field operations, supporting our findings’ validity in real-world settings. Their extensive experience ensures that the insights gathered are grounded in practical expertise, which is crucial for the exploratory nature of this study. Key insights derived from the interview include the following:
The experts remarked that the delay paths of PC component installation frequently occurred in the field, emphasizing the practical applicability of the research findings.
The experts suggested that identifying delay paths enables the prevention and effective response to issues such as lifting delays with components, work risks, safety issues, difficulty in securing skilled labor, and workforce planning.
The experts confirmed that the complexity of factors with a collective impact, such as component characteristics (regularity, size), environmental conditions (wind), and workforce availability, contributes to the formation of delay paths.
The experts pointed out that some issues, such as control problems with irregular components, an increased distance from the crane, and a reduced work speed, can be addressed through the analysis of delay paths.
Thus, this study is anticipated to provide practical assistance in enhancing risk prevention and efficiency in PC component installation. By incorporating expert opinions through a focus group, the study bridges the gap between theoretical findings and practical application, thereby reinforcing the scientific rigor and relevance of the research. Table 6 provides some direct quotes from the experts.
4. Discussion
The findings of this study illuminated the complex interplay of multiple delay factors in the installation process of precast concrete (PC) components, which significantly impact project schedules and costs. By employing clustering and quantitative analysis of multidimensional PC component installation data, we addressed a gap in previous research that often overlooked the combined effects of concurrent delay factors.
Our analysis revealed that specific combinations of factors lead to severe schedule disruptions during PC component installation. For instance, the most severe delay paths identified for columns (C1 and C2) involved large or irregular components, strong winds, limited workforce, and challenging installation positions—either low and external at a distance or high and external at a distance. Similar patterns were observed for beams and slabs, where the interplay of component size or irregularity, adverse environmental conditions, worker availability, and difficult installation locations collectively contributed to significant delays.
These findings underscore the importance of considering the compounded impact of simultaneous delay factors rather than evaluating them in isolation. Previous studies often treated delay factors individually or additively, failing to capture the complexity of real-world construction scenarios (e.g., [24,25]). By systematically identifying severe delay paths through clustering techniques and utilizing the delay intensity metric, this study provides a more nuanced understanding of how multiple factors interact to affect installation times.
The practical implications of this research are significant for project managers and practitioners in the PC construction industry. Recognizing the specific combinations of delay factors that lead to severe schedule disruptions enables more effective risk management and proactive planning. For example, if a project involves installing large, irregular components in high, external locations during periods of strong wind, managers can adjust schedules to avoid adverse weather conditions, allocate additional skilled workers, or implement alternative installation strategies such as using specialized equipment or temporary supports to mitigate potential delays.
Furthermore, the high agreement rates from our focus group interviews with industry experts validate the practical relevance of our findings. The experts confirmed that the identified delay paths align with challenges commonly encountered in PC construction projects. This alignment suggests that the insights from this study are not only theoretically sound but also applicable in real-world settings.
Comparing our results with the existing literature, this study advances the understanding of delay mechanisms in PC construction by highlighting the compounded effects of concurrent delay factors. While previous research identified various individual factors contributing to delays [9,28], our approach emphasizes the significance of their interactions. This holistic perspective is crucial for developing more accurate predictive models and formulating comprehensive strategies to minimize delays.
In summary, by revealing how specific combinations of delay factors interact to cause severe schedule disruptions, this study enhances the ability of project managers to anticipate and mitigate delays in PC construction projects. The insights gained contribute to improving the efficiency and reliability of construction processes, ultimately supporting the growth and sustainability of the construction industry.
5. Conclusions
Delays during the installation of the components in PC construction projects significantly impact project schedules and costs. Yet, previous research has been limited in its exploration and analysis of the complex mechanisms by which delay risk factors have an impact. To address that research gap, this study identified delay patterns and the most severe delay paths through clustering and quantitative analysis of multidimensional PC component installation data.
