Singularity functions for continuous precedence relations and nonlinear activity-time-production functions

Theoretically, proper modeling of overlapping activities has been impossible with traditional precedence relationships. This is due to the fact that traditional precedence relations create logic links only between endpoints of activities. Yet overlapping should be defined as a 'continuous' relation that uses time or work (e.g. location) units between all points of a predecessor activity and all points of its successor. Continuous precedence relations for scheduling techniques have been envisioned earlier, but the model presented there was able to function properly only if the successor was linear. The contribution of this paper is to derive an algorithm for activity pairs that are connected by a continuous relation and can be nonlinear. Comparing calculations based on traditional calculus and singularity functions validates the new approach.