Bayesian Updating of Copula-Based Probabilistic Project-Duration Model
Publication: Journal of Construction Engineering and Management
Volume 146, Issue 5
Abstract
This paper presents a generic copula-based method for accurate prediction of probabilistic time performance of projects. The proposed stepwise method first collates all uncertainties of the project activities and propagates them using a Monte Carlo simulation (MCS) in cumulative progress S-curves and commercial project risk analysis software. By fitting the beta distribution function to every normalized simulated progress curve, the corresponding parameters of the so-called Beta-S model can be calculated and the best-fit marginal distribution functions of these parameters, including project completion time, and the correlation matrix can be established. In an innovative approach, a multivariate copula function then is employed to bind the marginal distribution function of these random variables together and produce their prior joint probability distribution as a single closed-form function. The merit of this copula-based function is that it alleviates the incorrect assumption of the independence of random variables in the Beta-S model. The actual progress data of the project are used for efficient Bayesian updating of the model by means of the Metropolis-Hastings (M-H) algorithm. The applicability of the proposed methodology is demonstrated on a project, and it is shown to outperform the existing probabilistic model with independent variables and the earned schedule method as a deterministic method.
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Data Availability Statement
Data generated or analyzed during the study are available from the corresponding author by request. Information about the Journal’s data-sharing policy can be found here: http://ascelibrary.org/doi/10.1061/(ASCE)CO.1943-7862.0001263.
References
Abdel Azeem, S. A., H. E. Hosny, and A. H. Ibrahim. 2014. “Forecasting project schedule performance using probabilistic and deterministic models.” HBRC J. 10 (1): 35–42. https://doi.org/10.1016/j.hbrcj.2013.09.002.
Acebes, F., J. Pajares, J. M. Galán, and A. López-Paredes. 2013. “Beyond earned value management: A graphical framework for integrated cost, schedule and risk monitoring.” Proc. Soc. Behav. Sci. 74 (Mar): 181–189. https://doi.org/10.1016/j.sbspro.2013.03.027.
Ang, A.-H. S., and W. H. Tang. 2006. Vol. 1 of Probability concepts in engineering: Emphasis on applications to civil and environmental engineering. 2nd ed. New York: Wiley.
Banerjee, A., and A. Paul. 2008. “On path correlation and PERT bias.” Eur. J. Oper. Res. 189 (3): 1208–1216. https://doi.org/10.1016/j.ejor.2007.01.061.
Barraza, G. A., W. Edward Back, and F. Mata. 2004. “Probabilistic forecasting of project performance using stochastic S curves.” J. Constr. Eng. Manage. 130 (1): 25–32. https://doi.org/10.1061/(ASCE)0733-9364(2004)130:1(25).
Batselier, J., and M. Vanhoucke. 2015. “Evaluation of deterministic state-of-the-art forecasting approaches for project duration based on earned value management.” Int. J. Project Manage. 33 (7): 1588–1596. https://doi.org/10.1016/j.ijproman.2015.04.003.
Batselier, J., and M. Vanhoucke. 2017. “Improving project forecast accuracy by integrating earned value management with exponential smoothing and reference class forecasting.” Int. J. Project Manage. 35 (1): 28–43. https://doi.org/10.1016/j.ijproman.2016.10.003.
Bolstad, W. M. 2009. Understanding computational Bayesian statistics. 1st ed. New York: Wiley.
Bouyé, E., V. Durrleman, A. Nikeghbali, G. Riboulet, and T. Roncalli. 2000. “Copulas for finance: A reading guide and some applications.” Accessed March 7, 2000. https://ssrn.com/abstract=1032533.
Caron, F., F. Ruggeri, and A. Merli. 2013. “A Bayesian approach to improve estimate at completion in earned value management.” Project Manage. J. 44 (1): 3–16. https://doi.org/10.1002/pmj.21303.
Casella, G. 2008. Monte Carlo statistical methods. Gainesville, FL: Univ. of Florida.
Chen, H. L., W. T. Chen, and Y. L. Lin. 2016. “Earned value project management: Improving the predictive power of planned value.” Int. J. Project Manage. 34 (1): 22–29. https://doi.org/10.1016/j.ijproman.2015.09.008.