From May to July 2022, 1881 valid observations of PC component installation and related delay factor data were collected from a construction site. These observations were grouped into 15 sets with different component types and work steps. After preprocessing and dimensional reduction using MinMaxScaler and PCA, k-means clustering was applied to divide each set into four clustered groups, each with a particular characteristic. Then, this study utilized the delay intensity as a metric to assess the clustered groups quantitatively regarding their deviation from the median duration and thus their capacity to cause delays. Based on the findings, this study identified the main delay paths that ran through the five work steps and caused severe schedule disruptions (i.e., combinations of delay factors causing severe schedule disruptions) during PC component installation.
The risk factors of the most severe delay path for column installation (C1) include a large-sized component, strong wind, small number of workers, and low and external installation position at a distance. The second most severe path C2 is formed from an irregular and large-sized component, strong wind, and high and external installation position at a distance. As for beam installation, the most severe delay path (B1) is formed from the use of an irregular and large-sized component, strong wind, and high and external installation location at a distance. The second most severe path for beam installation (B2) is similar to B1 except that it uses a standard component instead of an irregular one. Finally, the most severe delay path for slab installation (S1) is a result of delay factors comprising a large-sized component, small number of workers, installation in a high and external location at a distance, and strong wind. The second most severe delay path (S2) is similar to S1, but the component size is smaller than that of S1. Our focus group interview results supported these findings with high agreement rates.
This study contributed to PC construction management theory as we have systematically identified and analyzed complex factors causing delays in the PC component installation process and proposed specific delay paths for different types of components. This provides project managers with a basis for effectively optimizing project schedules and precisely managing risks. The research findings should help project managers plan PC component installation, as was suggested in our focus group interview, contributing to the overall efficiency and success rates in PC construction projects and the industry.
This study has presented pathways of delays in the installation of PC components, which can be further developed in future research. First, this study is based on data collected from a single construction site, though it provides systematic analysis through 1881 detailed observations for theory building in an area where such comprehensive field data are notably difficult to acquire. Validation across multiple projects with diverse environmental and socioeconomic conditions to enhance the generalizability of the delay paths. A broader dataset encompassing different regions and project contexts would strengthen the universal applicability of our findings. Second, installation work, further research needs to consider the impacts of broader external factors such as seasonal weather patterns, material supply chains, and labor market dynamics for comprehensive project delay prediction. Third, although this study was data-driven and reinforced by expert opinions through focus group interviews, future research could enhance this work in several ways: (1) validating the findings through actual case applications across diverse PC construction projects to verify the practical applicability of identified delay paths, (2) employing statistical methods such as multivariate regression or Bayesian networks to capture nonlinear effects and complex interdependencies among delay factors, and (3) developing predictive models that integrate real-time weather data and machine learning techniques for dynamic schedule adjustments, (4) exploring techniques such as deep learning and autoencoders with larger datasets to identify more complex delay patterns, while ensuring their practical implementation in real construction operations, and (5) investigating additional interaction effects between weather conditions and component characteristics, including non-linear relationships, threshold effects, and seasonal variations with emphasis on their validation through real-world applications. Fourth, while this study focused on identifying delay patterns, future research could employ supervised learning techniques like random forests or gradient boosting to leverage historical data for more accurate delay predictions. Through such further studies, researchers can deepen our understanding of delay issues in PC construction projects and propose practical solutions.
Conceptualization, T.W.K.; Methodology, T.W.K.; Software, J.J.; Validation, E.J.; Formal analysis, J.J. and E.J.; Investigation, J.J.; Resources, T.W.K.; Data curation, J.J., E.J. and J.C.; Writing—original draft, J.J. and T.W.K.; Writing—review & editing, J.J. and T.W.K.; Visualization, J.J., E.J. and J.C.; Supervision, T.W.K.; Project administration, T.W.K.; Funding acquisition, T.W.K. All authors have read and agreed to the published version of the manuscript.
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
The authors declare no conflict of interest.
Footnotes
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Enlarge this image.Figure 2. Identification of the elbow point for the clustering analysis. The x–axis represents the number of clusters (k) and the y–axis shows the Sum of Squared Errors (SSE). The elbow point at k = 4 indicates the optimal number of clusters.
Enlarge this image.Figure 4. The silhouette coefficient analysis results for validation of clustered data. The y-axis represents the silhouette coefficient value ranging from −1 to 1, where values closer to 1 indicate better clustering quality.
