Improving the Model for Estimating the Number of Construction Workers for Apartment Construction

Abstract

Because the construction industry is labor-intensive, predicting the number of workers is important for estimating various factors that influence construction, such as the construction worker fatality rate and construction financing plan. In South Korea, the number of full-time workers is estimated based on the total construction cost; however, this estimation method does not reflect the characteristics of specific construction types. This study presents a simple model that uses real data to predict the number of construction workers and calculates correction factors in two ways to improve reliability. This study involved three steps: (1) collecting data, (2) calculating and validating the estimated labor rate, and (3) calculating correction factors. The model predicted the number of workers with an average error rate of 7.60% without correction factors. To improve reliability, this research suggests two-way correction factors, and the results show that correction factor one reduces the average error rate to 0.06% and correction factor two reduces the average error rate to 0.00%. The proposed model can be used for estimating project costs and predicting construction worker fatalities for a project.

1. Introduction

Construction is a labor-intensive industry. Therefore, the number of workers is used to calculate various factors, such as construction cost, duration, and number of safety breaches [1]. Therefore, many countries have tried to estimate the number of workers in different ways. In the United Kingdom, the number of construction workers is estimated through surveys and sampling inspections [2]. The number of construction workers in China is estimated in the same way as in the United Kingdom [3], whereas the number of construction workers in Singapore is estimated through a survey conducted by the Labor Force Survey [4]. In South Korea, the number of workers is calculated using an equation known as the full-time equivalent worker, according to South Korean law [5].

The number of workers is used for various reasons in the construction industry. The first is inspecting the fatality rate in South Korea, according to a report on industrial accidents in 2021 by the Korea Occupational Safety and Health Agency. The construction industry has a 1.13% injury rate and 1.75‱ fatality rate. Consequently, the construction industry is more dangerous than others [6]. Full-time equivalent workers, which are calculated using construction cost, labor ratio, and labor cost, are used to calculate the injury and fatality rates [7]. However, this is problematic because a fixed labor ratio is applied regardless of the type of construction. Therefore, this method produces unreliable results [8]. Hence, labor ratios that consider construction type must be developed. Many workers are involved in high-rise construction. High-rise construction involves various stages, such as earthwork, structural work, and finishing work. Among these stages, the structural work requires more labor-intensive tasks performed mainly by workers. Conversely, in road construction, construction machinery is primarily used, which reduces the number of required workers. Therefore, the number of workers required in high-rise construction is generally higher than in road construction [9]. Second, labor costs account for a significant portion of the total construction costs, typically 40–60% [10]. The labor ratio is an important factor in calculating labor costs. Therefore, the reliability and accuracy of the labor ratio are valuable factors for assessing the total construction cost [11,12]. As mentioned above, in South Korea, the number of construction workers is calculated using the labor ratio. To obtain reliability and accuracy of labor or labor costs, previous studies have attempted to estimate labor or labor costs using methods such as machine learning, uncertainty analysis, and regression analysis. For example, Huang and Hsieh [13] attempted to predict labor costs using a random forest and linear regression. The authors used a completed building information modeling (BIM) project to develop a prediction model for labor costs. However, it is difficult for non-experts to use machine learning or BIM.

Third, most countries conduct sampling inspections to investigate the number of construction workers [14]. However, sampling inspection has low reliability and accuracy compared to real data. Therefore, a method for estimating the number of workers with high accuracy is required.

Considering all points of view, estimating the number of construction workers involved is very important. As mentioned above, conventional methods have several limitations, such as low accuracy and difficulty for nonexperts. To overcome these limitations, this study developed a simplified estimation model for the number of workers using a correction factor based on real data. Thus, this research shows that the number of construction workers can be easily estimated with high accuracy and reliability in the construction work package based on real data. The research question was: How can the number of workers be estimated based on real data? The main contribution of this study is as follows:

(i)

Development of a model that estimates the number of workers based on real data

(ii)

Considering different labor ratios for each work package type in apartment construction

(iii)

Suggestion of correction factors based on a statistical method. These factors improve the reliability of estimating the number of workers available to construction sites

2. Literature Review

2.1. Status of Previous Research

This study estimates the number of construction workers with high reliability and accuracy using a correction factor for work package types in an apartment construction project. Therefore, to improve research quality, this study investigates previous studies to suggest research insights into limitations for estimating the number of construction workers by construction work package type. Previous studies can be categorized as follows: (i) research related to estimating the labor cost in the construction work package and (ii) research related to estimating the number of workers in the construction work package (see

Table 1. Literature review.

