Research on Fine Scheduling and Assembly Planning of Modular Integrated Building: A Case Study of the Baguang International Hotel Project

Abstract

There exist various challenges in constructing a large in-city project, such as narrow construction sites, limited surrounding roads, heavy construction periods and tasks, various types of vehicles, and affected cargo transport. Considering construction needs, transportation characteristics, and site conditions, this paper puts forward the overall planning for modular integrated construction (MiC) transportation and on-site assembly. Meanwhile, the traffic organization and transportation scheduling method are designed for smart construction sites and different engineering materials are coordinated in the space-time dimension during the overall period from construction delivery. Meanwhile, an integer programming model is developed to solve the truck scheduling matching problem between the supply side and the construction side. The weighted loss time of the truck is set as the optimization objective function, and time, space, and material type are the constraints. For this model, this paper proposes an operations scheduling solution method by combining operations research and actual field construction scheduling experience. The traditional empirical scheduling method and the proposed operations research scheduling model are compared through a case study of actual engineering scheduling data. The experimental results show that the operations research scheduling model is better than the traditional empirical scheduling method at different traffic levels. In addition, the implementation of the scheme is guaranteed through measures such as pre-data analysis, management framework, and information technology equipment. The planning and scheduling cover the whole process of MiC module transportation and on-site assembly, which have practical guiding significance for the project and ensure the timely success and acceptance of the project.

1. Introduction

1.1. Background

Since the outbreak of COVID-19, the transmission mode and speed of the Delta and other variants have evolved, leaving ordinary hotels no longer suitable for isolation, hence the need of building qualified ones. As a populous port city and transportation hub, Shenzhen is under considerable pressure in epidemic prevention and control, especially in managing imported cases. It was against this backdrop that many quarantine hotel projects in Shenzhen were launched to prevent the import of overseas epidemics.

In this paper, we take the construction project of Shenzhen Baguang Epidemic Prevention and Control Hotel as the research object. The existing organization of the project lacks refined traffic scheduling. The circulation of materials starts with the project manager, who contacts the manufacturer to arrange delivery. After the truck arrives in the vicinity of the construction area, the construction manager arranges personnel to guide the truck into the construction site. The truck is beyond the reach of the traffic scheduling system after leaving the factory until it arrives at the construction site. In addition, the lack of a traffic buffer along the road could result in damaging the traffic efficiency during peak hours. Due to the lack of elaborate division of functional areas in the construction site, materials are often stacked and placed in a disorderly manner, and unloading vehicles are parked at will, which can easily cause traffic paralysis. Therefore, unreasonable and casual traffic organization and transportation scheduling schemes could lead to queuing and congestion, which will not only affect the road traffic, increase the construction cost, but also delay the overall progress. If the transportation organization and scheduling are carried out in a global, systematic, and intelligent manner, it can smooth the traffic inside and outside the site, lessen the construction cost and ensure the arrival of materials on time.

Smart construction sites are highlighted by elaborate traffic organization and dynamic transportation scheduling. Fine traffic organization includes traffic route selection, the layout of the off-site buffer areas, and the division of on-site functional areas. Dynamic transportation scheduling refers to predicting traffic flow based on construction demand and arranging delivery by manufacturers accordingly, where trucks are dispatchable in the whole process. The on-site dispatcher plans the arrival time and place of the truck according to the overall traffic conditions. To ensure successful dispatching, information equipment is equipped to monitor and guide truck drivers throughout the process. This method can avoid queue congestion during the peak period, and increase the traffic capacity of the whole project by improving the accuracy and reliability of the schedule, thus ensuring the timely supply of materials.

1.2. Literature Review

1.2.1. Modular Integrated Construction

In recent years, prefabricated construction has received a lot of attention in the development of the construction industry [1]. Prefabricated construction can play an important role in clean production in the construction industry by achieving high productivity and quality through repetition and mass customization, thus reducing material use and construction waste for energy conservation, low carbon development and environmental protection capabilities [2,3,4].

Prefabricated construction is usually of modular structure. The benefits of modular structure come from manufacturing building units in the factory environment, which can achieve higher efficiency and quality. Off-site construction (OSC) reduces the space requirements of on-site storage for materials or equipment and significantly shortens the assembly process. MiC is a new building method, which divides the whole building into modules. These modules are produced in off-site factories and then transported to the construction site by trucks for assembly. Thanks to such characteristics, MiC completes most of the construction processes off-site, thus reducing labor consumption and increasing operational efficiency. Pan and Hon [5] proposed MiC as a game-changing, disruptive and innovative approach that transforms the construction of a building or facility from a fragmented and cast-in-place manner into an integrated one that is driven by prefabricated modules.

For construction, the supply of materials or components is essential in ensuring the efficient operation of construction. The supply source of traditional construction projects is usually composed of multiple suppliers, which directly transport raw materials to the construction site. In this mode, raw building materials are sent to the site according to the construction demand, and the whole supply form is relatively simple. On the contrary, the raw materials in modular construction projects are transported to the manufacturing plant first, where they are converted into modular products and components [5,6] before being transported to the construction site. Generally, the consumption of modular construction is less than that of production. Whereas, the limited storage space in the construction site highlights the necessity of off-site temporary storage for MiC [7].

Given the particularity of MiC supply, scholars have studied the transportation of MiC components. From the perspective of the supply chain, some scholars believe that all links of the supply chain should be considered as a whole to design the transportation of MiC components including production, storage, and construction [8,9]. Many scholars also analyzed the delay of MiC transport to construction progress [10] and its correlation with extra cost [11]. However, as far as the author knows, no scholar has ever studied the transportation planning of MiC components from production to construction, or has presented feasible refined construction transportation schemes both inside and outside the site in an actual project and successfully implemented them.

1.2.2. Transportation Organization

Transportation organization is a key issue in urban MiC construction [12]. Generally speaking, transportation organization refers to the method of transporting materials from one place to another by any specified transportation mode. It includes various transportation modes such as highways and railways, which determines the transportation efficiency, transportation operation, and storage cost of materials [13,14].

