A Label-correcting Tracing Algorithm for the Approximation of the Probability Distribution Function of the Project Completion Time

When facing projects with uncertain factors, most of the project managers are interested to secure the pdf of the completion time of the project so as to have full insights into its randomness. For large-size SAN with general types of pdf for the duration of activities, the project managers must turn to the techniques of discretization since the other approaches in the literature become too demanding in computational loading. In this study, we find that there are two problems when applying the techniques of discretization to obtain an approximated probability density function (pdf) of the project completion time in stochastic activity networks. Namely, first, there exists neither exact data structure nor systematic scheme for the computer programming when applying the techniques of discretization; and second, error may arise from assuming independency between sub-paths in the activity network. Therefore, we are motivated to propose a Label-Correcting Tracing Algorithm (LCTA) to improve the techniques of discretization. To evaluate the performance of the proposed LCTA, we randomly generate 20 sets of 100-node instances in our numerical experiments. Using the pdf’s resultant from Monte Carlo simulation using 20,000 samples as the benchmark, we compared the pdf’s obtained from the PERT model, Dodin’s [10] algorithm and the proposed LCTA. Based on our experimental results, we conclude that the proposed LCTA significantly outperforms the others in both the run time and the precision aspects.