Temporal Constraints in Linear Scheduling with Singularity Functions: Case of Calendarization

Abstract

Construction managers must develop and implement their plans to satisfy numerous constraints, many of which are related to time. Developing realistic schedules and integrating other essential elements, e.g., financial considerations and resource utilization, requires the ability to model such temporal constraints in an integrated yet customizable manner. Many phenomena in practice depend on calendar dates. This paper therefore develops new theory in a novel application of singularity functions, which are flexible range-based mathematical expressions, to perform a complete and transparent calendarization. It solves the challenges of incorporating leap years, distinguishing weekdays, and inserting nonworking holidays into a schedule. A five-step algorithm is provided for linear schedules, which explicitly contain more information than network schedules and thus have more analytical potential. The new model is validated with commercial software. It enables an integrated treatment of different types of constraints and can lead toward improving algorithmic optimization approaches for planning construction projects.