No.	Reference	Purpose	Research Gap
Research related to estimating labor cost
1	Huang et al. [13]	The authors suggested the method for estimating labor cost used in nine BIM projects.	This study analyzed the estimated labor cost rate using real data
2	Dyacova et al. [15]	The authors used standardization and market pricing methods to estimate labor costs in construction project costs.
Research related to estimating the number of workers
3	Kosha guide [16]	The author suggested a labor cost rate to improve the reliability of the estimation of the number of workers.	This study suggests an estimated labor cost rate by work package type and calculates a correction factor to improve reliability
4	Sim et al. [12]	The authors analyzed the national method of estimating the number of workers.
Research related to estimating methods used in building factors
5	Huang et al. [17]	The authors developed an air conditioner with a visual recognition capacity using a convolutional neural network (CNN). The visual recognition system can recognize human bodies through a camera.	This study suggests a simple estimation model using calculations
6	Zhao et al. [18]	The author analyzed methods presented in 78 literature reviews related to estimating building occupancy and their accuracies.
7	Guo et al. [19]	The authors analyzed small and imbalanced datasets of estimations in buildings using predictive modeling.
This research		This study estimates the number of construction workers with high reliability and accuracy using a correction factor for work package types in an apartment project.	-

).

A few studies have attempted to estimate the labor cost in the construction industry [13,14,15,16]. Huang and Hsieh [13] used various methods to estimate the labor costs of BIM projects. The authors used 19 BIM projects and suggested a methodology that merges simple linear regression and random forest to estimate BIM labor costs. The authors introduced methods for collecting and clustering data and a training method to estimate BIM labor costs. To collect the data, they used the proposed cost breakdown structure, divided the details of the data on the BIM project, and used linear regression to improve stability. Using different numbers of BIM projects, the authors compared the accuracy of the random forest model with that of the linear regression model, and the linear regression model was superior [13]. Dyacova et al. [15] used standardization and market pricing methods to estimate labor costs in construction projects and built a nine-step algorithm model to reflect labor characteristics, such as employee labor behavior and production tasks in the design and construction stages [15].

The number of workers in the construction industry have been analyzed [12,16]. The Korea Occupational Safety and Health Agency (KOSHA) studied the estimation of the number of full-time workers at construction sites. The study suggested a method for estimating the number of workers in the construction work package that corrects the labor rate work package type. South Korea’s standard labor rate for the estimated number of workers is 27% regardless of project type or work package type. However, the authors suggested a different correction rate by industry type (civil (89.0%), construction (104.6%), and others (104.6%)) and multiplied it by 12 months to calculate the number of workers [16]. In South Korea, the number of workers is required to calculate the fatality rate. The author analyzed the number of workers to calculate the national fatality rate. Japan, the United Kingdom, and Singapore use sampling inspection; however, South Korea calculates the number of workers by multiplying the labor rate (27%) by the total construction cost and dividing by the average monthly wage [12].

Building-based estimations have also been studied [17,18,19]. Huang and Hao [14] developed a CNN-based visual recognition sensor and installed it on an air conditioner. The author suggests measuring four impact quantities, distance, and angle of indoor human users essential for controlling air conditioners using visual cameras and CNNs [17]. Zhao and Li [18] analyzed seventy-eight literature reviews on buildings from 2011 to 2021 to estimate building impacts. The authors analyzed the inspection accuracy and methodology. Most of the reviewed papers used machine-learning methods and cameras for estimations [18]. Guo and Amayri [19] introduced occupancy estimation using predictive modeling in imbalanced domains. The authors suggest occupancy estimation using oversampling and predictive distribution. In addition, the results show that the six-sample model with oversampling has an accuracy of 78.94%, which is better than that of the model without sampling (71.06%). Therefore, assuming a lack of data, oversampling, and the suggested framework, the accuracy is higher [19].

2.2. Research Gap

Although previous studies have provided valuable insights, they have several limitations. First, previous studies used BIM or machine learning and used statistics to estimate labor costs. However, unlike previous studies that used machine learning or statistical methods, the proposed model is user-friendly and can be easily used by non-experts. Additionally, the model takes into account the specific characteristics of each work package type, which is an improvement over previous methods that applied a fixed labor ratio regardless of the type of construction. The use of real data and the development of correction factors also contribute to the model’s reliability and accuracy. Therefore, this study provides a new approach to estimating the number of construction workers that can be more easily implemented in practice and provide more accurate results. Second, the construction workers involved differ according to the construction work package type. However, previous studies have estimated the number of workers at the project or country level. To enhance accuracy, the number of workers was estimated at the work level.

To reduce the gap between previous studies and this study, this study developed a user-friendly, simplified estimation model for the number of construction workers with high reliability and accuracy based on real data.

3. Problem Statement

This study shows the development of a model for estimating the number of workers for each work package type. Previously, several countries did not suggest a labor ratio or calculation for estimating the number of workers. In addition, there are no labor ratios for work package types [8].

