A revised critical path method for networks including both overlap relationships and variable-duration activities

Over the years, various extensions of the Critical Path Method have been proposed that include more general precedence relationships. The need for such relationships arises when one wishes to include in the project network aggregated activities, because simple strict precedences are often inadequate models of the work flow relationships between such activities and others in the network. The authors demonstrate that diagrammatic approaches to model overlap relationships (e.g., splitting activities in an activity-on-node diagram, the Precedence Diagramming Method) also fail to provide correct models when variable rates of activity operation are allowed. To overcome these deficiencies, we introduce a generalized model of activity operation involving the tracking of an intensity curve that indexes the resource loading curves for the activity. The authors formulate inventory balance-type relationships between intensity curves of dependent activities so as to correctly model activity work flow dependencies. As a replacement for basic CPM calculations, they develop procedures that calculate earliest and latest intensity curves for each activity subject to the inventory balance constraints. This generalized model of activity operation and of work flow dependencies leads to generalized notions of activity criticality and activity slack expressed in terms of cumulative intensity curves. The authors define and interpret such measures of slack.