Doucet, A., M. K. Pitt, G. Deligiannidis, and R. Kohn. 2015. “Efficient implementation of Markov chain Monte Carlo when using an unbiased likelihood estimator.” Biometrika 102 (2): 295–313. https://doi.org/10.1093/biomet/asu075.
Elmaghreby, S. E. 1989. Advances in project scheduling. 1st ed. Amsterdam, Netherlands: Elsevier.
Firouzi, A., and M. Vahdatmanesh. 2019. “Applicability of financial derivatives for hedging material price risk in highway construction.” J. Constr. Eng. Manage. 145 (5): 04019023. https://doi.org/10.1061/(ASCE)CO.1943-7862.0001639.
Firouzi, A., W. Yang, and C.-Q. Li. 2016. “Prediction of total cost of construction project with dependent cost items.” J. Constr. Eng. Manage. 142 (12): 04016072. https://doi.org/10.1061/(ASCE)CO.1943-7862.0001194.
Gatz, J. 2007. Properties and applications of the student T copula. Delft, Netherlands: Univ. of Delft.
Kamburowski, H. 1992. “Bounding the distribution of project duration in PERT networks.” Oper. Res. Lett. 12 (1): 17–22. https://doi.org/10.1016/0167-6377(92)90017-W.
Kendrick, T. 2015. Identifying and managing project risk: Essential tools for failure-proofing your project. 3rd ed. New York: American Management Association.
Kerkhove, L. P., and M. Vanhoucke. 2017. “Extensions of earned value management: Using the earned incentive metric to improve signal quality.” Int. J. Project Manage. 35 (2): 148–168. https://doi.org/10.1016/j.ijproman.2016.10.014.
Kerzner, H. 2003. Project management: A system approach to planning, scheduling, and controlling. 8th ed. New York: Wiley.
Khamooshi, H., and A. Abdi. 2017. “Project duration forecasting using earned duration management with exponential smoothing techniques.” J. Manage. Eng. 33 (1): 04016032. https://doi.org/10.1061/(ASCE)ME.1943-5479.0000475.
Khamooshi, H., and H. Golafshani. 2014. “EDM: Earned duration management, a new approach to schedule performance management and measurement.” Int. J. Project Manage. 32 (6): 1019–1041. https://doi.org/10.1016/j.ijproman.2013.11.002.
Khayyati, M., and A. Firouzi. 2018. “Project risk analysis using an integrated probabilistic beta-S model and multi-parameter copula function.” Amirkabir J. Civ. Eng. 51 (3): 51–60. https://doi.org/10.22060/ceej.2018.13596.5443.
Kim, B. C. 2007. Forecasting project progress and early warning of project overruns with probabilistic methods. College Station, TX: Texas A&M Univ.
Kim, B. C., and K. F. Reinschmidt. 2009. “Probabilistic forecasting of project duration using Bayesian inference and the beta distribution.” J. Constr. Eng. Manage. 135 (3): 178–186. https://doi.org/10.1061/(ASCE)0733-9364(2009)135:3(178).
Kim, B. C., and K. F. Reinschmidt. 2010. “Probabilistic forecasting of project duration using Kalman filter and the earned value method.” J. Constr. Eng. Manage. 136 (8): 834–843. https://doi.org/10.1061/(ASCE)CO.1943-7862.0000192.
Kim, S. D., R. K. Hammond, and J. E. Bickel. 2014. “Improved mean and variance estimating formulas for PERT analyses.” IEEE Trans. Eng. Manage. 61 (2): 362–369. https://doi.org/10.1109/TEM.2014.2304977.
Li, C. Q., A. Firouzi, and W. Yang. 2017. “Prediction of pitting corrosion–induced perforation of ductile iron pipes.” J. Eng. Mech. 143 (8): 04017048. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001258.
MacCrimmon, K. R., and C. A. Ryavec. 1964. “An analytical study of the PERT assumptions.” Oper. Res. 12 (1): 16–37. https://doi.org/10.1287/opre.12.1.16.
