Simulation-based framework for optimal construction equipment allocation considering construction noise emissions

ABSTRACT As construction noise has been a major environmental emission from the construction sites, construction equipment allocation should be planned to preemptively manage construction noise emissions while considering productivity. Therefore, this study aims to propose a simulation-based framework for determining optimal construction equipment allocation to manage construction noise and improve economic performance. The optimal construction equipment allocation in terms of direct cost and noise exposure was determined using a Web-based CYCLic Operation NEtwork (WebCYCLONE) and exhaustive search technique. The feasibility of the proposed framework was validated through a case study of a real project. The proposed framework could predict direct costs and noise emissions of the construction process within the allowable error. Based on the simulation-based prediction, the optimal allocation in terms of direct cost and noise exposure level reduces USD 2,186.65 (24.6%) out of USD 8,873.84 in the direct cost or 4.4 dB (5.0%) out of 88.59 dB in noise exposure level of residents. Moreover, the optimal allocation in terms of direct cost and compensation cost reduces USD 881.45 (0.6%) out of USD 154,316.63 in the overall costs. Finally, the proposed framework could help construction managers establish a plan to improve the economic and environmental performances in the planning stage.


Introduction
High levels of construction noise on construction sites are one of the major pollutants detrimental to the urban environment (Liu et al. 2017;Hong et al. 2021;Jung et al. 2020). In addition, construction noise arising from the operation of construction equipment during repetitive construction activities causes damage to the quality of life and health among residents living near the construction site (Miedema 2007;Lee, Hong, and Jeon 2015). Particularly, people around the construction site (e.g., residents, construction workers, and site managers) exposed to continuous construction noise are likely to suffer from various mental and physical disorders such as psychological stress, hearing loss, and cardiovascular disease (Ibrahim, El-Anwar, and Marzouk 2018;Clark and Paunovic 2018;Kwon et al. 2016;Hong et al. 2022a;van Kempen et al. 2018). Therefore, construction companies are obliged to manage construction noise emissions in accordance with administrative guidelines and regulations (Gazette 2013;National Environmental Conflict Resolution Commission 2019). If the construction companies do not meet their obligations to deal with construction noise problems, they may have conflicts, especially with the residents. Then, they suffer greater economic losses due to social costs incurred from civil complaints from residents and disputes with residents Ballesteros et al. 2010;Kwon et al. 2018). Particularly, in South Korea, in 2020, damages for disputes caused by noise in construction and transportation sectors amounted to about $1.6 million (ECC (Central Environmental Conflict Mediation Commission) 2020). Accordingly, in order to minimize economic losses due to noise emissions, construction companies need to reduce the damage caused by construction noise exposure, especially of residents, among those around the construction sites.
There are still limits in reducing construction noise after its generation. Therefore, the establishment of a plan considering construction noise emissions in the planning stage is important to effectively manage construction noise (refer to Table 1). In this regard, many previous studies have been conducted regarding the preemptive management of construction noise. First, previous studies attempted to predict construction noise levels at various locations based on numerical formulas and sound propagation simulation tools. Gannoruwa and Ruwanpura (2007) and Hong et al. (2014) substituted the distribution of construction noise levels for construction equipment into the noise attenuation formula to predict the construction noise level at a specific point. Xiao, Li, and Zhang (2016) predicted the noise exposure level of residents living in nearby buildings by substituting a single construction noise level for construction equipment collected via field monitoring into acoustics simulation software. Lee, Il Chang, and Park (2008) developed a noise mapping framework to predict the construction noise level in an area around a construction site assuming all the construction equipment as a singlepoint source. Second, other studies were designed to reduce the construction noise exposure level by establishing mitigation measures in the planning stage based on the construction noise prediction. Ning et al. (2019) and Hammad, Akbarnezhad, and Rey (2016) reduced construction noise exposure by determining the optimal construction site layout for facilities. Jung et al. (2020) considered the impacts of noise on residents' health and the installation cost of barriers to determine the optimal barrier height.
