1. Introduction
As working space in construction sites is limited, simulation models are essential tools for managing and analyzing the construction processes, specifically for the dynamic workspace required for construction activities [
1]. Construction practice demands space to maintain safety and efficiency. Often ignored in project planning, space is a limited resource in construction projects. Time–space conflicts occur when there is a working space needed for two activities that overlap in a given period, either partially or entirely [
2]. The limitation of the workspace leads to time–space conflicts, which increase with a higher number of activities per unit of time. As a result, effective resource planning is required to avoid high operation costs and reduce safety hazards [
3]. Available space in construction sites is divided into the space needed for building elements under construction, temporary facilities, workers, building materials, and construction equipment [
4]. Over recent decades, various simulations and scheduling techniques, such as bar charts and Gantt charts, and network-based scheduling techniques, such as Critical Path Method (CPM), have been utilized to improve time–space planning. However, only activities’ temporal interferences have been considered in planning construction logistics [
5].
Time–space conflicts make construction management a challenging process. Time–space conflict management in construction projects includes time–space conflict identification and assessment and finding solutions to prevent their negative effects [
2,
4,
6]. Considering crowded construction sites filled with labor, materials, and equipment, dynamic and complex time–space conflict management can be very challenging, even for experienced managers. Therefore, an integrated approach to mapping the temporal and spatial relationships between construction activities can be a very useful tool. Such tools can optimize the timing of activities, improve efficiency, construction quality, and safety, and reduce conflicts, rework, and unwanted impacts on already finished work [
7,
8].
Various methods have been applied to detect and resolve time–space conflicts. We have categorized these methods into three types:
1. Management and Investigation Methods: A categorization of the temporal and spatial conflicts between two activities was developed by Akinci et al. [
9,
10], who proposed a 4D framework in which workspace interactions are automatically recognized, classified, and prioritized. Guo [
2] manually overlapped activity workspace requirements derived from CAD drawings to identify conflicts in construction projects. In this method, the project manager/scheduler should decide on several criteria for manual conflict analysis and resolution strategies. Winch and North [
11] applied an allocation strategy on activity space types and presented a 3D simulation environment with an automatic 2D-based critical space conflict check to solve space loading issues for the scheduled critical path. In a real-world case study, Thomas et al. [
12] minimized workplace congestion in a multi-story building project and documented the effects of workspace conflicts on labor productivity.
2. Mathematical Modeling Methods: Lucko et al. [
13] provided a mathematical method to generate efficient schedules and presented a flexible workspace model as a decision support tool. To guarantee laborers’ safety, Isaac et al. [
14,
15] developed a support tool to allocate project time and workspace using an integrated multidimensional model linking site layout, schedule, and safety plans. Roofigari-Esfahan and Razavi [
6] incorporated spatial and temporal constraints into a linear scheduling problem and proposed an uncertainty–aware optimization framework to minimize time–space conflicts. Tao et al. [
16] investigated repetitive project scheduling for optimum resource reallocation and minimum congestion. They proposed a multiobjective mixed-integer programming model to optimize the cost, time, and congestion of repetitive construction projects. Although mathematical modeling methods need a significant amount of time and effort, they can suitably help in minimizing time–space conflicts in construction sites.
3. Building Information Modeling (BIM)-based Methods: Haque and Rahman [
17] linked a 3D BIM model with the construction schedule and space requirements as a 4D model to simulate space conflicts for a multi-story construction project. Zhang and Hu [
18] proposed a 4D-BIM framework for conflict management in construction projects. In their method, time–space conflicts are recognized by calculating bounding boxes for clashing objects. Su and Cai [
19] introduced a life-cycle approach for workspace modeling and planning. In their study, no scientific method is provided for the rapid and automatic generation of space requirements. As a BIM-based active simulation system, Moon et al. [
20] implemented a Genetic Algorithm (GA) procedure for an alternative schedule to minimize the levels of simultaneous interference of schedule workspaces. Moon et al. [
21] proposed a 4D-BIM optimization framework to find a plan with minimum workspace interference. This method automatically moves the activities within their CPM Total Floats (TF) to decrease workspace conflicts. Kassem et al. [
22] used an Industry Foundation Class (IFC) compliant 4D tool for workspace management. In their interactive resolution method, time–space conflicts are identified and visually represented. Using a 4D-BIM method, Choi et al. [
8] proposed a workspace planning framework to identify workspace requirements, represent workspace occupation, and detect time–space conflicts. Rohani et al. [
23] proposed a method for managing time–space conflicts in construction projects by combining 5D BIM and time–cost tradeoff analysis. Mirzaei et al. [
24] introduced a 4D-BIM time–space system detecting conflicts regarding labor movement. Recently, Getuli et al. [
1,
25] introduced a method using BIM technologies and immersive VR applications for manual activity workspace planning. As a result, they evaluated the historic passive and active data from the worker’s immersive VR activity simulation and improved workspace planning.
