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

• Published in: Automation in construction Vol. 79; pp. 31 - 38
• Main Authors: Hajdu, Miklós, Lucko, Gunnar, Su, Yi
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.07.2017; Elsevier BV
• Subjects: Calculus; Continuity (mathematics); Continuous precedence relation; Links; Logic; Mathematical analysis; Mathematical models; Modelling; Network scheduling technique; Production functions; Scheduling; Sequential scheduling; Singularity function; Singularity function; Continuous precedence relation; Network scheduling technique
• ISSN: 0926-5805; 1872-7891
• DOI: 10.1016/j.autcon.2017.01.012

Two fundamental limitations of the Precedence Diagramming Method (PDM), which currently hinder the proper modeling of construction projects are discussed and overcome. Activities in the original model are (1) assumed to progress linearly from their start to their finish, which is rarely true in construction projects, and (2) connected only via their end points. The extension that is presented here therefore enables a general description of activity-time-production functions: A new type of precedence relation is defined and this new model can handle nonlinear activities. 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. •Major generalization of Precedence Diagramming Method is introduced.•The use of non-linear activity production-time functions is discussed.•Continuous type of precedence relation is developed to model activity overlapping.•The use of singularity functions is presented in time analysis.