To sum up, most of the previous studies sought to predict construction noise emissions through various methods and establish construction and site plans to reduce construction noise emission in the planning stage. Despite these efforts, there were still limitations in reducing construction noise through proper scheduling for construction equipment, a main source of noise in the construction process: (i) lack of research designed to reduce construction noise through construction equipment scheduling; and (ii) failure to reflect the actual work of construction equipment when predicting construction noise. First, studies on reduction construction noise through construction equipment scheduling were insufficient since the main purpose of construction equipment scheduling is not to reduce construction noise. In the construction industry, the main purpose of construction equipment scheduling is to improve productivity and reduce construction duration through the proper allocation of construction equipment during the construction project. Therefore, construction equipment scheduling is an important planning factor for the successful completion of a construction project from an economic point of view (Zhang 2012;Wang et al. 2020;Karshenas and Haber 1990;Chan, Chua, and Kannan 1996). Zhang (2012) minimized project duration by solving a multimode resource-constrained project scheduling. Wang et al. (2020) optimized trackless equipment scheduling in underground mines to minimize working time and working interval. Karshenas and Haber (1990) developed project schedule optimization model to minimize the total project cost. In other words, construction equipment scheduling that only considers construction noise emissions without regard to the management of the construction noise emissions or vice versa may result in the economic failure of the construction project. Therefore, optimal construction equipment allocation should be decided considering the direct costs of construction equipment and construction noise emissions during the construction process. Second, most of the studies have limitations in that they only take into account the location or type of construction equipment but fail to reflect the execution time taken to perform the actual work when predicting construction noise. The inadequate consideration of the actual execution time of construction equipment leads to an overestimation or underestimation of the construction noise emissions. For example, if idle time for construction equipment is not considered, excessive construction noise reduction measures may be applied due to the overestimation of the construction noise emissions. In particular, since there is a precedence relationship between several tasks in the construction process, all equipment may not work although large amounts of construction equipment were mobilized (Monghasemi and Abdallah 2021). Therefore, it is necessary to predict construction noise more accurately, which varies depending on the construction equipment allocation plan, in the planning stage for preemptive management of construction noise emissions.
In this regard, this study aims to propose a framework for determining the optimal construction equipment allocation considering the construction cost and construction noise emission with the use of a simulation tool in the planning stage. To this end, a simulation model using the Web-based CYCLic Operation NEtwork (WebCYCLONE), a discrete-event simulation (DES) technique capable of simulating the cyclic construction process of multiple activities that comprise tasks, is built for the cyclic construction process to predict the direct cost of allocating construction equipment and noise exposure level of residents (Halpin 1973;Senior 1995;Lu and Chan 2004;Lu and Olofsson 2014). In the construction industry, the DES technique has been used for optimizing the construction process to achieve the individual objectives of the construction project, as in this study. Ahn et al. (2022) synchronized the factory and the construction site in off-site construction by optimizing the truckdispatching schedule using the DES technique. Dashti et al. (2021) proposed the integrated approach based  (2016); Jung et al. (2020) on DES, building information modeling (BIM), and rapidly exploring random tree path planning to manage the time-space conflicts in a construction site automatically. Frough, Khetwal, and Rostami (2019) predicted the utilization factor and advance rate of tunnel boring machines in tunneling projects by modeling the tunneling process using the DES technique.
In addition, the process to find the optimal construction equipment allocation using exhaustive search technique to minimize the multiple objectives is proposed. In order to verify the effectiveness of the proposed framework, a case study was conducted on earthwork containing bedrock from which high levels of construction noise arise due to the operation of heavy equipment (Xiao, Li, and Zhang 2016;Choi et al. 2021). It is expected that the proposed framework can allow construction managers and companies to more accurately predict the cost and noise emission of the construction process and determine the optimal construction equipment allocation, thereby contributing to improving the economic and environmental performances of the construction project.