For the problems of MiC transportation organization, the literature indicates that the transportation management scheme of MiC components should be designed according to the particularity of the MiC supply process and considering all links of the supply chain as a whole [8,9]. When formulating the MiC transportation organization plan, we should consider all aspects of its impact on the construction, including the delay of MiC transportation on the construction progress, the correlation with additional costs, the impact of weather, etc. [10,11].

On-site box transportation organization is an important aspect of MiC transportation organization. The existing literature adopts the simulation of construction transportation and crane operation and optimizes the transportation organization mode through their respective optimization models to improve construction efficiency. Gonzales et al. studied the sustainability of the road construction process, obtained the optimal number of trucks and cranes and realized environmental protection and high efficiency of construction by applying discrete event simulation (DES) to reduce gas emissions [15]. Kim et al. used multi-agent-based simulation to evaluate the traffic flow of construction equipment on the construction site and studied its impact on the efficiency of the construction site [16]. However, these studies neither involved the specific layout planning of the site nor achieved refined traffic management.

1.2.3. Vehicle Dispatching

In 1959, Dautzig and Ramser first proposed the vehicle routing problem (VRP) [17]. The vehicle routing problem is an important link in the construction process. Its optimization can improve the efficiency of materials distribution and reduce its cost. The reasonable scheduling of vehicles is crucial for the development of construction work. Desrochers, Kohl, Madsen, Fisher, and others have conducted relevant research on vehicle scheduling by using accurate methods such as network flow algorithm, branch definition, dynamic programming, and cut plane [18,19].

In 1996, Higgins proposed an optimization model for scheduling trains on a single-line track [20]. Koehler presented the German Kassel distribution system, which enabled a significant reduction in truck travel time through co-distribution, thereby reducing the number of trucks for urban materials distribution [21]. Ghoseiri et al. used a multi-objective planning approach to optimize the energy consumption and waiting time in scheduling trains [22]. By establishing a multi-stage dynamic scheduling method, Subtill et al. reduced the high transportation cost via truck scheduling in an open pit environment [23]. Centikaya et al. proposed an integration strategy for truck scheduling by combining several small orders into a single order shipment to save transportation costs [24]. Ariano et al. developed an optimization model for train operation scheduling with a greedy algorithm, which was based on a discrete-event simulation system aiming for the shortest travel time for passengers [25].

1.3. Summary

Existing studies on MIC lack detailed analysis and planning of MIC field assembly. In the research on transportation organization, the organization of content is less reasonable with ambiguous coverage and an unclear hierarchical structure, as well as a lack of connection with scheduling. In terms of vehicle scheduling, most of the existing studies focus on intra-city vehicle scheduling, train scheduling or off-site scheduling of construction sites, while scheduling within construction sites remains to be studied. Therefore, this paper will take the following questions as the research objectives.

(1)

MIC assembly planning and detail study.

(2)

Refined traffic organization, including the layout planning of construction site outside, construction site inside, and even special construction vehicles.

(3)

Multi-level traffic scheduling and corresponding assurance measures.

(4)

Operation research modeling study for off-site delivery end and in-site construction end truck scheduling.

The remainder of this paper is structured as follows: Section 2 introduces the basic methods for traffic organization and scheduling, including MIC field assembly, refined traffic organization, and three-level transportation scheduling; Section 3 focuses on the operational research model for traffic scheduling; Section 4 presents a practical case study of the model and compares it with a traditional method; Section 5 summarizes the conclusions.

2. Basic Method for Traffic Organization and Scheduling

Firstly, this section studies the on-site assembly analysis of MiC and the planning in the construction process. At the same time, aiming at a global, systematic, and intelligent construction project traffic scheduling, this section studies the traffic organization and transportation scheme for intelligent construction sites, as shown in Figure 1.

For the refined traffic organization scheme, the off-site/on-site traffic organization and the layout planning of the crawler crane and MiC module vehicles are proposed. A three-level scheduling method is proposed, to schedule the vehicles which transport MiC components from the material production plant to the construction site. The first-level schedule starts from leaving the factory to the stage area. The second-level schedule is from the stage area to the waiting area. The third-level schedule is from the waiting area to the designated docking point.

For the second-level and third-level scheduling, the research object is the on-site construction vehicle scheduling, and the operations research model is established with weighted truck loss time as the objective function. Then, the scheduling planning solution algorithm based on operations research is proposed for the model in Section 3.

2.1. MiC Field Assembly Planning

2.1.1. Construction Background

The Baguang international hotel project is located in plots A and B on both sides of Paiyashan Road, Dapeng new area, Shenzhen. It is 91km away from Shenzhen airport and 68 km away from Shenzhen North high-speed railway station. The geographical location is shown in Figure 2. Six 7F multi-storey hotels and supporting facilities need to be built in plot A. The project duration is only 42 days. Each hotel is an independent epidemic prevention unit. Once completed, the hotel can accommodate 1400 people for isolation purposes (including 1200 guests and 200 medical staff). Modular integrated construction (MiC) is introduced in plot A of the project to respond to the challenge of the limited construction period.

2.1.2. Analysis of Elevation Details

The construction diagram of MiC is shown in Figure 3. The exterior wall decorations of MiC mainly include the curtain wall, grille, and other decorative components. The glass curtain wall adopts 8 + 12a + 8 hollow tempered double ultra-white Low-E glass, and the aluminum plate curtain wall is a 3mm thick aluminum veneer. The grid adopts the vertical design to offset the vision difference caused by the uneven left and right boxes; the grille is designed to be openable to facilitate the replacement and maintenance of the air conditioner.

2.1.3. MiC On-Site Horizontal-Vertical Operation Planning

The plane planning of the construction site needs to be considered from the spatial and temporal dimensions [26]. In terms of time, considering the sequence and characteristics of the construction process, the admission time of trucks in each construction unit should be staggered. Spatially, according to the red line range of each construction unit, the storage yard area and the parking area of the engineering vehicles should be arranged discretely.