Manning, S. 2008. “Embedding projects in multiple contexts—A structuration perspective.” Int. J. Project Manage. 26 (1): 30–37. https://doi.org/10.1016/j.ijproman.2007.08.012.
Meucci, A. 2011. “A short comprehensive practical guide to copulas.” Risk Prof. J. 22–27. https://doi.org/10.2139/ssrn.1847864.
Moselhi, O. 2011. “The use of earned value in forcasting project durations.” In Proc., 28th Int. Symp. on Automation and Robotics in Construction. Seoul: International Association for Automation and Robotics in Construction. https://doi.org/10.22260/ISARC2011/0129.
Naeni, L., S. Shadrokh, and A. Salehipour. 2014. “A fuzzy approach for the earned value management.” Int. J. Project Manage. 32 (4): 709–716. https://doi.org/10.1016/j.ijproman.2013.02.002.
Narbaev, T., and A. D. Marco. 2014. “An earned schedule-based regression model to improve cost estimate at completion.” Int. J. Project Manage. 32 (6): 1007–1018. https://doi.org/10.1016/j.ijproman.2013.12.005.
Neal, R. M. 1993. Probabilistic inference using Markov chain Monte Carlo methods. Toronto: Univ. of Toronto.
Pelissier, R., and F. Goreaud. 2015. “ads package for R: A fast unbiased implementation of the K-function family for studying spatial point patterns in irregular-shaped sampling windows.” J. Stat. Software 63 (6): 1–18. https://doi.org/10.18637/jss.v063.i06.
PMI (Project Management Institute). 2011. Practice standard for earned value management, 7–27. Newtown Square, PA: PMI.
PMI (Project Management Institute). 2013. Project management body of knowledge. 5th ed. Newtown Square, PA: PMI.
Pontrandolfo, P. 2000. “Project duration in stochastic networks by the PERT-path technique.” Int. J. Project Manage. 18 (3): 215–222. https://doi.org/10.1016/S0263-7863(99)00015-0.
Shanmugam, R., and R. Chattamvelli. 2015. Statistics for scientists and engineers. 1st ed. New York: Wiley.
Shemyakin, A., and A. Kniazev. 2017. Introduction to Bayesian estimation and copula models of dependence. 1st ed. New York: Wiley.
Trietsch, D., and K. R. Baker. 2012. “PERT 21: Fitting PERT/CPM for use in the 21st century.” Int. J. Project Manage. 30 (4): 490–502. https://doi.org/10.1016/j.ijproman.2011.09.004.
Vanhoucke, M., and S. Vandevoorde. 2017. “A simulation and evaluation of earned value metrics to forecast the project duration.” J. Oper. Res. Soc. 58 (10): 1361–1374. https://doi.org/10.1057/palgrave.jors.2602296.
van Ravenzwaaij, D., P. Cassey, and S. D. Brown. 2018. “A simple introduction to Markov chain Monte-Carlo sampling.” Psychonomic Bull. Rev. 25 (1): 143–154. https://doi.org/10.3758/s13423-016-1015-8.
Warburton, R. D. H., and D. F. Cioffi. 2016. “Estimating a project’s earned and final duration.” Int. J. Project Manage. 34 (8): 1493–1504. https://doi.org/10.1016/j.ijproman.2016.08.007.
Wauters, M., and M. Vanhoucke. 2015. “Study of the stability of earned value management forecasting.” J. Constr. Eng. Manage. 141 (4): 04014086. https://doi.org/10.1061/(ASCE)CO.1943-7862.0000947.
Yang, I. T. 2005. “Simulation-based estimation for correlated cost elements.” Int. J. Project Manage. 23 (4): 275–282. https://doi.org/10.1016/j.ijproman.2004.12.002.
Young, G. A., and R. L. Smith. 2010. Essentials of statistical inference. 1st ed. Cambridge, UK: Cambridge University Press.
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Published In
Journal of Construction Engineering and Management
Volume 146 • Issue 5 • May 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Feb 18, 2019
Accepted: Oct 28, 2019
Published online: Mar 14, 2020
Published in print: May 1, 2020
Discussion open until: Aug 14, 2020
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