Materials and methods
The simulation-based framework for determining optimal construction equipment allocation considering construction noise emissions was developed in three steps (refer to Figure 1). First, in order to establish the basic data to predict the cost and noise emission of the construction process in the planning stage, a simulation model of the construction process is established using the WebCYCLONE. Second, the two objective values (i.e., (i) direct costs of the construction process and (ii) noise exposure levels and compensation costs of residents on construction noise) according to construction equipment allocation is estimated based on productivity, the number of cycles for each activity, and their average durations per cycle resulted from the established WebCYCLONE simulation model. Third, the optimal construction equipment allocation is determined in terms of direct cost and noise exposure level, with the compensation cost using the exhaustive search technique. Before determining the optimal construction equipment allocation, data as shown in Table 2 should be collected through an interview with a construction site manager.

Establishment of the construction process simulation model using WebCYCLONE
In cyclic construction processes, tasks are performed repeatedly, and there is a precedence relationship in each task that should precede the execution of the next task. To take this into account, this study performed a simulation of the cyclic construction process using the WebCYCLONE (WebCYCLONE simulation) developed by (Halpin 1973). WebCYCLONE is a simulation technique that graphically represents the logical relationships of various activities in the cyclic construction process and optimizes the construction process based on deterministic or stochastic variables of activities. In many previous studies, it was used for data generation and productivity analysis on cyclic construction operations and processes, and their accuracy and usability were verified (Kim et al. 2021;Han et al. 2006;Cheng and Yan 2009). In this study, more realistic productivity and execution time for each construction equipment to perform activities is required for a more accurate prediction of direct cost and noise exposure level. Therefore, the WebCYCLONE simulation is conducted as the following procedure. First, in the WebCYCLONE, the construction process can be modeled by defining nodes related to the activities constituting each task and establishing a precedence relationship between nodes (refer to Table 3). Elements with different shapes represent different types of nodes, while arrows represent precedence relationships between nodes. NORMAL elements represent activities that can be performed immediately when the previous node completes its execution. Thus, activities in NORMAL elements can be performed without constraints such as availability of construction materials or resources. COMBI elements represent activities like NORMAL elements, but differ from NORMAL elements in that they can be executed after precedent constraints are met. For instance, concrete pumps can transfer liquid concrete by pumping only when the constraint that an available concrete pump is prepared from a ready-mixed concrete truck has been met. QUE elements represent the idle state of a resource entity and become precedent constraints for the execution of the nodes defined as the COMBI elements. Therefore, the nodes defined as the COMBI elements should be connected after the nodes defined as the QUE elements. GEN and CON elements indicate that a single unit of a resource entity is divided into several entities and merged into a single unit again. The COUNTER element performs a function that accumulates one each time the unit passes to measure the number of cycles in the entire construction process. Productivity can be calculated based on the accumulated number of cycles counted by this element. Further information regarding the WebCYCLONE can be found in (Halpin and Riggs 1992).
Second, the duration of each activity should be entered in the WebCYCLONE simulation model. Therefore, duration data corresponding to the nodes of NORMAL and COMBI elements should be collected. The duration data are composed of the type of distribution and values that can represent each distribution for probabilistic simulation. In general, the duration data are collected by directly measuring at construction sites and determining the proper distributions and parameters using statistical methods such as goodness-of-fit test (Maio et al. 2000;Fente, Schexnayder, and Knutson 2000;AbouRizk and Halpin 1990). However, in this study, the construction process is to be simulated in the planning stage to find the optimal construction equipment allocation by predicting the direct cost and noise exposure. Therefore, the duration data of activities are indirectly collected via Standard of  What construction process do you want to target? 2 What activities does the target construction process consist of? 3 What about the precedence relationship between activities? 4 What types of construction equipment are used in the target construction process, and where are their working areas? 5 What is the minimum allocation for each construction equipment required to carry out the target construction process?
Construction Estimate and planning information of the construction process (KICT (Korea Institute of Civil Engineering and Building Technology) 2022). Finally, based on the established construction process model and generated data, a WebCYCLONE simulation of the cyclic construction process is conducted. The simulation process is set to perform a sufficient number of cycles until a steady state was reached because the productivity at the initial state where all resources are available is not stable. The simulation results include productivity (cycle per second) for the whole construction process, the number of cycles for each activity, and their average durations per cycle. The simulation results are used as basic data for estimating the direct cost and noise exposure level.

Estimation of objective values
In order to determine the optimal construction equipment allocation, the values of multiple objectives defined in this study are calculated based on the WebCYCLONE simulation results. First, the direct costs of construction equipment used in the construction process are calculated. Second, the noise exposure level of residents around the construction site and the compensation costs for construction noise they can receive from construction companies are calculated. In particular, objectives related to noise emissions can be either noise exposure level or compensation cost. If the noise exposure level is directly defined as one of the multiple objectives with the direct cost, Pareto optimal solutions for direct cost and noise exposure level are obtained and one of the solutions can be decided. Therefore, progress of construction and current site conditions can be reflected to the final decision by site managers to accurately consider the current workload. Meanwhile, if compensation cost is defined as one of the multiple objectives with the direct cost, the multiple objectives can be transformed into the single objective since both the direct cost and compensation cost are the economic value. However, compensation cost can be estimated when residents are exposed to construction noise over a period of time. Accordingly, assumptions for the daily workload are needed, and errors may occur due to changes in the condition and schedule of the actual construction project. Therefore, the single optimal allocation can be effective for the whole construction process planning in the early stage. The detailed calculation procedures for each objective are presented in the following sections.

Direct cost of the construction equipment
Direct costs consist of the cost of materials consumed to operate construction equipment, the cost of labor operating the construction equipment, and expenses that refer to all costs (e.g., depreciation cost, operation cost, etc.) excluding the material and labor costs (Lee, Son, and Lee 2014). In particular, the direct cost of construction equipment is calculated by multiplying the rent hours of construction equipment by the rental rate. In other words, the input of an appropriate number of construction equipment in the construction process makes it possible to reduce working hours due to high productivity and thus save direct costs. Therefore, the working hours required to carry out the construction process were calculated based on productivity calculated in the WebCYCLONE simulation and required amount of work. In addition, the hourly unit cost of material, labor, and expenses for each construction equipment can be collected from the Standard of Construction Estimate (KICT (Korea Institute of Civil Engineering and Building Technology) 2022). As a result, the direct cost for each construction equipment is calculated by multiplying the estimated working hours by the sum of material and labor costs and expenses for each construction equipment. The final direct cost is calculated by summing the direct cost of all the construction equipment (refer to Eq. (1)).
where, Direct cost is the direct cost of the construction process, Working hours is the working hours of the construction process, C i material is the material cost per hour for construction equipment i, C i labor is the labor cost per hour for construction equipment i, and C i expenses for the expenses per hour for construction equipment i.