The MiC vertical operation process is shown in Figure 3, and includes the following steps:

(1)

Pour reinforced concrete as the foundation;

(2)

Transport MiC modules and corridor precast slabs vertically;

(3)

Fix MiC module with structural glue and bayonet device;

(4)

Install building curtain wall, façade decorative components, and waterproof facilities. The installation steps of the curtain wall unit are shown in Figure 4. Based on the procedures in Figure 5 and MiC installation schedule in Figure 6, the specific installation steps are: install the bottom sink, install the top material, install the indoor unit plate, and fix the unit plate.

2.1.4. Indoor Plane Planning

The plane of a single building is planned by different areas and groups of quarantined guests and service staff. Furthermore, epidemic prevention personnel, basic emergency medical care, security personnel, community grid office, etc., are all involved. The first floor of each hotel is equipped with a comprehensive outpatient department and health diagnosis and treatment area to meet the needs of all kinds of personnel. The general plan of the first floor is shown in Figure 7.

2.1.5. MiC Engineering Transportation Coordination

The vehicle arrival time (accurate to hours) is planned according to the construction schedule and procedures. GPS dispatching equipment provides a recommended speed and waiting time in the service area for each freight vehicle, thus assisting the vehicles to arrive at the waiting area on time. Ideally, the time for freight vehicles to arrive at the waiting area is equal to the time specified in the schedule, and the vehicles separately arrive in time and enter the site one after another according to the needs of construction, forming a coordinated layout for the horizontal transportation of materials, which ensures the efficient utilization of resources on the construction site.

Due to the particularity of the MiC module, the construction process is considerably simplified compared with traditional construction. After the MiC module is lifted to the designated position by the crawler crane, the high rider carries the construction personnel who will install the module with structural glue and a bayonet fixing device. Meanwhile, the low-rise curtain wall, facade decorative components, and waterproof facilities are installed at the same time. The three processes work in turn, coexist in time, and coordinate with each other vertically. Well-organized vertical operation is the driving force for the rapid advancement of the construction process.

2.2. Refined Traffic Organization

The refined traffic organization scheme mainly includes traffic route selection, the layout of the off-site buffer area, and the division of the on-site functional area.

2.2.1. Off-Site Traffic Organization

The off-site traffic jam can be avoided according to the following principles: The road width can accommodate two construction trucks. Appropriate waiting areas shall be arranged along the route. An appropriate amount of roadside queuing areas should be set near the construction area. Traffic roads and transfer areas must be marked in the construction area. The traffic flow line in the construction area should be defined according to the traffic conditions.

Specific measures are as follows:

(1)

Despite their large size, freight trucks have smaller acceleration and lower average speed than small cars. Merging into the road will inevitably reduce the traffic capacity. To reduce the impact on daily travel, the daily traffic volume of the road section along the line shall be investigated before planning the traffic route. If the monthly average daily peak traffic volume of a single lane is greater than 900 veh/h, the road section can be avoided. In addition, considering the small angular speed and the long starting time of trucks, traffic route planning should avoid large-signal intersections and minimize the number of turns;

(2)

Large trucks have a weight limit of 30 t and a length of 17.5 m whose average speed is much lower than that of small cars. If a one-way lane can only accommodate one vehicle, trucks will have a major impact on daily traffic. During the peak period of the project, the traffic volume of trucks can reach 1000 veh/h, while if the number of available one-way lanes is less than two, it is easy to cause traffic congestion. In addition, the turning radius of 17.5 m freight cars is 16~20 m, and the turning radius of a single lane cannot meet such turning requirements. Therefore, the number of available lanes should be no less than four and the road width should be at least 15 m;

(3)

According to the characteristic of the car-following process, setting diversion nodes and waiting areas can avoid intensive queuing of vehicles. The waiting area should be placed near the traffic nodes along the line to facilitate drivers, such as the expressway service area and the entrance of the construction site. If the distance between the nodes exceeds 6 km, a waiting area should be added. The waiting area can choose a private car parking lot, planned open space, or temporarily borrow the roadside, in which the roadside parking time should not exceed 6 h. If the waiting time is expected to exceed 6 h, the parking lot and planned open space should be given priority;

(4)

Setting a roadside waiting area can avoid traffic congestion at the entrance of the construction area and provide sufficient space and time for the accurate dispatch of each truck. The capacity of the roadside waiting area shall be set according to the traffic volume in peak hours to satisfy the traffic volume in peak hours. Due to the slow speed of the crane, the parking position of the crane should be given priority in the roadside waiting area. The expected waiting time should not exceed 0.5 h;

(5)

The construction area should be divided into main roads and branch roads via red paint or isolation guardrails. No parking signs should be set on the main road to emphasize that any construction activities shall not be occupied, thus ensuring smooth traffic in the construction area. To meet the needs of freight cars, the width of the main road shall be no less than 7 m. The branch road shall accommodate at least a single truck, and the width shall be no less than 3 m. If the width of the branch road is less than 7 m, a transfer area should be set to satisfy the meeting of 17.5 m freight cars;

(6)

The meeting time of the trucks is directly related to the road width and truck length. When the road width is less than 6 m and the vehicle length is more than 15 m, the meeting time can reach 3 min. Long meeting time can easily reduce the vehicle turnover rate and cause traffic congestion. Therefore, in case of limited road conditions in the construction area, the one-way streamline in the site should be defined.

2.2.2. On-Site Traffic Organization

The principles of on-site traffic organization shall be carried out according to the following points:

(1)

Vehicle speed limit principle. The maximum speed limit can ensure traffic safety at the site and prevent traffic accidents;

(2)

Surrender principle. Give way by separating vehicles and pedestrians to ensure the traffic order at the site;

(3)

One-way traffic principle. One-way traffic is an economical and effective traffic control measure that can make full use of the capacity of the existing road network

At the same time, the loading of the MiC module increases the horizontal space required for the running of flat-panel transport vehicles. The limited space will restrict the free passage of freight vehicles, and it is difficult for freight vehicles to meet and turn in the site. In addition, MiC module vehicles are different from other types of vehicles in the field in terms of traffic characteristics. The above factors need to be considered when organizing on-site traffic operations.

