The critical path in a PERT/CPM network is determined in various textbooks by finding the path with associated minimal slack for the network arcs or by finding the path with associated minimal slack for the network nodes. This paper points out that the use of nodes can result in a network path being incorrectly identified as a path of maximum length.

The critical path method (CPM), project evaluation and review technique (PERT), and stochastic PERT, the most widely used tools for project management, each require different forms of activity duration information: fixed time, three-time estimates and an a priori distribution function, respectively. While PERT and stochastic PERT allow for uncertainty in activity durations unfortunately they require a number of strong statistical assumptions. In this paper, uncertainty in project activity duration is treated in a managerial context rather than as random factors. A linear programming (LP) formulation of the project activity network is constructed and a new simplex-type tabular solution algorithm is developed to find a critical path (CP). While the proposed approach requires a time estimate for each activity duration, it provides the manager with the allowable simultaneous, independent or dependent changes of the estimates that will preserve the current CP. The results of these analyses empower the project planner and manager to assess and monitor various types of activity-duration uncertainties encountered in real life situations. It is assumed the reader is familiar with LP terminology.

The use of arcs and nodes for the determination of critical paths in pert/cpm networks

Citations

Managing project activity-duration uncertainties

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