This uses the following steps to develop an estimation model (See Figure 1):

• Estimating the labor ratio by work package type for the construction of an apartment building
• Development of correction factors to improve reliability, comparing the estimated data to real data

3.1. Summary of the Mathematical Model

A common practice in South Korea is to use an equation for estimating the number of workers, as shown in Equation (1) [6].

$$Estimated number of workers=\frac{Construction total cost \left(yearly\right) \times labor ratio}{Monthly worker wage \times 12}$$

(1)

In contrast, this study used real data from “B”, a company in the South Korean construction industry which has completed 24 apartment construction projects. The data collected included the total cost and number of workers for each work package and construction type. Therefore, this study used reverse tracking to estimate the labor ratio. Further, this study classifies 15 types of work package, from “Interior Architecture Works” to “Electrical Work” based on the “Framework Act on the Construction Industry”, “Electrical Construction Business Act”, “Telecommunication Business Act”, and “Firefighting Facility Construction Act” in South Korea. Subsequently, the study classified 28 work types, from “Carpentry” to “Electronic wire work” that were included in each work package based on “Enforcement Decree of the Framework Act on the Construction Industry”. In addition, “Initial Cleaning” and “Working with construction equipment” were added as construction work types to “Non-categorized” as a work package type, because “Non-categorized” is not mentioned in “Enforcement Decree of the Framework Act on the Construction Industry” but is necessary work in construction sites [20]. Therefore, this study considered 16 types of work packages and 30 types of construction work. Subsequently, the study selects the activity types of each work based on “Project Cost Estimating 2022” [21]. According to the Construction Association of Korea [22], average worker wages and the number of construction workers classified based on work package were collected in this study. Also, notations used in calculation have shown in

Table 2. Notation list.

Type	Parameter	Unit
Parameter	Wj	Dollar/Person
	Nij	Person
	Clij	Dollar/Site
	Ctij	Dollar/Site
	Rij	%
Decision variables	Neij	Person
	Rej	%
	Fmj	Num
	Fecj	Num
	Nfmij	Person
	Nfecij	Person

.

3.2. Calculation and Validation of the Estimated Labor Ratio

Based on the previous section, this section calculates the estimated labor cost by multiplying the number of workers with the W_j based on 24 construction sites that are collected from the “B” construction company by Equation (2).

$${Cl}_{ij}=N_{ij}\times W_j$$

(2)

where Cl_ij is the estimated labor cost of the j-th work package type in the i-th construction site, N_ij is the number of workers for work package type j in construction site i, and W_j is the average wage for work package type j.

Re_ij is calculated by dividing the estimated labor cost by the total work package cost and multiplying it by 100 to obtain a percentage. The average estimated labor ratio is referred to as Re_j per work package type.

$$R_{ij}(\%)=\frac{{Cl}_{ij}}{{Ct}_{ij}}\times 100$$

(3)

$${Re}_j=\underset{i\to 24}{\lim }\frac{\sum _{i=1}^{24}{R}_{ij}}{i}$$

(4)

where Re_ij is the estimated labor ratio of the j-th work package type in the i-th construction site, Cl_ij is the estimated labor cost of the j-th work package type in the i-th construction site, Ct_ij is the total work package cost of the j-th work package type in the i-th construction site, and the number of construction sites i is the number of construction sites, including construction sites with the j-th work package type.

To estimate the number of workers, the type of cost of the type of work packages is multiplied by the estimated labor ratio for that work packages type and divided by the average worker wage for the work package type. The calculated value is called Ne_ij for each type of work package.

$${Ne}_j=\frac{{Ct}_j\times {Re}_j}{W_j}$$

(5)

where Ne_j is the estimated the number of workers for work package type j in construction site i.

To demonstrate the accuracy of the estimated number of workers for a given type of work package, this study employs the error rate in Equation (6). The error rate can be compared between the estimated and actual number of workers based on real data.

$${Error rate}_{ij}=\frac{\left|N_{ij}-{Ne}_{ij}\right|}{N_{ij}}\times 100$$

(6)

3.3. Calculation of Correction Factors

To guarantee the high reliability and accuracy of the number of estimated workers, this study calculates the correction factor. The correction factor is obtained in the two subsections below.

3.3.1. Calculation of Fm_j

The mean square error (MSE) is the sum of the square differences of real and estimated values [21]. Also, Equation (7) indicates the mean square error (MSE), the difference between the real value and the estimated value. Therefore, this study employed Fm_j, which is one of the factors, to determine the minimum MSE for the number of estimated workers. The minimum MSE was calculated using Equation (8).

$$MSE=\frac{1}{n}\sum _{i=1}^n{\left(\widehat{Y_i}-Y_i\right)}^2$$

(7)

$${Fm}_{ij}=Min\underset{n\to 24}{\lim }\frac{1}{n}\sum _{i=1}^n{\left(N_{ij}-{Fm}_j{Ne}_{ij}\right)}^2$$

(8)

where Nj is the number of workers for work package type j and Fm_j is the minimization MSE for work package type j in construction site i.

After using Fm_j to calculate the minimum MSE, the error rate was calculated using Equation (5).