4. Neural network based path planning technique: A Neural Network-Based Navigation Approach for Autonomous Mobile Robot Systems involves the use of neural networks, which are machine learning models inspired by biological brain structures, to assist in navigating mobile robots. It has emerged as a promising method for solving the path planning problem in robotics, which is essentially about finding the optimal and safest path from a starting point to a destination [
26,
27]. Chen et al. [
28] discusses the importance of obstacle avoidance in navigation problems and presents a neural network model that was trained using human decisions on motion types in various obstacle scenarios. The model was tested in a mobile robot navigation simulator and showed an accuracy level close to 90%. Jaradat et al. [
29] propose a new approach to mobile robot path planning in dynamic environments using Q-learning. The authors propose a new definition for the state space to limit the number of states and reduce the size of the Q-table, improving the speed of the navigation algorithm. The paper also discusses the challenges of path planning in mobile robot navigation. For instance, changes in the environment can make path planning difficult. The robot may need to constantly update its plan as new obstacles appear or existing obstacles move. Duguleana et al. [
30] propose a new approach to solve the problem of autonomous movement of robots in environments that contain both static and dynamic obstacles. The solution uses Q-learning and a neural network planner to solve path planning problems. The algorithm has been tested in both virtual reality and on a real mobile robot for experimental validation.
Although several studies have been conducted in the area of time–space conflict management, the following gaps exist in the literature.
The majority of prior studies have primarily employed conventional network-based scheduling techniques for time–space planning. However, these methods, including the CPM, have some intrinsic limitations when applied to time–space planning. CPM-based scheduling strategies do not consider space as a restrictive factor in coordinating activities. They focus mainly on time management, often overlooking the spatial aspect. This omission can result in conflicts and inefficiencies, as space is a vital resource in project execution. Hence, this points to a significant limitation of these conventional scheduling methods, especially in scenarios requiring simultaneous management of both time and space. Furthermore, the majority of prior research has primarily focused on identifying and reporting time–space conflicts throughout a project’s duration. However, one of the significant challenges in time–space planning involves finding solutions for these identified conflicts. In most earlier studies, it was left up to the practitioners to address the reported conflicts by adjusting the project timeline or delaying nonessential tasks. To the authors’ understanding, no previous study has suggested an automated method for managing these identified conflicts. Therefore, we propose this approach as a method of time–space conflict management to automatically detect and resolve time–space conflicts in construction projects.
4. Methods
Our method implements Informed-RRT* path planning, DES, and geometry to automatically detect and resolve time–space conflicts in construction projects. In our case, same-size spheres were randomly placed in the construction site to represent static obstacles. Also, we considered two hauling trucks (SmallTruck and LargeTruck), represented by cubes (red and blue cubes, respectively), serving two construction activities with different priorities. If the trucks’ travel paths overlap at a given time, either partially or entirely, the truck serving the higher-priority construction activity has the right of way to avoid conflicts.
Table 1 shows the assumptions of our case study, which can be modified for various scenarios. In addition, the assumed coordinates of the loading areas, dump sites, starting points, and endpoints are listed in
Table 2. Our construction site is centered at (0, 0). The locations of site materials and equipment are randomly selected and can be changed.
Figure 3 provides our proposed method framework. In the following subsections, the development steps are described in further detail.
4.1. Case Study Modeling Using Discrete Event Simulation
Methods such as trial and error or postponing conflicts to resolve during construction highly affect project time and budget. Simulating operations can effectively save both time and costs while providing more realistic results within a short time frame.
Using DES, we modeled the operation in the Simphony Modeling Environment which is an integrated environment for building special-purpose simulation tools for modeling construction systems. Simphony offers a number of services that make it simple for developers to manage various behaviors using tools they have created, including simulation behaviors, graphical representation, statistics, and animation [
37]. We simulate the sequence of the activities and the resources required to create activities as an imitation of the real operation progress over time. The simulation process is shown in
Figure 4.
