Work-Path Modeling and Spatial Scheduling with Singularity Functions

Current construction scheduling lacks an integrated planning approach that considers not just the time aspect of resources but also the physical workspace in which they interact. Therefore, this research creates a mathematical model to support allocating time and workspace with concurrent activities and under safety constraints. A time-space chart represents crew movements along work paths on a site with two dimensions; time is measured on the third axis. Total project duration is minimized by expressing work paths as singularity functions. These range-based expressions are extended to the third dimension to determine distances between activities and compact them. The approach ensures that temporal and spatial buffers between work paths are maintained. It links scheduling with site layout planning and safety management, which allows generating a work plan that is both efficient to achieve and safe to execute. Model feasibility is validated by applying it to a case study of a major real-world construction project.