Enlarge this image.Figure 5. Delay paths of PC column installation (* indicates intersection relation of multiple factors).
Enlarge this image.Figure 6. Delay paths of PC beam installation (* indicates intersection relation of multiple factors).
Enlarge this image.Figure 7. Delay paths of PC slab installation (* indicates intersection relation of multiple factors).
Number of observations collected for analysis by component type and work step.
| PC Type | Rigging | Lifting | Assembling | Unrigging | Returning | Total |
|---|---|---|---|---|---|---|
| Columns | 122 | 118 | 133 | 134 | 102 | 609 |
| Beams | 140 | 137 | 141 | 142 | 127 | 687 |
| Slabs | 118 | 122 | 116 | 118 | 111 | 585 |
| Total | 380 | 377 | 390 | 394 | 340 | 1881 |
Main identified delay factors for each work step.
| Work Step | Main Delay Factors |
|---|---|
| Rigging | Component area, Component length, Component height, Component type, Number of lifting inserts |
| Lifting | Component weight, Component area, Component type, Departure distance, Arrival distance, Crane angle, Elevation, Temperature, Wind speed |
| Assembling | Component weight, Component type, Arrival distance, Crane angle, Location type, Number of lifting inserts, Temperature, Wind speed |
| Unrigging | Component area, Component length, Component height, Component type, Number of lifting inserts |
| Returning | Departure distance, Arrival distance, Crane angle, Location type, Wind speed |
Delay intensity of clustered groups representing PC column installation.
| Phase | Cluster ID | Characteristics of Cluster | Average Duration (sec) | Delay Intensity |
|---|---|---|---|---|
| Rigging | CR1 | Standard and large-sized component | 146.25 | 4 |
| CR2 | Irregular and large-sized component | 137.63 | 1 | |
| CR3 | Standard and small-sized component | 125.84 | −1 | |
| CR4 | Irregular and small-sized component | 108.88 | −2 | |
| Lifting | CL1 | Standard component; distant location; windy | 355.83 | 3 |
| CL2 | Irregular component; distant location; windy | 324.91 | 2 | |
| CL3 | Irregular component; close location; windless | 310.85 | −1 | |
| CL4 | Standard component; close location; windless | 310.74 | −1 | |
| Assembling | CA1 | Standard and large-sized component; external location; small number of workers; windy | 550.44 | 3 |
| CA2 | Irregular and large-sized component; external location; large number of workers; windy | 439.83 | 2 | |
| CA3 | Standard and small-sized component; internal location; large number of workers; windless | 405.50 | −1 | |
| CA4 | Irregular and small-sized component; internal location; small number of workers; windless | 348.36 | −2 | |
| Unrigging | CU1 | Irregular and large-sized component; high location | 167.79 | 3 |
| CU2 | Irregular and small-sized component; low location | 150.58 | 1 | |
| CU3 | Standard and large-sized component; low location | 101.89 | −1 | |
| CU4 | Standard and small-sized component; high location | 92.85 | −2 | |
| Returning | CRT1 | Distant location; windy | 275.23 | 4 |
| CRT2 | Close location; windy | 236.20 | 2 | |
| CRT3 | Distant location; windless | 165.64 | −1 | |
| CRT4 | Close location; windless | 152.39 | −2 |
Delay intensity of clustered groups representing PC beam installation.