Noise exposure level and compensation cost for residents
Construction noise arises from the activity of construction equipment. Therefore, the time taken for construction equipment to perform the activity is estimated to predict the noise exposure level of residents. In addition, the compensation costs for residents are estimated. In this study, more realistic productivity and execution time for each construction equipment to perform activities is required for a more accurate prediction of noise exposure level.
First, the execution time for each construction equipment to perform activities is calculated based on the WebCYCLONE simulation results, which include the number of cycles of activities and its average duration per cycle. Therefore, the duration of the activity is obtained by multiplying the number of cycles for each activity and duration per cycle. Then, the execution time for each construction equipment is calculated by summing the duration of activities performed by construction equipment. After that, the execution time per unit of construction equipment is calculated by dividing it by the number of units. For instance, if two units of construction equipment are assumed to be engaged in three activities of which number of cycles is 3, 6, and 4 and durations per cycle are 10 s, 20 s, and 10 s, respectively, during working hours of the construction site. The durations of those activities are then estimated as 30 s, 120 s, and 40 s. As a result, the execution time per unit of the construction equipment is 95 s (i.e., 190 s/2 units).
Second, the average noise exposure level of residents is calculated for construction noise arising from the activity of construction equipment during the construction process. Therefore, the equivalent noise level (Leq), which is an environmental noise measure adopted by the Environmental Protection Agency (EPA), was calculated (World Health Organization 2018). The Leq can represent the average exposure level to environmental noise that changes for a certain period of time. The method of calculating the noise exposure level among residents in building a for all construction equipment (Leq (all,a) ) used during the construction process is as follows: First, to estimate the sound pressure level of construction equipment i measured in building a (SPL (i,a) ), the attenuation by the distance from the operating location of construction equipment i to building a is subtracted from the SPL (i,15m) measured at the reference radius (i.e., the standard of the distance at which SPL is measured and 15 m in South Korea) (refer to Eq. (2)) (Hong et al. 2014). Next, in order to convert the SPL applied with the noise attenuation to Leq that represents the average noise exposure level during working hours for the construction process, the Leq of residents in building a for construction equipment i (Leq (i,a) ) is calculated using the ratio of execution time of construction equipment i during working hours for the construction process (refer to Eq. (3)) . Lastly, the Leq (all,a) was calculated by synthesizing the Leq of residents in building a for all construction equipment (refer to Eq. (4)).
where SPL (i,a) is the sound pressure level at building a for construction equipment i, SPL (i,15m) is the sound pressure level of construction equipment i at the reference radius distance, r (i,a) is the radius between construction equipment i and building a, r r is the reference radius (15 m), Leq (i,a) is the equivalent noise level at building a for construction equipment i, ET i is the execution time of construction equipment i, Working hours is the working hours of the construction process, Leq (all,a) is the equivalent noise level at building a for all construction equipment, and n is the number of all construction equipment.
Third, compensation costs that a construction company should pay to residents can be estimated based on regulations and legal guidelines. In accordance with the standards of compensation costs to be paid to residents according to the noise exposure level and exposure period of construction noise set by the Ministry of Environment (MOE) in South Korea, the minimum compensation cost for a noise exposure level of 66 dB for at least 6 months is USD 120.9, while the maximum compensation cost for a noise exposure level of 85 dB within the same period is USD 1,250.5 (Central Environmental Conflict Resolution Commission 2022). Based on the above standards, the compensation cost is calculated according to the noise exposure level in units of 1 dB via linear interpolation. Since the calculated compensation cost for each building is paid to the residents of each building, the final compensation cost was calculated by multiplying the number of residents in each building.

Determination of the optimal construction equipment allocation using exhaustive search technique
In this section, the process for determining the optimal construction equipment allocation considering noise emissions is presented. An exhaustive search technique is used to find the optimal construction equipment allocation based on the estimated objective values. The exhaustive search technique finds the optimal solution by exploring all the possible alternatives of decision variables which are the number of allocations for each type of construction equipment in this study. Although the upper bound of the number of allocations is not limited itself, there exist the maximum numbers of allocations for each type of construction equipment that can improve the productivity of the construction process. Therefore, the following process is proposed for effectively determining the maximum number of allocations (refer to Figure 2). This process can be applied to any construction process where multiple-construction equipment is used.
In the first step, the set and parameter related to the termination condition of this process are defined. Initially, the set is defined to be empty, and the parameter is defined as the number of elements in the set. In the second step, the minimum number of allocations for each type of construction equipment is entered as an initial value that could be increased to the maximum number of allocations. In the third step, the target equipment is selected among types of construction equipment not included in the set, and the number of allocations for the target equipment increases by one. This step is repeated until productivity no longer increases. In the fourth step, if productivity does not increase, the corresponding construction equipment is included in the set. Then, it is checked whether the termination condition of the process is satisfied. The termination condition in this process is whether the number of elements in the set is equal to the number of types of construction equipment. If the termination condition is not satisfied, the process returns to the third step. The third and fourth steps are repeated until the termination condition is satisfied. In the fifth step, if the termination condition is satisfied, the current number of allocations for each type of construction equipment is determined as the maximum number of allocations.
Based on the found maximum number of allocations, the possible alternatives of construction equipment allocation are decided. In addition, direct cost, noise exposure level, and compensation cost of those alternatives are estimated as presented in Section 2.2. Finally, Pareto optimal construction equipment allocations in terms of direct cost and noise exposure level and single optimal construction equipment allocation in terms of direct cost and compensation cost are obtained by comparing the estimation results of all alternatives.

