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Critical Path Stability Region: A Single-Time Estimate Approach
Abstract
Models transform the managerial inputs into useful information for managerial decision. The Project Evaluation and Review Technique (PERT) is the most widely used model for project management. However, it requires three estimates for the duration of each activity as its input. This uncertainty in the input requirement makes the Critical Path (CP) unstable, causing major difficulties for the manager. A linear programming formulation of the project network is proposed in this chapter for determining a CP based on making one estimate for the duration of each activity. Upon finding the CP, Sensitivity Analysis (SA) of Data Perturbation (DP) is performed using the constraints of the dual problem. This largest DP set of uncertainties provides the manager with a tool to deal with the simultaneous, independent, or dependent changes of the input estimates that preserves the current CP. The application of DP results to enhance the traditional approach to PERT is presented. The proposed procedure is easy to understand, easy to implement, and provides useful information for the manager. A numerical example illustrates the process.
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