3.3.2. Calculation of Fe_cj

In addition, this study suggests the use of Fe_cj, which can reduce the error rate in any type of work package. So, Equation (9) shows the number of workers for industry type, in classified construction costs, indicating the average of the number of workers for industry type in construction sites, classified by construction cost. Also, Equation (10) shows the estimated number of workers for industry type in classified construction costs, indicating the average of the estimated number of workers for industry type in construction sites, classified by construction cost.

When applying Fe_cj, the minimum error rate for each work package type can be determined using Equation (11).

$$N_{cj}=Avg \left(N_{cij}\right)$$

(9)

$${Ne}_{cj}=Avg \left({Ne}_{cij}\right)$$

(10)

$${Fe}_{cj}=Min \frac{\left|N_{cj}-{Fe}_{cj}{Ne}_{cj}\right|}{N_{cj}}$$

(11)

where Fe_cj is the minimization error rate for work package type j in classified construction cost c.

The Fe_cj differs from the range of work package costs. It is difficult to determine the minimum error rate in terms of the total work package cost. This is because the input of construction workers is different for different work packages. Therefore, this study classifies work package costs into five ranges. The ranges are presented in Section 4.2.2.

4. Results

4.1. Results of Estimating the Labor Ratio for Work Package Type in Apartment Construction

This study collected real data from the “B” construction company in South Korea, which has completed 24 construction projects. The data included the total cost and number of workers for each type of work package and work type. This study considers 16 types of work packages and 30 types of work. Subsequently, the study selected the activity types that were included in each work type based on “Project Cost Estimating 2022”. Considering the Construction Association of Korea, the average wages of workers and number of construction workers classified based on work package were collected (see

Table 3. Value of W_j.

$\mathbf{Type} \mathbf{of} \mathbf{Work} \mathbf{Package} \left(\mathit{j}\right)$	2013	2015	2016	2017
Interior architecture work	81.94	90.02	99.88	106.39
Earth work	79.57	87.47	95.00	102.64
Plastering and waterproofing, masonry work	79.09	86.70	96.45	103.48
Stone work	83.50	89.63	99.11	105.91
Painting work	76.45	83.51	91.61	98.21
Scaffolding, demolition work	83.20	90.62	99.69	106.85
Metal structure, window and doors work	81.43	88.78	97.96	104.58
Roofing, sheet metal, prefabrication work	77.80	83.33	92.61	99.10
Reinforced concrete work	88.62	100.81	111.36	119.23
Facilities and mechanical works, firefighting system installation work	77.49	84.56	92.76	99.37
Landscape gardening work	78.92	87.99	94.98	101.78
Elevator and escalator installation works	79.80	89.30	97.75	104.83
Gas facilities work	90.65	98.67	108.82	114.42
Non-categorized work	75.59	81.45	90.06	96.20
Electronic work	74.59	81.04	89.37	95.60

).

First, this study considers 16 types of work package. Because there is a lack of data on road pavement work, this study removed road pavement work to ensure the reliability of the results. Finally, this study considered 15 types of work packages, from interior architecture work to electronic work. Further, considering the collected data, the data not provided were excluded to ensure the reliability of the results.

We calculated the estimated labor ratio using Equations (2)–(4) (see

Table 4. Value of Re_j.

$\mathbf{Type} \mathbf{of} \mathbf{Work} \mathbf{Package} \left(\mathit{j}\right)$	Rej
Interior architecture work	13.50%
Earth work	26.96%
Plastering and waterproofing, masonry work	38.08%
Stone work	18.35%
Painting work	19.42%
Scaffolding, demolition work	23.08%
Metal structure, window and doors work	4.23%
Roofing, sheet metal, prefabrication work	15.02%
Reinforced concrete work	62.24%
Facilities and mechanical work, firefighting system installation	21.72%
Landscape gardening work	13.72%
Elevator and escalator installation work	5.22%
Gas facilities work	10.72%
Other work	12.79%
Electronic work	22.46%

). The results revealed that the estimated labor ratio for the type of work package was high: 62.24% for “Reinforced concrete work”, 38.8% for “Plastering and waterproof work”, and 26.96% for “Scaffolding, demolition work”. In contrast, the estimated labor ratio for work package was low: 4.23% for “Metal structure, window and doors work”, 5.22% for “Elevator and escalator installation work”, and 10.72% “Gas facilities work”. Considering all types of work packages, the average estimated labor ratio was 20.39%. The estimated labor ratio is utilized in Equation (5) to calculate the estimated number of workers.

Table 5. Value of N_j and Ne_j and error rate.