| Phase | Cluster ID | Characteristics of Cluster | Average Duration (sec) | Delay Intensity |
|---|---|---|---|---|
| Rigging | BR1 | Irregular and large-sized component | 108.80 | 2 |
| BR2 | Standard and large-sized component | 92.73 | 1 | |
| BR3 | Irregular and small-sized component | 83.68 | −1 | |
| BR4 | Standard and small-sized component | 80.64 | −2 | |
| Lifting | BL1 | Irregular component; distant location; windy | 347.33 | 4 |
| BL2 | Standard component; distant location; windy | 307.36 | 2 | |
| BL3 | Irregular component; close location; windless | 263.86 | −1 | |
| BL4 | Standard component; close location; windless | 261.51 | −1 | |
| Assembling | BA1 | Irregular and large-sized component; external location; windy | 462.56 | 3 |
| BA2 | Irregular and small-sized component; internal location; windless | 438.72 | 2 | |
| BA3 | Standard and large-sized component; external location; windy | 342.26 | −1 | |
| BA4 | Standard and small-sized component; internal location; windless | 333.36 | −1 | |
| Unrigging | BU1 | Irregular and large-sized component; windy | 41.65 | 2 |
| BU2 | Standard and large-sized component; windy | 40.53 | 2 | |
| BU3 | Irregular and small-sized component; windless | 35.98 | −1 | |
| BU4 | Standard and small-sized component; windless | 32.00 | −2 | |
| Returning | BRT1 | Distant location; windy | 227.19 | 4 |
| BRT2 | Close location; windy | 160.42 | 1 | |
| BRT3 | Distant location; windless | 146.10 | −1 | |
| BRT4 | Close location; windless | 141.98 | −2 |
Delay intensity of clustered groups representing PC slab installation.
| Phase | Cluster ID | Characteristics of Cluster | Average Duration (sec) | Delay Intensity |
|---|---|---|---|---|
| Rigging | SR1 | Small-sized component; small number of workers | 41.33 | 4 |
| SR2 | Large-sized component; small number of workers | 24.75 | 3 | |
| SR3 | Small-sized component; large number of workers | 20.93 | −1 | |
| SR4 | Large-sized component; large number of workers | 19.09 | −2 | |
| Lifting | SL1 | Large-sized component; windy | 184.41 | 3 |
| SL2 | Small-sized component; windy | 177.20 | 3 | |
| SL3 | Large-sized component; windless | 145.85 | −2 | |
| SL4 | Small-sized component; windless | 145.00 | −2 | |
| Assembling | SA1 | Large-sized component; distant, external, and high location; windy | 124.79 | 2 |
| SA2 | Small-sized component; distant, external, and high location; windy | 113.03 | 1 | |
| SA3 | Large-sized component; close, internal, and low location; windless | 107.64 | −1 | |
| SA4 | Small-sized component; close, internal, and low location; windless | 96.54 | −2 | |
| Unrigging | SU1 | Large-sized component; windy | 13.86 | 1 |
| SU2 | Small-sized component; windy | 13.36 | 1 | |
| SU3 | Large-sized component; windless | 10.17 | −2 | |
| SU4 | Small-sized component; windless | 10.13 | −2 | |
| Returning | SRT1 | Distant and high location; windy | 176.16 | 3 |
| SRT2 | Distant and low location; windy | 142.61 | 2 | |
| SRT3 | Close and high location; windless | 115.52 | −2 | |
| SRT4 | Close and low location; windless | 115.40 | −2 |
Expert quotes from a focus group interview.
| PC Type | Expert Quote |
|---|---|
| Column | “When the lifting of components is delayed, it causes significant disruptions to the entire process. By identifying the path, field managers can prevent such delays and minimize process disruptions.” (Expert A) |
| “Handling the path with large components increases work difficulty, heavily relying on skilled workers. The challenge is that it’s not easy to secure enough labor. By identifying the path, field managers can strengthen skilled labor acquisition and workforce planning.” (Expert F) | |
| Beam | “The combination of strong wind and large components carries considerable work risks. By preemptively identifying the path, field managers can prepare for these risks and safety issues.” (Expert B) |
| Slab | “The size of components plays a significant role in installation tasks. By identifying the path, field managers can determine the causes of work speed reduction and increase installation efficiency.” (Expert C) |
| “Increasing distance from the crane introduces various risk factors. By identifying the path, field managers can be aware of crane distance issues in advance and reduce response delays.” (Expert E) | |
| “The combination of strong wind and large components carries considerable work risks. By preemptively identifying the path, field managers can prepare for these risks and safety issues.” (Expert B) |
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; Tae Wan Kim 2
1 Division of Architecture & Urban Design, Incheon National University, 119 Academy-ro, Yeonsu-gu, Incheon 22012, Republic of Korea;
2 Division of Architecture & Urban Design, Incheon National University, 119 Academy-ro, Yeonsu-gu, Incheon 22012, Republic of Korea;