Case study
To verify reliability and applicability of the developed framework, a case study was conducted on the construction project of "M" school building. The site of the construction project was located in Seoul, where most civil complaints about construction noise are reported in South Korea (Central Environmental Conflict Mediation Commission 2020). Particularly, since only vehicles for construction work could pass the nearby roads of the construction site, which were designated as the traffic control area, the effect of background noise from nearby traffic could be removed. Moreover, since residential buildings are located near the site, construction equipment allocation needs to be planned considering construction noise emissions. As the target construction process to be simulated, the crushing and transportation process of bedrock in the underground area from which high levels of construction noise arise was determined based on an interview with the construction site manager. Specifically, the interview selected the noisiest construction process as the target construction process. It included details about the target construction process (e.g., activities, precedence relationship between activities, working area, etc., of the process) and the minimum number of allocations of the construction equipment. Table 4 and Figure 3 present an overview and the site plan of the construction project of "M" school building.

WebCYCLONE based construction process simulation model
The target construction process consists of four tasks using four types of construction equipment (breakers, excavators, crawler cranes with a bucket, and dump trucks): (i) the breaker crushes rock located underground; (ii) the excavator transports the crushed rock and loads it into a bucket connected to a crawler crane; (iii) the crawler crane lifts the bucket and loads the crushed rock into a dump truck located on the ground; and (iv) the dump truck transports the crushed rock to a disposal area outside the construction site. The model for the target construction process of crushing and moving rock in underground is shown in Figure 4.
First, a total of 18 nodes constituting the target construction process were defined (refer to Table 5). Nodes 1, 4, 8, 15, 16, and 17 were defined as NORMAL elements representing activities that can be performed immediately when the previous node completes its execution. For instance, node 4, "Excavator travel to crawler crane" is located after node 3, "Excavator load rock" because the excavator can run immediately after loading the rock. In addition, node 1, "Breaker crush rock", the starting node of the activities, is started without the previous node in the first cycle. Whereas, in the subsequent cycles, node 1, "Breaker crush rock", is located after node 3, "Excavator load rock" because the breaker can crush rock immediately after new rocks to be broken appear by loading the rock. Nodes 3, 6, and 12 were defined as COMBI elements representing activities can be executed after precedent constraints are met. For instance, node 3, "Excavator load rock" can be executed only when the constraint that the rock crushed by the breaker (i.e., node 2) and the returned excavator (i.e., node 9) exist has been met. Nodes 2, 5, 9, 11, 13, and 18 were defined as QUE elements representing the idle state of a resource entity. For instance, node 5 (i.e., "Excavator wait for unloading") and 13 (i.e., "Crawler crane queue") become the precedent constraints of node 6 (i.e., "Excavator unload rock to bucket") that represents the excavators' activity to unload the rock to the bucket  connected to the crawler crane. Nodes 13 and 18 were defined as GEN elements indicating that a single unit of a resource entity is divided into several entities. Nodes 10 and 14 were defined as CON elements indicating several entities merged into a single unit. For instance, since the capacity of the bucket of the crawler crane (3 m 3 ) at node 13 was twice that of the excavator (1.5 m 3 ), GEN 2 was applied to node 13 to divide the capacity of the bucket of the crawler crane by 2 and reemerge it through CON 2 at node 10, which allows node 11 to be executed after node 6 has been executed twice. Node 7 was defined as a COUNTER element measuring the number of cycles. In this study, the number of passes of the excavator was calculated using the COUNTER element. Second, duration data corresponding to the nodes of NORMAL and COMBI elements (i.e.,nodes 1,3,4,6,8,12,15,16,and 17) were generated based on the Standard of Construction Estimate and planning information of the construction process (KICT (Korea Institute of Civil Engineering and Building Technology) 2022). For nodes 3 and 6, the time taken for the excavator to perform one cycle of loading and unloading rock activity was calculated using Eq. (5) given in the Standard of Construction Estimate. Since the base cycle time varies depending on the rotation angle, and the frequency of all rotation angles is evenly distributed in the target construction process, it was defined as a uniform distribution. In addition, the values corresponding to half of the cycle time calculated using Eq. (5) were entered because the time taken for the loading and unloading activity should be entered into nodes 3 and 6, respectively. For node 1, the cycle time (0.025 hr/m 3 ) of rock crushing using the breaker according to the Standard of Construction Estimate was entered as a deterministic value. For nodes 4 and 8, the distance that the excavator needs to move was calculated based on the rated speed of the excavator (12 km/h). In accordance with the site plan, the excavator has to move 0 m to 49 m and make a round-trip frequently around the center of the work area. Therefore, it was entered as a triangular distribution. For node 12, the cycle time of crawler crane with the bucket can be calculated by adding additional time according to the lifting distance to the base cycle time in accordance with the Standard of Construction Estimate (refer to Eq. (6)). In the target construction process, the lifting distance continued to increase from 5.5 m to 9.5 m, and it was thus entered as a uniform distribution. For nodes 15 and 17, the traveling time for 60 km, the distance to the disposal area, was entered based on the speed of loaded and empty dump trucks (50 km/h and 55 km/ h) given in the Standard of Construction Estimate. For node 16, the unloading time of the dump truck given in the Standard of Construction Estimate was entered as 30 s. The generated duration data are summarized in Table 5. where t exc is cycle time of loading and unloading of an excavator (cycle/s), cm is base cycle time according to the rotation angle (i.e., from 17 s for 45° to 23 s for 180°), K, f , and E are coefficient of bucket (0.55 for crushed rock), volume conversion (0.77 for soft rock), and efficiency (0.45 for crushed rock), respectively, t crane is cycle time of a crawler crane (cycle/s), c is coefficient of working rate according to the rotation angle (i.e., 0.78 for 45°), t 1 is the base cycle time of the crawler crane, and t 2 is the additional cycle time according to the lifting distance h, which is from 5.5 m to 9.1 m in the target construction process.

