New concepts for activity float in resource-constrained project management

The concepts of float and critical path are central to analyzing activity networks in project management. In resource-constrained projects, schedule multiplicity makes it difficult to calculate float and identify critical activities accurately. In this work, new concepts of float and critical activity are developed to ascertain critical activities more precisely without reference to activity start and end times in specific schedules. The notions of float, group float, float set, negative float and zero critical activity are introduced, which the project manager can use to deal more effectively with critical activities, duration uncertainty, activity buffering, and resource allocation than the currently available tools in literature. For practical implementation, algorithms are provided and tested to calculate the new measures on the PSPLIB benchmark instances, specifically the J30, J60 and J120 test sets, for the resource constrained project management, illustrating the effectiveness of the proposed concepts in helping to identify flexibility in scheduling activities.