Construction spatial modeling and scheduling with three-dimensional singularity functions

Previous approaches for construction project scheduling have been limited to one dimension of time for bar charts and two dimensions for linear and repetitive scheduling approaches, which added a measure of work quantity. The question therefore arises if and how it is possible to derive a three-dimensional and ultimately multi-dimensional model. Reviewing mathematical theory finds that traditional functions lack the capability to express intervals for activities. Singularity functions are therefore chosen to newly derive stationary and directional activities in a Cartesian coordinate system, wherein the two dimensions of the floor plan area plus one dimension of time are explicitly modeled in an integrated manner. They are implemented into a conflict-avoiding heuristic scheduling algorithm that minimizes total project duration, which is computerized and validated with example calculations.