Our simulation scenario includes: (1) Two elements of “CreateLargeTruck” and “CreateSmallTruck” along with their specific attributes for earthwork operation are created. (2) The “Execute 1” element is created to formulate and assign the “TimeNow” value to each truck by using the Simphony engine. (3) The “Hauling 1” task is created to initiate the earthwork operation. This task defines the trucks’ travel duration from the starting point to the loading area. In the following sections, the calculations are explained in further detail. (4) The trucks start the “Loading” resource-dependent task and wait for a loader to complete the loading operation. The loader loads the trucks on a first-come-first-serve basis. (5) Loaded trucks enter the “Hauling 2” task, which defines the trucks’ travel duration from the loading area to the dump site. (6) The trucks start the “Dumping” resource-dependent task and wait for a spotter to supervise the dumping operation. The spotter supervises dumping on a first come first serve basis. (7) The empty trucks start the “Return” task, which defines the trucks’ travel duration from the dump site to the starting point. (8) The “Execute 2” element is designed to compute the total duration of earthwork performed by each truck. This not only quantifies the individual operational times but also generates an average duration representative of the entire truck simulation process. This element consists of three sections, which are shown in
Figure 5. (9) Then a “Conditional Branch” element is designed to route an arriving entity out of one of two branches depending on the trucks’ specific attributes. (10) Finally, the empty trucks proceed to the “Counter2” and “Counter3” elements, which are designed to capture the duration each truck requires to complete the earthwork operation.
4.2. Case Study Simulation in Unity
Unity is a cross-platform game engine used for interactive 3D projects, such as architectural visualizations, training simulations, and virtual reality experiences. Unity can create realistic and engaging scenarios that help users understand complex processes and procedures in a safe and controlled environment. We developed our case study in Unity as it allows the creation of highly immersive and interactive simulations to enhance the user’s perception and visualization of the model. Also, the sequence of construction activities, travel routes, and durations was simulated in Unity according to the following 2 steps. Step 1: calculate the shortest path for each truck without colliding with obstacles. Step 2: find a solution for when trucks’ shortest travel paths overlap at a given time.
As Unity supports C# programming, the Visual Studio environment was used to develop the simulation API.
Figure 6 shows a sample view of the simulation environment with all project assumptions.
4.2.1. Finding Trucks’ Shortest Paths without Colliding with the Obstacles
Informed-RRT* path planning is a powerful algorithm used in motion planning and robotics to find the shortest path between a start and goal configuration in a high-dimensional configuration space. It is designed to consider the cost of motion and other objective functions, such as collision avoidance and smoothness. In this case study, we used the Informed-RRT* algorithm to find the shortest path in which the trucks avoid colliding with the obstacles.
Blue and red cubes, with the dimensions (K) and (L), represent the LargeTruck and SmallTruck, respectively. Same-size spheres with the radius (r) represent static obstacles that were randomly placed throughout the construction site. Also, bounding boxes and bounding spheres were used to enclose and define the boundaries of trucks and obstacles based on their dimensions. These 3D bounding boxes (such as shown in
Figure 7) and spheres represent the minimum area completely covering the objects.
As an Informed-RRT* path-finding parameter, the Safety Distance (sd) between the trucks and the obstacles was used to ensure that the paths generated by the algorithm safely avoid collisions with obstacles throughout the construction site. To be more specific, sd is the minimum distance that the algorithm maintains between the moving object and the obstacles during the pathfinding process. The sd parameter can be adjusted based on specific safety considerations.
We evaluated the trucks’ travel paths in Equation (1) as a way to avoid conflicts between them and the obstacles (
Figure 8). Here, Point C (x
c, y
c) and (r) are the center and the radius of the obstacles bounding sphere, respectively. P
1(x
1, y
1) and P
2 (x
2, y
2) are the cube’s center points representing the truck at the starting and the random points, respectively. P
3 (x
3, y
3) is a point on the line between P
1 and P
2 with the shortest distance from point C.
For the line
, there are two cases to consider. 1: Line
does not intersect and is outside of the sphere, in which case the value of
will either be the same or greater than
. 2: Line
intersects the sphere, or the sd requirement is not met. Therefore, if Equation (1) is true (case 1), there is no collision between the trucks and the obstacles during travel from P
1 to P, and P
2 is added to the list of probable points along the trucks’ probable path. Otherwise, if Equation (1) is false (case 2), a collision occurs, P
2 is removed from the list of probable points, and another random point is generated. The iteration continues until the obtained random point P
2 is the truck’s endpoint along the path. Therefore, the shortest truck’s path is found to avoid a collision with the construction site’s obstacles.