First, limit the speed of all vehicles. There are various types of vehicles operating at the same time on the construction site, and the construction personnel often need to shuttle to both sides of the road for work. Therefore, the driver’s vision may be blocked by other vehicles and materials in the yard, so that the shuttling construction personnel cannot be observed directly. In particular, the mass of the MiC module vehicle is large, and the motion state of the vehicle is not easily changed. The maximum speed of vehicles on the site shall be limited to ensure that drivers have enough time to respond to emergencies and avoid traffic accidents, thus securing the orderly operation of construction on the site.

Secondly, given the crucial role of the MiC module in the project, it is stipulated that vehicles shall give way to pedestrians; vehicles entering the site shall give way to vehicles leaving the site, and other vehicles shall give way to MiC module vehicles. The safety of construction personnel is the cornerstone of building construction, and the comity between vehicles and pedestrians is the premise of on-site traffic safety. Vehicles entering the site can leave the site swiftly under the premise of limited capacity, which is conducive to the operation of vehicles on the site. MiC module is the top priority of the MiC project. Only when the MiC module arrives at the hoisting site in time can the construction process advance. Other vehicles give way to MiC module vehicles, which can reduce the risk of construction stagnation.

Finally, considering the size of the MiC module and the width of the on-site channel, one-way traffic is used to facilitate the operation of on-site vehicles and the meeting of MiC module vehicles. The road network of construction area A is planned as a one-way Lane crossroad network. Trucks, unloading vehicles, and other vehicles mainly dispatch, load, and unload materials along with the road network. The setting of the traffic flow lines shown in Figure 8 is based on the off-site road traffic conditions connected by the four openings. Vehicles on the north side of BaiShaWan Road turn right first and then drive into the west entrance, before leaving from the east exit, and finally returning along BaiShaWan Road. However, vehicles on the south side of Paiyashan Road first drive in from the south entrance, then drive out from the north exit, before finally returning along BaiShaWan Road. The traffic flow line realizes the extent to which the diversion of vehicles on the two main roads of BaiShaWan Road and Paiyashan Road before entering the site reduces the off-site traffic pressure.

2.2.3. Layout Planning of Crawler Crane and MiC Module Vehicles

The completion of high-rise MiC largely depends on the safe and efficient module installation using a tower crane [27]. The space between buildings on the construction site is too limited to deploy tower cranes. The position of the crawler crane in the field is fixed, which plays the role of a tower crane. Therefore, a reasonable layout of the crawler cranes is essential [28].

See Figure 2 for the layout of vehicle parking spots of the crawler crane and MiC module. Considering the limited space on the site in Figure 9, two crawler cranes are arranged on the northern and southern sides of each building unit, and the vehicle parking spot of the MiC module is arranged nearby within the working range of the crawler crane. For some crawler cranes whose nearest parking area cannot meet their minimum working radius, the parking area will be arranged on the other side of the road in the field. On the premise of not affecting the traffic, the parking spots on the northern and southern sides of the road can borrow the off-site northern and southern roads.

2.3. Three-Level Transportation Scheduling and Guarantee Measures

2.3.1. Transportation Scheduling Principle

To guarantee the efficient implementation of the construction project, the transportation scheduling needs to meet the following principles: the delivery sequence and time are arranged according to the construction needs [29]; the storage yard should be designated according to construction requirements and site conditions; the selection of truck type and the setting of departure interval should consider the construction needs and traffic conditions; it is suggested the type and quantity of unloading vehicles are to be arranged according to the construction needs and site conditions of the construction area; when the dispatching distance is long, nodes should be divided and managed at different levels, and real-time adjustments are supposed to be made according to the situation; the transportation scheduling shall take into account the demand of the storage yard, the number, and characteristics of trucks and unloading trucks.

The specific implementation of the transportation schedule is as follows:

(1)

By signing a contract with the supplier, arrange the production quantity, sequence, and time of materials according to the construction schedule, and require the manufacturer to deliver materials on time in strict accordance with the scheduling requirements. To avoid a delay in construction period due to unexpected conditions, multiple contracts shall be signed with different suppliers;

(2)

The location, type, and size of the yard should meet the construction needs, and be adjusted in time based on different stages of the construction. In addition, the stacking sequence and location of materials should also consider the construction process. If the available space of the storage yard is insufficient, the off-site storage yard can be adopted and the materials can be transferred. The whole process of transshipment shall be arranged by the dispatcher;

(3)

The truck should be selected according to the road conditions, such as performance requirements calculated via horizontal and longitudinal alignment. In addition, the appropriate vehicle size should be selected according to the road width and turning radius at the construction site. The departure interval shall consider the construction demand and traffic capacity. In case of traffic saturation or traffic congestion, the departure shall be delayed or reduced;

(4)

The dispatching of unloading trucks should consider the conditions of trucks, storage yards, and the space of the construction area. In addition, the unified dispatching of unloading vehicles can improve their utilization rate. To save space, unloading vehicles should occupy the minimum space that satisfies the unloading requirements. If the on-site vehicles undertake the unloading and hoisting tasks at the same time, they should unload first to improve the turnover rate of trucks;

(5)

The hierarchical scheduling of transportation with a long space-time span is conducive to the timely adjustment of the scheduling scheme in accordance with the construction needs and traffic conditions to achieve accurate scheduling. Hierarchical scheduling needs to arrange management personnel at each node to implement the scheduling scheme. The dispatcher should make dispatching arrangements according to the dynamics of materials, trucks, unloading vehicles, construction needs, and traffic conditions;

(6)

Goods production, truck transportation, and unloading by unloading trucks are closely related. The materials, trucks, and unloading trucks are supposed to be systematically dispatched based on the construction demand and in accordance with the production efficiency of materials, spatial distance, traffic capacity, freight capacity, and working capacity of unloading trucks, to ensure the timely supply of materials.

