Float Types in Linear Schedule Analysis with Singularity Functions

This paper describes how float can be calculated exactly for linear schedules by using singularity functions. These functions originate in structural engineering and are newly applied to scheduling. They capture the behavior of an activity or buffer and the range over which it applies and are extensible to an infinite number of change terms. This paper builds upon the critical path analysis for linear schedules, which takes differences between singularity functions and differentiates them. It makes several important case distinctions that extend the earlier concept of rate float. Time and location buffers act along different axis directions. Together with different productivities between and within activities, this can create a complex pattern of critical and noncritical segments. Depending on starts and finishes, areas of float precede or follow these noncritical segments. The schedule of a small project is reanalyzed with case distinctions to demonstrate in detail what float types are generated.