Figure 9 shows an example of a truck’s travel path mapping obtained by Informed-RRT*.
4.2.2. Trucks’ Travel Priorities
Time–space conflicts may occur in construction sites, leading trucks’ travel paths to overlap at a given time, either partially or entirely. To avoid such conflicts, our solution is to consider trucks’ priorities. We consider that the truck serving the higher-priority construction activity has the right of way to avoid conflicts. Our case study assumes that the SmallTruck (red cube) serves the higher-priority construction activity and, therefore, has the right of way. Therefore, if time–space conflicts occur during the trucks’ travel, the LargeTruck (blue cube) waits until the SmallTruck (red cube) leaves the intersection zone. Setting the travel priorities includes the following steps:
Finding the intersection points of the trucks’ paths
Finding the stop and start point for the blue cube
Modeling all possible scenarios for the cubes’ travel paths
Finding the Intersection Points of the Trucks’ Paths
In this section, we calculated the following attribute lists for the trucks’ travel paths to find probable intersection points.
path list. Contains the points
on the blue cube travel path according to Equations (2) and (3).
timeLablePath list. Contains the time it takes for the blue cube to reach any point of the path which was calculated based on the distance between any two consecutive points of the path and the trucks’ speed (Equations (4) and (5)). Here,
is the time taken by the blue cube to reach a point
, and
represents member
i of the
.
slope (m) and intercept (b) list. The slope and the intercept of the line between any two consecutive points of the
were calculated and stored in the
and
b lists, respectively (Equations (6)–(9)). Here,
and
are the X and Y coordinates of the point
, respectively.
and
are the slope and the intercept of the line between
and
, respectively.
Similarly, the three attributes of the red cube’s travel path from the origin point to a given destination point were calculated. An example of the blue cube’s path with path’s points
, slopes
, intercepts
, and the time taken to reach the points along the path
are shown in
Figure 10.
To find the intersection points of the trucks’ path, such as
, the intersection points between each line in the path of the blue cube and each line in the path of the red cube were calculated (
Figure 11).
The Stop and Start Point for the Blue Cube
In this section, we defined 4 critical points of
, and
to be used in our calculations. If the blue cube passes the points
and
it will enter and exit the critical conflict area. Similarly, if the red cube passes the points
and
, it will enter and exit the critical conflict area. Also, the critical point
is the optimal point where, if the blue cube stops, no collision with the red cube occurs. If the blue cube passes through the point
and then stops, time–space conflicts will occur.
Figure 12 shows the described points in the conflicting area along the travel paths of the blue and red cubes.
The distance between
and
, and between
and
is considered
and
, respectively. The distances between points
and
and
are also named
and
, which are equal to
and
, respectively (
Figure 13).
Here is the unit vector of and is the unit vector of . and are the lengths of the blue and red cubes, which are in the same direction of local vector. and are the widths of the blue and red cubes, which are in the same direction of local vector and is the angle between the and on which point is located. We describe our calculations based on and avoid describing the other conditions for brevity. However, our model works for all values of .
There are two possible scenarios for the truck travel paths:
The Absence of time–space conflicts in trucks’ travel paths. If during the blue cube’s travel from the critical point to the , the red cube is not traveling from to , time–space conflict does not occur. Therefore, the blue cube continues its path without stopping.
The Existence of time–space conflicts in the truck’s travel path. If during the blue cube’s travel from
to
, the red cube is traveling from
to
, a time–space conflict may occur. Using the
function,
Figure 14 shows the calculations of the precise time of cubes’ arrival at each of the critical points. In case of a time–space conflict during the trucks’ travel, the blue cube should stop at time
to avoid a collision and continue moving after the red cube exits the conflicting area, at time
.
The described calculations to obtain the critical points’ coordinates are correct, only if the blue cube’s travel path between the critical points and , and the red cube’s travel path between the critical points and remain unchanged. Otherwise, the critical points should be recomputed. In the following section, we describe all possible scenarios for the two cubes’ travel paths.
Modeling All Possible Scenarios for the Cubes’ Travel Paths
Generally, four different scenarios may occur when the cubes arrive at the critical points, while four other scenarios may occur when they exit. Each state includes two subsets of
and
. All possible simulation scenarios for the cubes’ travel paths are listed in
Table 3. For instance,
Figure 15 illustrates a scenario when the cube’s arrival follows the number (2) scenario, and the cube’s exit follows the number (7) scenario, while
.