2.3.2. Three-Level Transportation Scheduling of Trucks

The primary dispatching of truck transportation is to estimate the material demand in the next five days and inform the manufacturer to deliver them on time. The time when trucks enter the site is scheduled based on the overall traffic and the operational capacity of the site. Trucks are then dispatched to the service area, the mobilization time of trucks is planned, and the dispatch and arrangement of the trucks in the service area is organized. After the trucks leave the service area, they are diverted according to the dispatching arrangement and driven into the designated waiting area, and the dispatcher directs the trucks to park at the designated location in an orderly manner.

The purpose of secondary transportation scheduling is to estimate the waiting time of trucks according to the occupation rate of the storage yard and traffic conditions in the construction area. If the waiting time is less than half an hour, guide trucks enter the roadside waiting area, and give priority to 17.5 m steel structure vehicles. If the waiting time of trucks in the waiting area is expected to be long, arrangements are to be made for unloading vehicles to enter the waiting area to be unloaded. If there is enough space in the waiting area, arrangements should be made for 9 m transfer vehicles to transfer materials to the site.

The three-level tertiary transportation scheduling is to draw the distribution map of unloading time and space according to the truck type, cargo size, unloading time, and the layout of unloading spots in the site, thus realizing point-to-point dispatching that can maximize the utilization of time and space in the site. The calculation formula of saturation and gradation is shown in Equation (1) and

Table 1. Corresponding table of saturation and gradation.

Gradation	Saturation
A	[0.0, 0.2)
B	[0.2, 0.4)
C	[0.4, 0.6)
D	[0.6, 0.8)
E	[0.8, 1.0)
F	[1.0, +∞)

. The space-time distribution is shown in Figure 10, and the material numbers are shown in

Table 2. Material number correspondence.

Material Number	Material Type
1	Steel structure
2	Prefabricated staircase
3	Bottom pocket
4	Pressed steel plate
5	Column concrete
6	Floor concrete
7	Unit curtain wall
8	Renovation
9	Mechanical and electrical

.

$$Saturation=\frac{Ouccpied Hours}{24}$$

(1)

2.3.3. Guarantee Measures

To ensure elaborate traffic organization and smooth implementation of three-level transportation scheduling, various guarantee measures are also required in the construction process. The principles of guarantee measures are as follows:

(1)

Data analysis is the premise of traffic organization and transportation scheduling;

(2)

Establishing a hierarchical management system according to the dispatching scheme, and the on-site guidance of dispatching personnel is a necessary link of dispatching;

(3)

Effective management of time and space. Establish a punishment mechanism to ensure the implementation of the scheme by signing contracts;

(4)

Workers and information equipment should be managed jointly;

(5)

Auxiliary management equipment shall realize accurate positioning and communication functions;

(6)

Based on the three-level transportation scheduling and project planning, the delivery time of upstream manufacturers is managed by information technology to ensure smooth traffic in the surrounding controllable areas [30].

The specific implementation of guarantee measures is as follows:

(7)

The traffic organization and dispatching plan should calculate the total freight volume based on the construction mode, and analyze the traffic demand according to the transport capacity of trucks and unloading vehicles. The traffic characteristics of different stages of the project should be clarified by predicting the traffic flow based on the project cycle, thus planning the traffic organization and transportation scheduling plan in stages [29];

(8)

The dispatching of materials and trucks should specify the responsible person with whom a designated person from the relevant unit should interface. For example, the supplier shall work with the responsible person for materials dispatching to guarantee the implementation of the materials dispatching scheme. If the dispatching scope is large, consider dividing the responsibility area according to nodes;

(9)

Refined transportation scheduling includes two aspects: time and space. The error between the actual time of materials, trucks, and unloading trucks leaving the factory, reaching the traffic node and entering the designated position in the construction area, and the planned time shall not exceed 30 min. If the transportation time exceeds 48 h, the time error shall not exceed 1 h. Therefore, the dispatching management should be implemented by each vehicle through point-to-point guidance;

(10)

Establishing a contract is an effective way for the dispatching department to cooperate with suppliers and on-site subcontractors in traffic organization and transportation scheduling. The punishment mechanism shall be specified in the contract, and the legal effect shall be used to facilitate the cooperation among the three parties and ensure the implementation of the traffic dispatching plan;

(11)

Information equipment provides dispatchers with real-time information on materials, trucks, and unloading vehicles [31]. Dispatchers take professional knowledge as the theoretical basis and guide on-site dispatching according to the on-site situation and practical experience. Build an all-around, multi-angle, and high-level traffic organization and transportation scheduling;

(12)

The whole process of traffic scheduling, including factory production, materials transportation, and on-site construction, is operated in real-time. To ensure that the dispatching scheme is practical and reasonable, it is necessary to adjust the scheme in time according to the real-time information and guide the responsible person to implement it. Therefore, relevant personnel should be equipped with accurate positioning and real-time communication equipment to communicate in a timely manner and strengthen information communication [32].

3. Operational Research Model for Traffic Scheduling

3.1. Situation Description

Different vehicles will unload at different unloading spots in different buildings that are under construction at the same time. Due to the limited space, the number of unloading spots for each building is also limited. To overcome the tight schedule and the heavy workload of this project, this paper proposes an on-site scheduling plan model based on operations research that minimizes the negative impact imposed by the on-site vehicles on the construction progress. Figure 11 shows the conceptual diagram of the operational research model in this paper. The input of the model is the delivery information of each truck, and the output is the entry time and the unloading place in the construction site of each truck after optimization.

