# Space-Constrained Scheduling Optimization Method for Minimizing the Effects of Stacking of Trades
## 5 Conclusions  
This study proposes SSO, which finds the optimal space-constrained schedule that minimizes workspace conflicts and the effects of stacking of trades. First, SSO imports schedule information from the project database (e.g., Primavera P6), extracts IFC files of construction site area from the BIM model, and saves the data into the system memory. Then, the user classifies the entire site into specific work areas by considering the characteristics of the workspace and defines the occupation density function of each activity according to the attributes of each activity, allocated resources, and the rate of progress. Furthermore, SSO creates alternatives for the occupation density function (fs) obtained by changing the execution pattern of activity and defines the occupation density functions of the alternatives. SSO identifies an optimal space-constrained schedule using a GA optimization analysis technique. This method was developed as a MATLAB-based software, and users can operate the system easily by inputting the aforementioned information (i.e., P6 and BIM model interlinkage, specific work areas, occupation density function, and GA parameters). Furthermore, this system provides the user with visual information, such as (1) a set of alternatives for activity execution patterns, (2) a set of deferred start times of activities, (3) level of space interference, and (4) times when space interference occurred. This study provided, in detail, the computation process of calculating space interference levels, which change according to the combinations of alternatives for activity execution patterns and deferred start times of activities. According to the results of the case study, the near-global optimal solution that was identified by SSO resolved workspace conflicts, which are associated with construction delays and cost increases, and it reduced the space interference level (\(f_{SC}\)) by 328% compared to the EST schedule. Furthermore, SSO was validated for a large network. The effective time to execute the SSO method is after the  
Figure 9: Results of sensitivity analysis. framework construction is completed. This is because, after the framework is completed, various types of work, such as electrical and mechanical work, etc., are carried out at the same time in a narrow workspace, whereby interference problems occur frequently. This study utilizes (1) changing activity execution patterns and (2) deferring the start time of activities as a strategy for resolving workspace interference. However, the activity splitting approach is also being used in schedule management methods. Activity splitting is a resource allocation planning process that splits an activity into segments with re-allocated resources. Therefore, noncritical activities can be split to resolve the problem of space interference. In future studies, it is recommended to develop a methodology that incorporates activity splitting to find optimal space-constrained schedules. In addition, as mentioned in the case study, it is recommended that a follow-up study should be conducted to integrate image-processing-based progress management methods to develop an automated system that reduces user intervention in SSO. This study dealt with the space-constrained scheduling problem in a deterministic environment. However, since construction projects inevitably have duration and cost fluctuations, further research is needed on space-constrained scheduling optimization dealing with stochastic activity durations. Conceptualization, methodology, and software, H.-S.G.; validation, H.-S.G. and W.-S.S.; formal analysis and investigation, H.-S.G., W.-S.S. and Y.-J.P.; writing--original draft preparation, H.-S.G.; writing--review and editing, Y.-J.P.; visualization, W.-S.S. and Y.-J.P.; funding acquisition, H.-S.G. All authors have read and agreed to the published version of the manuscript. This work is supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (No. 2021R1F1A1051109). Not applicable.