Data for estimating the objective values
The data for estimating the three objective values were collected as follows: (i) direct cost; (ii) noise exposure level for residents; and (iii) compensation cost for residents. First, the data for estimating the direct costs of the construction equipment were collected. As shown in Eq. (1), the data on the working hours of the target construction process and the hourly unit cost of material, labor, and expenses for each construction equipment should be collected to estimate the direct cost. The working hours are estimated from the WebCYCLONE simulation results. Therefore, the data on the hourly unit cost of material, labor, and expenses were collected for four construction equipment used in the target construction process from the Standard of Construction Estimate (refer to Table 6) (KICT (Korea Institute of Civil Engineering and Building Technology) 2022). Second, the data for estimating the noise exposure level for residents were collected. As shown in Eq. (2) to (4), the data on SPL (i,15m) , the average distance from the operating location of each construction equipment to each building, the execution time of each construction equipment, and the working hours of the target construction process should be collected to estimate the noise exposure level for residents. The execution time and working hours are estimated from the WebCYCLONE simulation results. Therefore, the data on SPL (i,15m) were collected from Hong et al. (2014) (refer to Table 7), and the data on the average distance from the operating location of each construction equipment to each building were collected from an interview and geographic information system of buildings (refer to Table 8).
Third, the data for estimating the compensation costs for residents were collected. The data on the noise exposure level for residents of each building and the number of residents in each building should be collected to estimate the compensation costs for residents. Therefore, data on the number of residents in each building were collected (refer to Figure 3 and Table 9).

Alternatives of construction equipment allocation
All possible alternatives of construction equipment allocation in the target construction process were established to determine the optimal construction equipment allocation. The minimum allocation for each construction equipment required to perform the target construction process and was collected through an interview with the site manager, and the maximum allocation for each construction equipment was determined through exhaustive search process (refer to Table 10). The number of breakers, excavators, and crawler cranes to be used was set to a minimum of one to a maximum of four units. The number of dump trucks was set to be a minimum of six for a maximum of 25 units. As a result, a total of 1,280 alternatives were established.