$\mathbf{Type} \mathbf{of} \mathbf{Work} \mathbf{Package} \left(\mathit{j}\right)$	Nj	Nej	Error Rate
Interior architecture work	13,252	12,897	2.68%
Earth work	9153	9338	2.03%
Plastering and waterproofing, masonry work	13,157	13,018	1.05%
Stone work	2019	2389	18.33%
Painting work	1608	1578	1.85%
Scaffolding, demolition work	2185	2460	12.55%
Metal structure, window and doors work	3655	2999	17.95%
Roofing, sheet metal, prefabrication work	273	201	26.44%
Reinforced concrete work	54,210	55,308	2.03%
Facilities and mechanical work, firefighting system installation	11,843	11,952	0.92%
Landscape gardening work	2740	2249	17.90%
Elevator and escalator installation work	531	523	1.47%
Gas facilities work	386	412	6.93%
Other work	2569	2577	0.30%
Electronic work	8357	8493	1.63%

presents the results.

Referring to Table 5, N_j and Ne_j were calculated using Equation (5). The number of workers for work package type was calculated from real data. To compare N_j with Ne_j, Equation (6) was used.

The results are shown in Figure 2 and Table 5. For the average error rate, the three types of work package with the lowest error rate were “Non-categorized work” (0.30%), “Facilities and mechanical work and Fire system installation work” (0.92%), and “Plastering and waterproofing, masonry work” (1.05%). In contrast, the three types of work packages with the highest error rates were “Roofing, sheet metal, prefabrication work” (26.44%), “Stone work” (18.33%), “Metal structure, window and doors work” (17.95%). Additionally, the minimum and maximum error rates for the 15 types of work package at each construction site were analyzed. For each construction site, the maximum error rate represents the highest error rate among the 24 construction sites. In addition, the minimum error rate indicates the lowest error rate among the 24 construction sites. The three work package types with the highest maximum error rates were scaffolding and demolition (1117.70%), landscape gardening (1079.78%), and elevator and escalator installation (689.93%). On the contrary, for the minimum error rate, three types of work package had the lowest error rate: “Facilities and mechanical work, firefighting system installation” (0.08%), “Gas facilities work” (0.14%), and “Metal structure, window and doors work” (0.42%).

A comparison of Table 5 and

Table 6. Error rate per work package type at 24 construction sites.

$\mathbf{Type} \mathbf{of} \mathbf{Work} \mathbf{Package} \left(\mathit{j}\right)$	Max	Min
Interior architecture work	74.58%	2.98%
Earth work	238.50%	5.55%
Plastering and waterproofing, masonry work	44.72%	1.74%
Stone work	508.60%	3.23%
Painting work	321.58%	2.93%
Scaffolding, demolition work	1117.70%	7.88%
Metal structure, window and doors work	81.33%	0.42%
Roofing, sheet metal, prefabrication work	103.23%	3.11%
Reinforced concrete work	54.41%	4.94%
Facilities and mechanical work, firefighting system installation	50.67%	0.08%
Landscape gardening work	1079.78%	5.23%
Elevator and escalator installation Work	680.93%	1.50%
Gas facilities work	69.58%	0.14%
Other work	417.64%	2.97%
Electronic work	91.59%	1.55%

shows a very large deviation in the error rate. On average, the error rate was confirmed to be acceptable. However, the error rate at each construction site was not acceptable. Therefore, to estimate the number of construction workers with high reliability and accuracy, the error rate must be reduced at each construction site. Therefore, this study suggests two approaches using correction factors.

4.2. Results of the Correction Factors

4.2.1. Value of Fm_j

A correction factor was used in two ways in this study to reduce the error rate. First, this study suggests Fm_j, which can reduce the MSE for work package type at each construction site and is given by Equation (8). This correction factor makes it possible to guarantee high reliability and accuracy.

After applying Fm_j, the estimated number of workers Nfm_j was calculated. And Equation (12) shows the estimated number of workers; applied Fm_j.

$${Nfm}_{ij}={Fm}_j{Ne}_{ij}$$

(12)

The results revealed the MSE and Fm_j presented in

Table 7. Values of MSE and Fm_j.

$\mathbf{Type} \mathbf{of} \mathbf{Work} \mathbf{Package} \left(\mathit{j}\right)$	MSE	Fmj
Interior architecture work	10,600,897	1.04
Earth work	15,004,013	0.90
Plastering and waterproofing, masonry work	7,818,733	1.01
Stone work	425,468	0.82
Painting work	403,856	1.03
Scaffolding, demolition work	2,362,608	0.79
Metal structure, window and doors work	1,315,173	1.26
Roofing, sheet metal, prefabrication works	24,602	1.31
Reinforced concrete work	92,460,460	0.96
Facilities and mechanical work, firefighting system installation	8,273,049	0.99
Landscape gardening work	12,511,472	1.45
Elevator and escalator installation work	152,258	0.98
Gas facilities work	13,469	0.86
Other work	1,393,565	0.98
Electronic work	3,709,851	0.95

, and the N_j, Ne_j, Nfm_j are compared in

Table 8. Value of Nfm_j.