Here, is the distance between and , is the distance between and , represents the distance between and , represents the distance between and , and represents the distance between and .
Based on the described logic, we computed the critical points’ coordinates and for all possibly occurring scenarios. Using the function, we computed the precise time of the cubes’ arrival at the critical points as , and . If time–space conflicts occur during the cubes’ travels, the blue cube should stop at the time to avoid a collision and continue moving after the red cube exits the conflicting area at the time .
6. Discussions and Conclusions
The necessity for adequate space in construction practices to ensure safety and operational efficiency is often an underrepresented factor in the early stages of project management. It is essential to understand that space is not an infinite resource in construction projects. This limitation becomes more evident and problematic when two separate tasks require the same working space within an overlapping timeframe, giving rise to what is known as time–space conflicts. These conflicts become increasingly pronounced as more activities are introduced into the construction process, all competing for a finite amount of space within a given unit of time.
In the realm of a construction site, available space is allocated for various elements. This includes building components that are currently under construction, temporary facilities necessary for the operations, the construction workforce, building materials, and a range of construction equipment. The appropriate division and utilization of these spaces are integral for the progression of the project.
Over the past few decades, the industry has turned to various simulations, scheduling techniques, and tools to enhance time–space coordination. These tools include the use of bar charts and Gantt charts, which provide visual representations of the project schedule, and network-based scheduling techniques like the Critical Path Method (CPM). These techniques have proven to be valuable in planning and managing the timing of various project activities. However, it is important to note that these methods, while effective, have typically been utilized with a primary focus on managing temporal interferences between activities. The spatial component has often been given less emphasis in the logistics planning of construction projects. Therefore, further research and innovation are required to integrate spatial considerations into these planning techniques to prevent potential time–space conflicts and enhance overall project efficiency.
In this study, the developed simulation model successfully proposed an approach to resolve time–space conflicts, one of the most common issues in construction sites due to a large number of activities in a limited working space. Our method implements Informed-RRT* path planning, DES, and geometry to detect and resolve time–space conflicts in construction sites automatically. To evaluate the method’s capabilities, we defined a case study of an earthwork operation, including the loading, hauling, dumping, and return phases. In our case study, we consider two hauling trucks (SmallTruck and LargeTruck), represented by cubes (red and blue cubes, respectively), serving two construction activities with different priorities. If the trucks’ travel paths overlap at a given time, partially or entirely, the truck serving the higher-priority construction activity (SmallTruck) has the right of way to avoid conflicts. Therefore, if time–space conflicts occur during trucks’ travel, the LargeTruck should stop to avoid conflict until the SmallTruck leaves the conflicting zone. The trucks are responsible for hauling to their specific loading area, waiting for a loader to load the truck, then hauling to their specific dump site, and waiting for a spotter to supervise dumping. Also, construction equipment and materials are randomly placed on the construction site as obstacles. Finally, our method finds:
The shortest travel path and duration for trucks in each phase without colliding with obstacles.
Intersection points of the trucks’ paths and the stop and start time for the LargeTruck to avoid time–space conflicts.
The total duration of the earthwork operation for each truck.
In conclusion, implementing Informed-RRT* path planning combined with DES can provide useful planning insights for construction executives and superintendents to manage their crowded job sites and critical operations more efficiently.
There are a few distinct limitations that we have identified in our proposed methodology. In this study, our current approach makes the assumption that all obstacles within the scope of the project remain static, that is, their positions do not change over the course of the project. In reality, however, this is a simplification. Real-world environments are often dynamic, with obstacles moving and changing their positions over time. Whether it be due to natural causes or human intervention, changes in the positions of the obstacles could significantly impact the effectiveness of our methodology. For future studies, it is important to enhance our method to include scenarios where obstacles can change their positions dynamically. By doing so, we can ensure that our proposed model mirrors reality more closely and is able to handle more complex, dynamic scenarios.
We have applied this methodology in the context of a research study with a limited number of trucks. While this was effective for our initial testing and analysis, it may not fully reflect the true potential of the method. To better assess the capabilities and effectiveness of the proposed method, it would be more valuable to apply it in research involving a larger fleet of trucks. Furthermore, engaging with a more complex case study could provide greater insight into the robustness and adaptability of our method. In such a case, more variables and conditions could be included, allowing us to better understand the method’s performance under different scenarios, its scalability, and how it reacts to complex, unexpected situations. These improvements could give us a more comprehensive understanding of the utility and applicability of our proposed method.