Validation of the proposed framework
In this study, a WebCYCLONE simulation was used to predict direct cost and noise exposure level more accurately for determining the optimal construction equipment allocation. Therefore, the accuracy of the proposed methodology was verified by measuring working hours to estimate the direct cost and noise level of an actual site and then comparing them with the values predicted by the WebCYCLONE simulation. The WebCYCLONE simulation was set to run over the 8 hours with 250 cycles, according to the site work hours. In particular, a measurement date was decided as the day when only the target construction process was selected for the case study in Section 3 to remove the noise from other construction activities. The working hours were calculated by measuring the start and end times of the construction process. The noise level was measured inside the construction site to minimize the effect of noise outside the site, and measurements were conducted using the approved equipment (NL-42 (RION 2016)) at a location 1.5 m away from the soundproofing walls according to the environmental noise measurement standards of MOE (refer to Figure 3) (Ministry of Environment 2006). First, the accuracy of working hours calculated using the WebCYCLONE simulation was verified as shown in Table 11. The target construction process was performed using two breakers, one excavator, one crawler crane, and eight dump trucks for 8 hours, and 375 m 3 of rock was taken out of the construction site. Therefore, the measured productivity was 46.88 m 3 /h. Meanwhile, the same construction equipment allocation was entered into the WebCYCLONE simulation model, and a simulation was conducted on a construction process of 375 m 3 . As a result, productivity was calculated at 45.21 m 3 /h. It was thus found that there was a relative error of 3.56% between the measured productivity at the construction site and the estimated productivity in the WebCYCLONE simulation. Consequently, the estimated working hours were seen to take about 18 minutes longer than the measured working hours.
Next, the accuracy of the noise level calculated based on the WebCYCLONE simulation was verified (refer to Figures 5 and 6). The Leq for 8 hours measured at the construction site was 77.77 dB. Meanwhile, the execution time of one piece of construction equipment inside the construction site, which was calculated with the WebCYCLONE simulation to estimate the noise exposure level, was 8.29 h for a breaker, 4.67 h for an excavator, 1.21 h for a crawler crane, and 0.04 h for a dump truck, respectively. Based on the results, the estimated Leq of one construction equipment for the measurement point was calculated using Eq. (2) and (3), and it was calculated at 77.56 dB for a breaker, 65.96 dB for an excavator, 61.84 dB for a crawler crane, and 40.50 dB for a dump truck, respectively. In particular, although the execution time per unit of the breaker was 3.62 h less than that of the excavator, the Leq of the breaker was 11.60 dB higher than that of the excavator because the sound pressure level generated by the breaker was larger than that of the excavator. As a result, the noise level synthesized at the measurement point according to the input quantity of each construction equipment using Eq. (4) was 80.75 dB, which is an overestimated value of 2.98 dB (3.83%) for the measured noise level compared to the measured noise level. Overall, working hours and noise levels considering the precedence relationship and execution time of each construction equipment for the target construction process could be calculated using the WebCYCLONE simulation. The relative error of productivity calculated using the WebCYCLONE simulation was 3.5%, which was smaller than the relative error of 10% that indicates the validity of the construction duration prediction model (Lewis 1982;Kang et al. 2021;Hong et al. 2022b). Meanwhile, the analysis found that the error of the noise level calculated using the WebCYCLONE simulation was 2.9 dB, smaller than the national standard for error (6 dB) for generating a noise map in South Korea to which the target construction project belonged (MOE 2018). The results show that the working hours and noise exposure level predicted using the WebCYCLONE simulation are valid and can be used for finding the optimal construction equipment allocation.

Optimal construction equipment allocation
In order to determine the optimal construction equipment allocation, 1,280 alternatives of construction equipment allocation were established based on the minimum and maximum values for the input quantity of each construction equipment. The optimal construction equipment allocation in terms of noise exposure level was derived on the same day validated in the former section (i.e., the day when 375 m 3 of rock was taken out of the site). On the other hand, the optimal construction equipment allocation in terms of compensation cost was derived on the period when all work was completed with 375 m 3 set as the daily work volume for the total volume of rock corresponding to a work volume of about 3,000 m 3 that must be taken out through the construction process.

Pareto optimal construction equipment allocation in terms of direct cost and noise exposure level
For determining optimal construction equipment allocation in terms of direct cost and noise exposure level, daily direct costs and noise exposure levels for all established alternatives of the construction equipment were estimated. When the direct cost was calculated, the remaining alternatives, except for the alternative with the least amount of construction equipment among the alternatives with the same working hours of the construction process, were excluded from the analysis since they were disadvantageous in terms of both direct cost and noise exposure level. The noise exposure level was calculated as the average value of the noise exposure level in four surrounding residential buildings (i.e., buildings A to D) (refer to Figure 3). As a result, the direct cost and average noise exposure level of 120 alternatives of construction equipment allocation were calculated, and the distribution is shown in Figure 7. Among all the alternatives, 10 alternatives (i.e., from optimal Alts. 1 to 10) were located on the Pareto front that indicates the set of optimal solutions (refer to Table 12) (Ghannad, Lee, and Choi 2021;Jeong et al. 2019;An et al. 2019). The direct cost decreased from the optimal Alts. 1 to 10, but the noise exposure level increased. In particular, the allocated quantity of construction equipment increased from the optimal Alts. 1 to 10, but the working hours of the construction process decreased from 12.98 h to 4.7 h, so that the direct cost decreased from USD 8,873.84 to USD 6,687.19. However, as construction noise emissions were concentrated for a short period of time, the noise exposure level in surrounding buildings increased from 84.19 dB to 88.59 dB. Therefore, according to the importance of construction companies on the direct cost and noise exposure level, the best allocation among the optimal alternatives of the construction equipment allocations can be applied to the construction project. At the actual project, the optimal Alt. 4 was applied as it is not biased towards the direct cost or noise exposure level.
Consequently, it is difficult to convert short-term noise exposure into a direct economic value. Therefore, a construction manager can select one of the optimal alternatives of the construction equipment allocation in consideration of the occupancy distribution in the surrounding area around the construction site. That is, in a densely populated region, construction equipment allocation close to the optimal Alt. 1, which can reduce the noise exposure level, is advantageous, while allocation close to the optimal Alt. 10 to reduce direct costs is advantageous for regions with low population density. It is expected, therefore, that as several optimal alternatives are provided to construction managers, they will help in decision-making to resolve conflicts due to construction noise between construction companies and residents.