The parameters, variables, and sets required in the mathematical model are defined as follows:

The freight vehicles are numbered by 1, 2, ……, $j$; the collection of the freight vehicles is $J$; the corresponding building where freight vehicles unload is numbered as 1, 2, ……, $b$; the collection of the buildings is $B$; the type of materials transported are numbered as 1, 2, ……, $i$; the collection of material types is $I$; the corresponding parking spots for unloading is numbered by 1, 2, ……, $a$; the collection of parking spots is $A$; $D$ represents the weighted total delay of freight cars; $d_i$ represents the transportation delay of materials type $i$; $w_i$ represents the corresponding weight coefficient of materials type $i$; $a_{i,j,b}$ represents the expected arrival time of the freight vehicle; $e_{i,j,b}$ represents the arrival time of freight cars in the dispatching scheme, which is a decision variable; $u_{i,j,b}$ indicates the time when the truck is at the unloading point; $E$ is the set of $e_{i,j,b}$ which represents the mobilization time vector in the scheduling scheme; $p_{i,b}$ indicates the parking spot selected by the materials vehicle; $P$ is the set of $p_{i,b}$, which represents the vector of parking spot selection in the dispatching scheme; $x_a$ represents the number of vehicles at the parking spot; $c_a$ represents the maximum parking capacity; $t$ represents the system time; $T$ represents the time variation range of the system time; $f_{i,b}$ represents the upper limit of the decision variable; $t_{i,j,b}^{arrival}$ refers to the time when the truck arrives at the parking spot; $t_{i,j,b}^{leave}$ indicates the time when the truck leaves the parking spot.

The main purpose of the mathematical model constructed in this paper is to solve the optimal arrival time and parking spot selection of various types of freight vehicles, to minimize the total arrival delay of vehicles under the weight of the importance of freight vehicles.

The objective functions and constraints of the scheduling model are as follows:

$$min D\left(P\right)={\displaystyle \sum }_i{w}_i{d}_i\left(P,T\right)$$

(2)

$$s.t. d_i\left(P\right)={\displaystyle \sum }_j{\displaystyle \sum }_b\left(p_{i,j,b}-e_{i,j,b}\right) \forall i\in I$$

(3)

$$x_a\left(E,P,t\right)\le c_a \forall a\in A, \forall t\in T$$

(4)

$$a_{i,j,b}\le e_{i,j,b} \forall i\in I, \forall j\in J, \forall b\in B$$

(5)

$$e_{i,j,b}\le a_{i,j,b}+f_{i,b} \forall i\in I, \forall j\in J, \forall b\in B$$

(6)

$$t_{i,j,b}^{leave}-t_{i,j,b}^{arrival}=u_{i,j,b}$$

(7)

Equation (3) is the description of the arrival delay. The arrival delay of the truck is equal to the difference between the entry time and the arrival time. Equation (4) is the restriction on the number of parking counts at the parking spot. The parking spot here includes not only the parking spot of each building, but also the arrival restriction, that is, at each time, the number of vehicles entering the site will be restricted. Equations (5) and (6) are the constraints on the arrival time decision variables, that is, the arrival time can be neither less than the arrival time nor more than the waiting time delay. Equation (6) indicates that the dwell time of the truck in the parking spot equals the corresponding unloading time.

When building the model, the arrival time, one of the decision variables, is discretized into minutes, and integer programming appears. The arrival time set for each truck is the minute between the arrival time of the truck and the maximum delay time of the truck, while for dispatching vehicles this will be approximately ten to twenty in a day. The arrival time sets for different trucks are arranged and combined, resulting in an abnormally large solution space, and making the problem relatively difficult to solve.

To solve this problem, we need to combine integer programming with reality. In the actual dispatching process, for an incoming truck and its designated build, if the parking spot of the type of corresponding materials is relatively idle, and there are few trucks of the same type that need to enter the site in the same period, and vehicles of this type can usually enter the site directly for unloading. In the process of solving this problem, the arrival time of this vehicle is the optimal solution that is naturally generated and, as such, is called a “natural solution”. One of the key points of algorithm design is to judge whether there is a “natural solution” for each vehicle.

Another key point of algorithm design is to schedule the freight cars without a “natural solution”. When multiple trucks of the same designated building and type arrive at the same time in a certain period, there is no “natural solution” for these trucks. For trucks without natural solutions, if the enumeration method is used to determine the solution set, although the algorithm structure becomes simple, the solution space remains substantial and the solution time is still relatively long. Therefore, considering the arrival time and occupation time of freight vehicles arriving before and after, the algorithm performs scheduling rehearsal for freight cars without a “natural solution”, judges whether there will be situations that do not meet the constraints, and screens out the solutions of these situations, thus tightening the solution set of the arrival time of each freight car without “natural solution”, which saves the solution time and improves the efficiency of the algorithm.

After determining the solution set of each vehicle, the approach time set is combined, and the parking spot set is arranged to form the solution space. All feasible solutions are screened out by implicit enumeration for each constraint condition.

3.2. Algorithm Solution Steps

Step 1: initialize the corresponding transport materials type I and arrival time of the truck $j\in J$ according to the information collection $a_{i,j,b}$, service building $b$, the cargo weight coefficient $w_i$.

Step 2: determine the parking spot set $P_J$ selected by trucks $j\in J$ according to the type $i$ of materials transported by each truck and the corresponding service building $b$.

Step 3: according to the arrival time of each truck $a_{i,j,b}$ and the set upper limit of adjustment time $f_{i,b}$, determine the solution set $E$ of truck $j\in J$ approach time.

Step 4: according to the cargo type $i$ of each truck, the corresponding service building $b$ and arrival time $a_{i,j,b}$, determine whether there is a natural solution for the truck $j\in J$ for the vehicle $J_N$ with a natural solution. Go to step 5; For vehicles without natural solutions $J_{UN}$, go to step 6.

Step 5: for vehicles with natural solutions $J_N$. According to the order of arrival time, the time solution set $E_j$ should tighten to the natural solution.

Step 6: for vehicles without natural solutions $J_{UN}$, according to the cargo type $i$ of each truck, the corresponding service building $b$ and arrival time $a_{i,j,b}$, sorted according to the weight value. For vehicles with a weight value greater than 0.1, go to step 7, and for vehicles with a weight value less than 0.1, go to step 8.

