Critical clouds and critical sets in resource-constrained projects

Project managers need to identify critical tasks. Shortcomings of existing methods for the identification of critical tasks in resource-constrained projects in situations involving more than one unit of renewable resource are highlighted through examples. The concepts of critical set and critical cloud are proposed in this paper as an extension to the concept of critical task. They allow a consistent and unified treatment of criticality in projects with resource constraints and provide an unambiguous procedure to establish the critical sequence and its constituents. An algorithm to determine critical sets and critical clouds is proposed, and applied to a sample project. The results of this algorithm are presented in a condensed, project manager-friendly, graphical format.