$\mathbf{Type} \mathbf{of} \mathbf{Work} \mathbf{Package} \left(\mathit{j}\right)$	Nj	Nej	Nfmj
Interior architecture work	13,252	12,897	13,412
Earth work	9153	9338	8440
Plastering and waterproofing, masonry work	13,157	13,018	13,207
Stone work	2019	2389	1962
Painting work	1608	1578	1622
Scaffolding demolition work	2185	2460	1950
Metal structure window and doors work	3655	2999	3789
Roofing, sheet metal, prefabrication work	273	201	262
Reinforced concrete work	54,210	55,308	53,333
Facilities and mechanical work, firefighting system installation	11,843	11,952	11,791
Landscape gardening work	2740	2249	3262
Elevator and escalator installation work	549	523	449
Gas facilities work	386	412	404
Other work	2569	2577	2453
Electronic work	8357	8493	8083

.

4.2.2. Value of Fe_cj

Second, considering the range of total work package costs for each type of work package, this paper proposes Fe_cj to reduce the error rate. Fe_cj is given in

Table 9. Value of Fe_cj.

$\mathbf{Type}\mathbf{of}\mathbf{Work}\mathbf{Package}\left(\mathit{j}\right)$	Total Construction Cost(c) (100 Thousand USD $)	Fecj	$\mathbf{Work}\mathbf{Package}\mathbf{Type}\left(\mathit{j}\right)$	Total Construction Cost(c) (100 Thousand USD $)	Fecj
Interior architecture work	Under 1	1.00	Reinforced concrete work	Under 1	1.00
	1 to 5	0.74		1 to 5	1.21
	5 to 10	1.02		5 to 10	1.01
	10 to 15	0.87		10 to 15	0.96
	Over 20	1.19		Over 20	0.96
Earth work	Under 1	0.90	Facilities and mechanical work, firefighting	Under 1	1.00
	1 to 5	0.66		1 to 5	1.00
	5 to 10	1.06		5 to 10	1.11
	10 to 15	1.01		10 to 15	0.94
	Over 20	0.59		Over 20	1.22
Plastering and waterproofing, masonry work	Under 1	1.00	System installation	Under 1	1.00
	1 to 5	1.00		1 to 5	1.00
	5 to 10	1.00		5 to 10	0.57
	10 to 15	1.07		10 to 15	1.30
	Over 20	0.94		Over 20	1.00
Stone work	Under 1	1.00	Landscape gardening work	Under 1	1.00
	1 to 5	1.00		1 to 5	1.00
	5 to 10	1.00		5 to 10	1.00
	10 to 15	1.12		10 to 15	0.98
	Over 20	0.80		Over 20	1.06
Painting work	Under 1	1.00	Elevatorand escalator installation work	Under 1	1.00
	1 to 5	1.00		1 to 5	1.00
	5 to 10	1.00		5 to 10	1.00
	10 to 15	1.00		10 to 15	1.00
	Over 20	0.90		Over 20	0.94
Scaffolding, demolition work	Under 1	1.09	Gas facilities work	Under 1	1.00
	1 to 5	1.00		1 to 5	1.00
	5 to 10	1.00		5 to 10	1.00
	10 to 15	1.00		10 to 15	1.00
	Over 20	1.00		Over 20	1.00
Metal structure, window and doors work	Under 1	1.39	Other work	Under 1	0.26
	1 to 5	0.78		1 to 5	1.01
	5 to 10	1.00		5 to 10	0.94
	10 to 15	1.00		10 to 15	1.00
	Over 20	1.00		Over 20	1.00
Roofing, sheet metal, rrefabrication work	Under 1	1.30	Electronic work	Under 1	1.05
	1 to 5	1.00		1 to 5	0.96
	5 to 10	1.00		5 to 10	0.82
	10 to 15	1.00		10 to 15	1.00
	Over 20	1.00		Over 20	1.00

and calculated using Equation (11).

After Fe_cj was calculated, it was used to calculate the number of estimated workers Nfe_cij for the type of work package at each construction site. Equation (13) shows the estimated number of workers; applied Fe_cj.

$${Nfe}_{cij}={Fe}_{cj}{Ne}_{cij}$$

(13)

And

Table 10. Result of the error rate with Fe_j for work package type at a construction site.

$\mathbf{Type} \mathbf{of} \mathbf{Work} \mathbf{Package} \left(\mathit{j}\right)$	Nj	Nej	Nfej	Standard Deviation	Average Error Rate
Interior architecture work	13,252	12,897	13,252	6476.62	15.42%
Earth work	9153	9338	9158	4404.66	34.98%
Plastering and waterproofing, masonry work	13,157	13,018	13,157	4668.15	18.88%
Stone work	2019	2389	2019	1797.73	54.62%
Painting work	1608	1578	1608	606.04	42.27%
Scaffolding, demolition work	2185	2460	2185	717.66	120.02%
Metal structure, window and doors work	3655	2999	3655	1789.73	25.84%
Roofing, sheet metal, prefabrication work	273	201	273	125.56	58.38%
Reinforced concrete work	54,210	55,308	54,210	18,010.86	14.50%
Facilities and mechanical work, firefighting system installation	11,843	11,952	11,843	5019.15	17.73%
Landscape gardening work	2740	2249	2740	1725.50	76.27%
Elevator and escalator installation Work	549	523	549	251.80	104.04%
Gas facilities work	386	412	386	163.82	20.98%
Other work	2569	2577	2569	1081.56	62.08%

shows N_j, Ne_j, and Nfe_j.