Step 7: for vehicles with a transport weight value greater than 0.1, calculate whether there are free spots at the corresponding parking spot according to the arrival sequence, and arrange the arrival of the corresponding number of vehicles according to the number of free spots. The arrival time of these vehicles is decomposed into a set and $E_j$ is the right neighborhood of arrival time. If there are still vehicles that have not entered the site, calculate the idle time of the corresponding service parking spot again according to the unloading time of the vehicles that have entered the site, and the time solution set $E_j$ of these vehicles is the right neighborhood where idle time reappears.

Step 8: for vehicles with a transport weight value less than 0.1, if there is a corresponding idle parking spot, assume that they enter the site according to the arrival time, and judge whether there is a vehicle $J_p$ with a weight value greater than 0.1 and the same service point during unloading. If this does not exist, the approach time solution set of the vehicle $J_p$ is the right neighborhood of arrival time. If it exists, the approach time of the vehicle is solved to set $E_j$ delay to the last $J_p$ and is the right neighborhood of the time to leave the parking spot. If the parking spot is not idle, the arrival time of the vehicle is changed to the time when the parking spot is idle again; then go to step 8.

Step 9: solve $E_j$ for the arrival time of each truck is combined to find the solution set E of the overall approach time; and collect $P_J$ for the parking spots of each truck is arranged to find the overall parking spot set $P$.

Step 10: filter the solution set $\left(E,P\right)$ through the implicit enumeration method to select the feasible solution that meets the constraint conditions of the maximum number of those that can park at the parking spots.

Step 11: calculate the objective function of the feasible solution and find the optimal solution.

4. Discussion

4.1. Introduction to Basic Data

The expected arrival information of trucks is shown in

Table 3. Expected arrival information of freight cars.

Vehicle Number	Vehicle Type	Arrival Time	Service Building	Unloading Duration	Adjust Upper Time Limit	Item Number
1	C	8:00	1	2	8	1
2	C	14:00	1	2	8	1
3	C	22:00	1	3	8	1
4	C	6:00	1	2	8	2
5	D	6:00	1	2	8	3
6	D	12:00	2	1	8	1
7	D	14:00	2	1	8	1
8	D	16:00	2	1	8	1
9	D	16:00	2	1	8	1
10	D	18:00	2	1	8	1
11	D	16:00	2	1	8	1
12	D	18:00	2	1	8	1
13	D	20:00	2	1	8	1
14	D	20:00	2	1	8	1
15	D	16:00	3	2	8	1
16	D	16:00	3	2	8	1
17	D	16:00	3	2	8	1
18	C	16:00	4	2	8	1
19	C	20:00	4	2	8	1
20	B	23:00	4	1	8	4
21	C	16:00	4	1	8	8
22	D	18:00	5	3	8	1
23	D	10:00	5	2	8	3
24	C	12:00	5	2	8	9
25	A	7:00	6	2	8	9
26	A	9:00	6	1	8	9

, the corresponding table between truck parking spots and vehicle type is shown in

Table 4. Table of the parking spot and the corresponding vehicle type.

Building	Corresponding Vehicle Type	Parking Lot Number
1#	Parking spot for type B, C, D vehicle	1
		2
	Parking spot of type A vehicle	3
		4
2#	Parking spot for type B, C, D vehicle	5
		6
	Parking spot of type A vehicle	7
		8
3#	Parking spot for type B, C, D vehicle	9
		10
	Parking spot of type A vehicle	11
		12
4#	Parking spot for type B, C, D vehicle	13
		14
	Parking spot of type A vehicle	15
		16
5#	Parking spot for type B, C, D vehicle	17
		18
	Parking spot of type A vehicle	19
		20
6#	Parking spot for type B, C, D vehicle	21
		22
	Parking spot of type A vehicle	23

, and the weight coefficient of materials transported by trucks is shown in

Table 5. Weight coefficient table of materials transported by freight cars.

Item Number	Weight Coefficient
1	0.33
2	0.1
3	0.2
4	0.13
5	0.1
6	0.07
7	0.03
8	0.03
9	0

.

4.2. Solving Practical Examples

The 9600 sets of feasible solutions are calculated according to Section 3.1. The objective function is calculated for the feasible solutions, respectively, and the minimum value is selected as the optimal solution. At last, a total of 128 groups of optimal solutions are obtained. The objective function of the optimal solution is five.

Table 6. Set of one of the optimal solutions.

Vehicle Number	Mobilization Time	Arrival Time	Vehicle Number	Mobilization Time	Arrival Time
1	8:00	2	14	20:02	6
2	14:01	1	15	18:04	9
3	22:00	2	16	16:04	9
4	6:00	2	17	16:05	10
5	6:01	1	18	16:01	13
6	12:00	5	19	20:01	13
7	14:00	5	20	23:00	14
8	21:06	5	21	16:00	14
9	16:02	5	22	18:02	17
10	18:01	5	23	10:00	18
11	16:03	6	24	12:01	17
12	18:03	6	25	7:00	22
13	20:00	5	26	9:00	23

shows a set of optimal solutions obtained from the example solution. Figure 12 shows the distribution diagram and histogram of the objective function value of the feasible solution. It can be seen from Figure 12a that the optimal solution saves 5~10 vehicle waiting times more than other feasible solutions.

Based on the empirical dispatching, the dispatching process is to judge whether the corresponding parking spots are free in turn according to the importance of the materials transported, while considering those trucks that have arrived and the trucks that have not entered the site in the meantime: If it is idle, arrange trucks to enter the site; if it is not, let trucks wait. When a truck arrives carrying materials with a weight value of less than 0.1 and can enter the site, judge whether there are trucks with the same service parking spot and a weight value of more than 0.1 within 0.5 h after the arrival time. If so, let the front truck wait until the rear truck completes the unloading task before entering the site. If not, arrange the truck to enter the site.

Since the empirical scheduling solution does not meet the requirements of constraints in terms of arrival time, the solution obtained after adjusting the empirical scheduling solution according to the constraints is shown in

Table 7. Adjusted experience schedule.