Optimal construction equipment allocation in terms of direct cost and compensation cost
For determining the optimal construction equipment allocation in terms of direct cost and compensation cost, the direct cost required to complete all work of the construction process and the compensation cost according to the noise exposure level of residents in the surrounding buildings were calculated (refer to Figure 8). Since the alternatives of the Pareto front are the same as the optimal Alts. 1 to 10, the results for the optimal Alts. 1 to 10 were analyzed in this case. From the optimal Alts. 1 to 10, the direct cost decreased from USD 70,990.70 to USD 53,497.51, while the compensation cost increased from USD 86,396.92 to USD 104,705.45. Therefore, as the total cost of the optimal Alt. 3 was calculated at USD 153,435.18, the smallest value, the optimal Alt. 3 was determined as the optimal construction equipment allocation considering both the direct cost and the compensation cost due to noise exposure. In particular, it was found that the optimal Alt. 3 can reduce the total cost by USD 881.45 compared to the optimal Alt. 4 applied to the actual construction project.
As a result, for optimal construction equipment allocation in terms of compensation cost considering  long-term noise exposure, an optimal alternative could be selected based on the direct cost of the construction equipment and the compensation cost calculated for noise exposure of residents in the surrounding buildings. This allows construction companies to plan the most economic construction equipment allocation while managing noise emissions from the entire operation of the construction process.

Conclusion
This study developed a simulation-based framework for determining the optimal construction equipment allocation in terms of direct cost and noise exposure level using WebCYCLONE in the planning stage. Through a case study, it was verified that the developed framework is capable of determining the optimal construction equipment allocation, superior in terms of direct cost and noise exposure level with compensation costs. The implications and contributions of the developed framework are as follows.
• The developed framework is scientifically and intellectually meaningful in that it integrates the techniques of construction noise management and construction equipment scheduling, which are different fields in the construction industry. The integration of techniques has synergistic effects on managing construction noise and project costs.
To be more specific, the actual execution time calculated through the construction equipment scheduling technique (WebCYCLONE) has a positive effect on the predictive performance for construction noise, and construction equipment scheduling considering the construction noise has a positive effect on the project cost. In addition, the developed framework has resolved the knowledge gap. In this way, the developed framework has resolved the knowledge gaps in previous studies related to construction noise management. • The predictive performance for construction noise exposure based on the construction equipment allocation established using WebCYCLONE was allowable with an error rate of 3.83%. Based on realistic construction noise exposure prediction, construction companies can devise appropriate measures to effectively manage construction noise. • The optimal solution located on the Pareto front was obtained from among all construction equipment allocations, and the optimal construction equipment allocations for direct cost and noise exposure level from the short-term perspective were then determined. Based on the optimal construction equipment allocations, construction companies were able to save direct costs by up to USD 2,186.65 or reduce noise exposure by up to 4.4 dB. The developed framework provided various solutions depending on direct costs and noise exposure, which are in trade-offs in the short term, thus allowing construction companies to apply the best possible construction equipment allocation according to the characteristics of the construction project and the surrounding environment of the construction site. • The optimal construction equipment allocation, the most economic for construction companies, was determined considering direct costs and compensation costs for construction noise from a long-term perspective. In the case study, the construction company was able to save up to USD 881.45 by applying the optimal allocation. Therefore, it is possible for construction companies to manage construction noise most effectively from an economic viewpoint as they devise only the optimal allocation plan without introducing additional reduction measures.
Despite the implications and contributions of this study, the following should be considered in the future research. First, since this study focused on only one construction process, it did not consider a situation in which construction activities from which noise arises are carried out at the same time. Therefore, a method of selecting the optimal resource allocation by integrating several construction processes that generate construction noise needs to be developed in the future research. Second, this study focused on relatively simple construction process. Although a complicated construction process can be applied to the developed framework, the computational time to find the optimal resource allocation increases as the complexity of the construction process increases. Therefore, efficient exhaustive search or optimization techniques with good computational performance to find the optimal resource allocation need to be developed.

Disclosure statement
No potential conflict of interest was reported by the author(s).

Funding
This work was supported by the National Research Foundation of Korea [NRF-2018R1A5A1025137].