4.3. Analysis of the Correction Factors

4.3.1. Analysis of Fm_j

The error rate between N_j and Nfm_j was calculated using Equation (6) (see Figure 3). As shown in Figure 3, the error rate and error rate with Nfm_j, which indicate the error rate between N_j and Nfm_j, are comparable. Further, Figure 3 also includes the difference between the error rate and the error rate with Nfm_j and without Nfm_j.

The error rate can be reduced by applying Fm_j; for the maximum error, three work package types had the highest error rates: scaffolding and demolition (865.54%), elevator and escalator installation work (570.46%), and stone work (399.46%). In contrast, for the minimum error rate, three types of work package had the lowest error rates: “electronic work” (0.00%), “stone work” (0.27%), and “earth work” (0.31%). Compared to

Table 11. Calculation of the error rate with Fm_j for work package types at construction sites.

Work Package Type	Max	Min
Interior architecture work	81.55%	1.29%
Earth work	205.94%	0.31%
Plastering and waterproofing, masonry work	46.81%	2.01%
Stone work	399.64%	0.27%
Painting work	333.13%	2.27%
Scaffolding, demolition work	865.54%	1.89%
Metal structure, window and doors work	129.14%	16.48%
Roofing, sheet metal, prefabrication works	165.43%	3.89%
Reinforced concrete work	48.90%	0.32%
Facilities and mechanical work, firefighting system installation works	48.64%	38.17%
Landscape gardening work	100.00%	3.53%
Elevator and escalator installation work	570.46%	0.31%
Gas facilities work	66.16%	2.19%
Non-categorized work	392.66%	0.51%
Electronic work	82.34%	0.00%

, the error rate of the variation can be reduced.

As mentioned above, the category with the highest maximum error rate was “Scaffolding, Demolition work” (1117.70%). However, after applying Fm_j, the category with the highest maximum error rate was “Scaffolding, demolition work” (865.54%). Therefore, Fm_j made it possible to more accurately estimate the number of workers for each type of work package at each construction site.

4.3.2. Analysis of Fe_cj

Figure 4 shows the error rates without and with Fe_cj, which indicates the error rate between N_j and Nfe_j. Also, Figure 4 includes the difference between the error rates without and with Fe_cj.

After applying Fe_cj, the error rate and error rate of variation can be simultaneously reduced. “Scaffolding, demolition work” (847.92%), “Elevator and escalator installation work“ (725.37%), and “Stone work” (582.29%) had the highest maximum error rates. In contrast, three work package types had the lowest minimum error rates. The error rate was 0.00% for six work package types: “Interior architecture work”, “Earth work”, “Reinforced concrete work”, “Facilities and mechanical work, firefighting system installation work”, “Non-categorized work”, and “Electric work”.

The error rate was lowest with Fe_cj.

As mentioned above, the category with the highest maximum error rate was “Scaffolding, demolition work” (1117.70%). However, after applying Fe_cj, the category with the highest maximum error rate was “Scaffolding, demolition work” (847.92%). Therefore, using Fe_cj increases the accuracy of the estimation of the number of for each work package type at each construction site (Refer to the

Table 12. Error rate with Fe_cj per work package type in a construction site.

Type of Work Package	Max	Min
Interior architecture work	78.98%	0.00%
Earth work	259.16%	0.00%
Plastering and waterproofing, masonry work	54.30%	0.30%
Stone work	582.29%	1.00%
Painting work	278.60%	0.69%
Scaffolding, demolition work	847.92%	0.40%
Metal structure, window and doors work	79.13%	0.14%
Roofing, sheet metal, prefabrication work	159.50%	18.34%
Reinforced concrete work	48.51%	0.00%
Facilities and mechanical works, firefighting system installation work	52.69%	0.00%
Landscape gardening work	578.09%	3.43%
Elevator and escalator installation work	725.37%	0.32%
Gas facilities work	58.59%	0.39%
Non-categorized work	421.58%	0.00%
Electronic work	100.34%	0.00%

).

4.4. Discussion

The results of this study suggest a simplified estimation model by work package type using a correction factor based on real data from twenty-four apartment projects.

The results revealed that the type of work package with the highest labor ratio was reinforced concrete work (62.24%). Previous studies have shown that many construction workers are involved in reinforced concrete work, such as rebar, concrete, and form workers. When different types of workers were considered, worker input was higher than that in other types of work packages. Therefore, reinforced concrete work has the highest labor ratio compared with other types of work.