Vehicle Number	Arrival Time	Arrival Time	Vehicle Number	Mobilization Time	Arrival Time
1	8:00	2	14	20:03	6
2	14:01	1	15	18:05	10
3	22:00	2	16	16:04	10
4	6:00	2	17	16:05	9
5	6:01	1	18	16:02	13
6	12:00	5	19	20:02	13
7	14:00	5	20	23:00	14
8	15:00	5	21	16:01	14
9	17:00	5	22	18:03	17
10	18:02	5	23	10:00	18
11	16:07	6	24	12:01	17
12	18:04	6	25	7:00	22
13	20:01	5	26	9:00	23

. After the empirical solution is brought into the objective function calculation, the objective function value is 72.50.

The solution obtained by the algorithm is better than the empirical solution as building 2 is empty when the eighth truck arrives at 15:00, and the eighth truck will be dispatched to the site for unloading first. A longer unloading time will delay the trucks that arrive later, which have a higher weight. The optimal solution of the scheduling algorithm is to delay the arrival of the eighth vehicle to 21:06, and the high-weight vehicles arriving within 16:00~20:00 will enter after completing the unloading task, so the impact on the overall scheduling is less than that of the empirical scheduling method. In this case, when the low-weight truck arrives before the high-weight truck, the empirical scheduling method cannot judge whether to unload the low-weight truck first or wait for the low-weight truck. The scheduling planning based on operations research can accurately calculate the situation that has the least impact on the overall scheduling task, which shows that the scheduling planning based on operations research is better than empirical scheduling.

4.3. Results Comparison

We used the empirical scheduling and the operations research model to find out the scheduling solution for different arrival construction vehicle density conditions, respectively. Figure 13 shows the respective calculation results, while

Table 8. Adjusted experience schedule.

Density	Average Optimization Time	Average Optimization Percentage
Low	2	10%
Medium	13	17.3%
High	58	37.9%

shows the time and percentage optimized by the operations research method over the empirical scheduling method for different density conditions.

It can be seen that the operations research model outperforms the empirical scheduling in both density conditions. At low densities, the operations research approach outperforms the empirical scheduling approach by only 10%, due to the fact that at lower densities, the amount of scheduling tasks is low and scheduling is not even required. This is due to the empirical scheduling method still following its own set of empirical rules when the scheduling volume becomes large, while our model relies on the operations research model to complete the scheduling. In the high-density condition, the advantage of the operations research model increases to nearly 40%. This is due to the empirical scheduling at this time being prone to large congestions, or even in-field road jams, while trucks are less flexible and relatively large in volume, and congestion dissipates more slowly than congestion in car-based traffic flows. It is worth mentioning that, the empirical scheduling used for the experiments in this paper is somewhat better than the traditional manual scheduling at the construction site. This is sufficient to demonstrate that our operations research model is significantly better than the empirical scheduling.

5. Conclusions

The main challenges of the MiC project come from engineering factors (site, storage yard, efficiency, etc.), transportation (road network capacity, transportation distance, etc.), and cooperation with stakeholders [33]. Under the guidance of the government and the cooperation with stakeholders, this project successfully responds to the challenges of engineering and transportation by implementing a comprehensive plan. Compared with traditional practices where trucks arrive randomly, MiC transportation and on-site assembly focus on the overall process of the project and consider the engineering and transportation factors, thus scheduling vehicles from both the temporal and spatial perspectives. Generally speaking, a reasonable plan in the early stage alleviates the construction pressure caused by emergencies in the later stage, which contributes to better time and space control to ensure the project is carried out efficiently, safely and orderly.

Based on the rigorous traffic investigation and scientific data analysis in the early stage, the intelligent construction site traffic organization plans reasonable traffic routes and waiting areas to reduce the impact of trucks on daily traffic and avoid traffic congestion and queuing. In addition, the traffic organization should carefully divide the functional areas according to the construction needs and available space, clarify the on-site road lines and streamline, and improve the on-site space-time utilization rate and truck turnover rate. The transportation scheduling of smart construction sites should implement hierarchical scheduling of materials, trucks, and unloading vehicles based on construction demand and traffic conditions, and jointly ensure the timely supply of materials in combination with refined traffic organization. Furthermore, it should build a systematic management framework through applying hierarchical management and information equipment, thus ensuring the effective implementation of traffic organization and transportation scheduling. Moreover, the traffic organization and transportation scheduling of a smart construction site can improve the space-time utilization rate of the construction site and roads along the line, reduce the construction cost, improve the freight and loading and unloading efficiency, and escort the construction production through the overall, systematic and intelligent traffic scheduling method.

Taking the three-level transportation scheduling that manages trucks from the waiting area to the parking spots as the research object, an integer programming model with weighted truck loss time as the objective function is constructed, and a scheduling planning algorithm based on operations research is proposed for the model. Furthermore, the analysis of practical examples shows that vehicle scheduling based on operations research can solve the planning problem in three-level transportation scheduling. It is worth mentioning that although this paper uses an actual engineering project as a research case, however, the entire article studied can be applied to other similar studies.

Taken together, this paper has the following innovative points:

(1)

Existing studies on construction traffic organization are mostly on more macro processes, and there is a lack of research for fine-grained contents. In this paper, we propose fine-grained traffic organization content.

(2)

This paper proposes three-level traffic scheduling, which is more than the general construction scheduling, including the stage from the waiting area to the construction site, and also proposes measures to ensure the smooth implementation of three-level traffic scheduling.

(3)

This paper establishes the operation research model of integer planning for truck deployment from the waiting area to the construction site, and verifies its feasibility and reasonableness by comparison with the empirical scheduling method.

Compared with traditional architectural design and construction technology, today’s application of MiC has some disadvantages, such as high cost and limited floor height. However, it can save considerable construction time and reduce safety risks while ensuring project quality. Furthermore, it is conducive to energy conservation and emission reduction and follows the “carbon reduction” goal and the concept of sustainable development. In the project construction stage, the overall planning of the project will ensure the completion and delivery of the MiC project on schedule. In the foreseeable future, MiC design and installation technology will be widely popularized and applied.