Flexible modeling of linear schedules for integrated mathematical analysis

Developing and analyzing schedules is essential for successfully controlling the time aspect of construction projects. The critical path method of scheduling is by far the most widely use scheduling technique in the construction industry. However, several problems related to its concept and use have been identified in the literature. The lesser known linear scheduling method has much potential for handling the rich information that project managers handle on a daily basis. While being well-suited to linear and repetitive projects, it has been a predominantly graphical method without a comprehensive underlying mathematical model. This paper introduces a new method based on singularity functions using Macaulay bracket notation. It makes beneficial use of the strengths of these functions, including their flexibility and clarity, while remaining intuitive and requiring only basic geometry and algebra knowledge from users. An example from the literature is re-analyzed step-by-step and compared successfully with the critical path method.