Computation of Critical Path Probabilities by Modified PERT

Abstract

Detection of the critical path and the uncertainty of the estimated duration are important for the contactors. PERT and Modified PERT methods can estimate the uncertainty of construction duration. However, probability of a path being critical is not estimated by the aforementioned methods. Monte Carlo simulation is implemented for the detection of probabilities of activities being critical. However, Monte Carlo simulation requires significant computational demand and this method is not suitable for iterative optimization procedure. In this study, Modified PERT method is enhanced by considering every possible path completion combinations. As a result, probability of finishing a path at a certain time and finishing the remaining paths earlier than the corresponding time is computed. This enabled the computation of probability of a path being critical path. For large networks the number of path completion combinations increases which makes the probabilistic computations burdensome. The relationship between the path completion combinations and the statistical intersection operations is derived and a macro code which executes the intersection computations is generated. The algorithm is tested on four sample problems and the results are compared with Monte Carlo simulation. Analysis results interpret that the method is significantly faster than Monte Carlo simulation with similar probability estimations. 

Keywords

• PERT,Modified PERT,Monte Carlo Simulation,Uncertainty analysis

References

1. Ahuja, H. N., and Nandakumar, V. (1985). Simulation model to forecast project completion time. Journal of construction engineering and management, 111(4), 325-342.
2. Moder, J. J., Phillips C. R., and Davis E. W. (1983), Project management with CPM, PERT and precedence diagramming, 3rd Edition, Van Nostrand Reinhold Company, New York.
3. Ang, A. H., Chaker, A. A., and Abdelnour, J. (1975). Analysis of activity networks under uncertainty. Journal of the Engineering Mechanics Division, 101(4), 373-387.
4. Taroun, A. (2014). Towards a better modelling and assessment of construction risk: Insights from a literature review. International journal of Project management, 32(1), 101-115.
5. Helton, J. C. (1993). Uncertainty and sensitivity analysis techniques for use in performance assessment for radioactive waste disposal. Reliability Engineering & System Safety, 42(2-3), 327-367.
6. Cheah, C. Y., and Liu, J. (2006). Valuing governmental support in infrastructure projects as real options using Monte Carlo simulation. Construction management and economics, 24(5), 545-554.
7. Khamooshi, H., and Cioffi, D. F. (2012). Uncertainty in task duration and cost estimates: Fusion of probabilistic forecasts and deterministic scheduling. Journal of construction engineering and management, 139(5), 488-497.
8. Tao, L., Wu, D., Liu, S., and Lambert, J. H. (2017). Schedule risk analysis for new-product development: The GERT method extended by a characteristic function. Reliability Engineering & System Safety, 167, 464-473.

9. Choudhry, R. M., Aslam, M. A., Hinze, J. W., and Arain, F. M. (2014). Cost and schedule risk analysis of bridge construction in Pakistan: Establishing risk guidelines. Journal of Construction Engineering and Management, 140(7), 04014020.
10. Dawood, N. (1998). Estimating project and activity duration: a risk management approach using network analysis. Construction Management & Economics, 16(1), 41-48.
11. Lee, D. E. (2005). Probability of project completion using stochastic project scheduling simulation. Journal of construction engineering and management, 131(3), 310-318.
12. Lee, D. E., and Arditi, D. (2006). Automated statistical analysis in stochastic project scheduling simulation. Journal of Construction Engineering and Management, 132(3), 268-277.
13. Jevtic, V., Dobrilovic, D., Stojanov, J., and Stojanov, Z. (2011, September). Project Duration Assessment Model Based on Modified Shortest Path Algorithm and Superposition. In IEEE International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 2011 13th pp. 87-90.
14. Guo, Q. L., Maher, M., and Wamuziri, S. (2001). Risk analysis in construction networks using a modified stochastic assignment model. CIVIL ENGINEERING SYSTEMS, 18(3), 215-241.
15. Diaz, C. F., and Hadipriono, F. C. (1993). Nondeterministic networking methods. Journal of construction engineering and management, 119(1), 40-57.
16. Al-Sadek, O., and Carmichael, D. G. (1992). On simulation in planning networks. Civil Engineering Systems, 9(1), 59-68.
17. Bettemir, Ö. H., and Birgönül, M. T. (2017). Network analysis algorithm for the solution of discrete time-cost trade-off problem. KSCE Journal of Civil Engineering, 21(4), 1047-1058.