Project Tightness Index (PT): A Concise Metric of Schedule Tightness

Abstract

In this paper, we introduce Project Tightness (PT), a new topological indicator designed to assess the structural tightness of project schedules. The indicator combines information on the project’s network structure and activity durations, yielding a normalised measure on the [0,1] scale. PT quantifies the degree of schedule compression—or “tightness”—by integrating both activity floats and the configuration of the project’s critical structure. Unlike the classic XSLACK-R (average relative slack per activity), proposed by Patterson in Project Scheduling: The Effects of Problem Structure on Heuristic Performance (1976), the new indicator normalises total slack by the number of activities that do not belong to the dominant critical path (i.e., the critical path with the greatest number of activities). In doing so, PT penalises the presence of parallel critical branches—that is, critical activities outside the longest critical path—an aspect not captured by XSLACK-R. The paper formally develops the indicator’s definition and fundamental properties (boundedness, time-scale invariance, and monotonicity) and presents several illustrative examples to support its interpretation and practical use.