Three methodologies were used in this study to estimate the number of workers. The error rate was used to select the best methodology. First, the estimated number of workers was calculated using the estimated labor ratio. The error rate ranged from 1117.70% to 0.14%. This methodology had low accuracy in estimating the number of construction workers. Second, this methodology was employed to estimate the labor ratio and minimum MSE. Hence, to reduce the variation error rate, the correction factor, which can reduce the MSE for each type of work package at each construction site, was applied. The error rate for Fm_j ranged from 865.54% to 0.00%. The number of workers was estimated more accurately than the error rate. Third, this methodology was used to calculate the estimated labor ratio and Fe_cj for the minimum error rate of the total work package cost for each type of work package at each construction site. The error rate for Fe_cj ranged from 847.92% to 0.00%. Compared to the methods, this method had the lowest error rate variance.

Considering the three methods, this study suggests the third method as the best method for estimating the number of construction workers. Previous studies attempted to estimate the number of workers more accurately. However, they lacked real data, and their methods were difficult to use for non-experts. Given the limitations of previous studies, this study proposes a user-friendly, simple estimation model based on real data for the type of work package to ensure high reliability and accuracy.

Various areas were addressed using the estimated number of workers. First, the fatality rate in the construction work package can be calculated accurately for each work package type. At present, national reports on fatality rates only provide fatality rates for the entire construction industry. This is because they have no data on the number of workers in each type of work package. Therefore, if the most hazardous work package is identified, safety management can be strengthened for the work package to reduce the fatality rate. Second, the total construction cost in the pre-construction phases can be estimated based on the number of workers. Since labor costs account for 40–60% of the total cost, accurately estimating the labor cost for each work package type is important. In addition, when using Fe_cj, the number of construction workers can be estimated from the total work package cost. Previous studies estimated the number of workers using multiple regression widely. To verify the novelty of this model, this paper compared the result of the suggested model and the result using multiple regressor analysis and mean absolute error (MAE). Multiple regression analysis is a statistical method used to examine the relationship between a dependent variable and two or more independent variables. It is a powerful tool that allows researchers to assess the strength and direction of the relationship between the variables and to make predictions about the dependent variable based on the independent variables [23]. This paper used wage and construction cost as a dependent variable and the number of estimated workers as an independent variable. The result revealed that the equation was, following Equation (14):

$$y=4.35\times {10}^{-10}\times x_1+1.09\times {10}^{-3}\times x_2+0.10$$

(14)

where y is the estimated number of estimated workers, x₁ is the wage for type of section, and x₂ is the construction cost for type of section.

MAE is 467.4 and average error rate shows 48.2% and maximum error rate is 173.14%, minimum error rate is 2.56%. So, the suggested model is more accurate compared to multiple regression.

5. Managerial Insights and Practical Implications

If the manager of a construction company is available to adjust this model for cost planning or safety management, the model can be used to estimate the labor cost per work package type or the estimated number of workers to derive the fatality rate per work package type at construction sites. Details of the use of the model are as follows.

5.1. Economic Implication

In the design state, the manager plans a budget for construction costs. With the proposed model, the manager can more accurately budget for labor costs per work package type. The manager inputs the construction costs for work package type, uses the labor ratio obtained in this study for each work package type, and estimates the labor cost of the total construction project.

5.2. Safety Implication

The manager must manage the construction site to ensure safety management. However, managers often have limited human resources, budget, and time for managing the entire construction site. Therefore, this framework can be used to calculate the reliability of fatality rate estimates [16] or identify high-risk work package types at construction sites, which allows the manager to use their limited resources efficiently

6. Conclusions

The construction industry is labor-intensive, making the accurate estimation of the number of workers important. However, previous studies did not use real data, and their proposed methods were challenging for non-experts to use. To address these issues, this study developed a simple estimation model for the number of workers per work package type using a correction factor based on real data from an apartment project.

This study contributes to the literature in several ways. First, the proposed methods can be used in a framework to estimate the number of workers per work package type. Second, through the labor ratio of each work package type, the number of workers can be estimated with greater accuracy. In addition, this study suggests a framework for estimating the labor ratio of the total construction costs. Therefore, this framework can help decision makers plan for a construction project or calculate costs using factors such as construction costs or average wages. This framework can be applied to other work packages and countries using average wages, used to classify work packages by local law, and estimate construction costs. Furthermore, this study suggests a framework that enhances reliability using statistical methods.

This study has the following limitations. This study’s limitations include the limited data collection from a single construction company in South Korea and the need for further research to develop a more comprehensive estimation model that considers the entire construction project. Also, the proposed estimation model mainly focuses on the labor ratio by work package type and does not consider other factors that may affect the number of workers required for a construction project. Future studies could expand upon this research by collecting real data from multiple construction companies in various countries and industries to increase the generalizability of the proposed method. Additionally, the development of an estimation model that considers a wider range of variables, such as project complexity and workforce diversity, could be an area of future research.