# Space-Constrained Scheduling Optimization Method for Minimizing the Effects of Stacking of Trades
## 2 Current State of Space-Constrained Scheduling  
Most studies on SCS proposed methods for creating the workspaces needed to execute construction activities, methods for detecting workspace interference, and methods for finding strategies to resolve workspace interference. First, methods for creating the workspaces needed to execute construction activity have used modeling techniques, such as CAD, 4D CAD, and 4D BIM. [PERSON] et al. [2] proposed a methodology that extracts project-specific Industry Foundation Classes (IFC) from 4D CAD and creates activity workspaces based on a generic workspace ontology. [PERSON] [13] built a hierarchical structure of workspace demand and defined the workspaces needed to execute each activity based on CAD data. In addition, changes in workspace demand according to activity progress rates were incorporated into [PERSON]'s model. [PERSON] and [PERSON] [3] developed a 4D CAD-based space-time analysis model that identifies the workspace considering execution patterns as well as activity progress rates. [PERSON] et al. [4] proposed a method for real-time workspace management by combining the critical path method (CPM) and the 4D BIM model. [PERSON] et al. [14] proposed a method that classifies workspaces as fixed workspaces or flexible workspaces based on workspace movability and identifies workspace requirements and storage space requirements for executing activities from a 4D BIM model. [PERSON] et al. [15] introduced a 4D BIM model for automatically creating workspaces based on the space syntax analysis. The approaches of existing studies on workspace interference detection can be divided into three types: space interference, schedule interference, and workspace congestion. Most existing studies considered space interference. Space interference is defined as when workspaces that are needed to execute activities at the same time are physically overlapping. Therefore, it is closely related to standards for creating the workspaces needed to execute activities. However, in workspace interference, more than just physical overlapping occurs. There are also temporary overlaps between the tasks that make up the activities. This type of interference is called schedule (temporal) interference. [PERSON] and [PERSON] [3], [PERSON] et al. [5], and [PERSON] et al. [6] proposed space-constrained scheduling methods that consider space interference and schedule interference at the same time. Workspace congestion was rarely considered [5; 6; 9]. The workspace congestion was introduced to judge the importance of decision making when searching for workspace interference resolution methods. [PERSON] [13] used the concepts of interference space percentage and interference duration percentage to propose the concept of workspace congestion. [PERSON] et al. [5] introduced the schedule-workspace impact factor. [PERSON] et al. [6] introduced the \"severity of interference\" parameter to minimize schedule (temporal) interference. The severity of interference is calculated by dividing the overlapped duration by the activity duration. [PERSON] et al. [16] proposed a 4D BIM-based simulation model for automatic management of time-space conflicts in the pre-construction planning phase. This model enables the practitioners to detect all types of possible time-space conflicts automatically. [PERSON] et al. [17] proposed a 4D-BIM model for identifying time-space conflicts according to the labor crew's parameters movement and quantifying the impact of time-space conflicts on project performance. In addition, a study was conducted on developing an algorithm for detecting interference between resources in virtual construction site environments [18], as well as developing a GIS-based method for identifying time-space interference [19]. Existing studies on workspace interference detection have assumed that interference does not occur if activity workspaces do not overlap with each other even when several activities are executed within a limited work area.