Critical Duration Index: Anticipating Project Delays from Deterministic Schedule Information
Publication: Journal of Construction Engineering and Management
Volume 148, Issue 11
Abstract
Classical scheduling techniques are well-known to underestimate the average project duration, yet they remain widely used in practice due to their simplicity. In this paper, the new Critical Duration Index (CDI) is proposed. This index indirectly allows anticipation for the probability of a project ending late, as well as the average project duration extension compared with a deterministic project duration estimate. The accuracy of two simple regression expressions that use the CDI was tested on two representative data sets of 4,100 artificial and 108 empirical (real) projects. Results show that these regression expressions outperformed the only alternative index found in the literature. Besides allowing enhanced forecasting possibilities, calculating the CDI only requires basic scheduling information that is available at the planning stage. It can thus be easily adopted by project managers to improve their project duration estimates over prior deterministic techniques.
Practical Applications
Classical scheduling techniques like Gantt charts or the critical path method are known to underestimate the project duration. However, they remain widely used in practice due to their simplicity. In this paper, we have proposed the Critical Duration Index (CDI). This index allows anticipation for the probability of a project ending later than the estimate produced with a Gantt chart or the critical path method. It also allows an estimation for how much longer the project might take to be completed, that is, the extension of the delay. The accuracy of two simple regression expressions that use the CDI was tested on two representative artificial and real project data sets. Our results show that these regression expressions outperformed the only alternative index found in the literature. Besides allowing one to forecast the probability and extension of a project delay, calculating the CDI only requires basic scheduling information that is available at the planning stage. Hence, it can be easily adopted by project managers to improve their project duration estimates over other deterministic techniques.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, and code generated or used during the study appear in the published article. Namely, all artificial and empirical project data sets, as well as the two indices’ comparison, have all been included as Supplemental Materials.
Acknowledgments
This research is supported by the National Social Science Fund projects (No. 20BJY010); National Social Science Fund Post-Financing Projects (No. 19FJYB017); Sichuan-Tibet Railway Major Fundamental Science Problems Special Fund (No. 71942006); Qinghai Natural Science Foundation (No. 2020-JY-736); List of Key Science and Technology Projects in China’s Transportation Industry in 2018-International Science and Technology Cooperation Project (Nos. 2018-GH-006 and 2019-MS5-100); Emerging Engineering Education Research and Practice Project of Ministry of Education of China (No. E-GKRWJC20202914); Shaanxi Province Higher Education Teaching Reform Project (No. 19BZ016); and Humanities and Social Sciences Research Project of the Ministry of Education (21XJA752003).
References
AbouRizk, S. M., and D. W. Halpin. 1992. “Statistical properties of construction duration data.” J. Constr. Eng. Manage. 118 (3): 525–544. https://doi.org/10.1061/(ASCE)0733-9364(1992)118:3(525).
AbouRizk, S. M., D. W. Halpin, and J. R. Wilson. 1994. “Fitting beta distributions based on sample data.” J. Constr. Eng. Manage. 120 (2): 288–305. https://doi.org/10.1061/(ASCE)0733-9364(1994)120:2(288).
Acebes, F., M. Pereda, D. Poza, J. Pajares, and J. M. Galán. 2015. “Stochastic earned value analysis using Monte Carlo simulation and statistical learning techniques.” Int. J. Project Manage. 33 (7): 1597–1609. https://doi.org/10.1016/j.ijproman.2015.06.012.
Altuwaim, A., and K. A. El-Rayes. 2021. “Multiobjective optimization model for planning repetitive construction projects.” J. Constr. Eng. Manage. 147 (7): 04021072. https://doi.org/10.1061/(ASCE)CO.1943-7862.0002072.
Ansar, A., B. Flyvbjerg, A. Budzier, and D. Lunn. 2016. “Does infrastructure investment lead to economic growth or economic fragility? Evidence from China.” Oxford Rev. Econ. Policy 32 (3): 360–390. https://doi.org/10.1093/oxrep/grw022.
Ballesteros-Pérez, P. 2017a. “Modelling the boundaries of project fast-tracking.” Autom. Constr. 84 (Dec): 231–241. https://doi.org/10.1016/j.autcon.2017.09.006.
Ballesteros-Pérez, P. 2017b. “M-PERT: Manual project-duration estimation technique for teaching scheduling basics.” J. Constr. Eng. Manage. 143 (9): 04017063. https://doi.org/10.1061/(ASCE)CO.1943-7862.0001358.
Ballesteros-Pérez, P., A. Cerezo-Narváez, M. Otero-Mateo, A. Pastor-Fernández, and M. Vanhoucke. 2019a. “Performance comparison of activity sensitivity metrics in schedule risk analysis.” Autom. Constr. 106 (Oct): 102906. https://doi.org/10.1016/j.autcon.2019.102906.
Ballesteros-Pérez, P., A. Cerezo-Narváez, M. Otero-Mateo, A. Pastor-Fernández, and M. Vanhoucke. 2020a. “Forecasting the project duration average and standard deviation from deterministic schedule information.” Appl. Sci. 10 (654): 22. https://doi.org/10.3390/app10020654.
Ballesteros-Pérez, P., M. C. González-Cruz, J. P. Pastor-Ferrando, and M. Fernández-Diego. 2012. “The iso-score curve graph. A new tool for competitive bidding.” Autom. Constr. 22 (Mar): 481–490. https://doi.org/10.1016/j.autcon.2011.11.007.
Ballesteros-Pérez, P., G. D. Larsen, and M. C. González-Cruz. 2018. “Do projects really end late? On the shortcomings of the classical scheduling techniques.” J. Technol. Sci. Educ. 8 (1): 86–102. https://doi.org/10.3926/jotse.303.
Ballesteros-Pérez, P., E. Sanz-Ablanedo, A. Cerezo-Narváez, G. Lucko, A. Pastor-Fernández, M. Otero-Mateo, and J. P. Contreras-Samper. 2020b. “Forecasting accuracy of in-progress activity duration and cost estimates.” J. Constr. Eng. Manage. 146 (9): 1–13. https://doi.org/10.1061/(ASCE)CO.1943-7862.0001900.
Ballesteros-Pérez, P., E. Sanz-Ablanedo, D. Mora-Melià, M. C. González-Cruz, J. L. Fuentes-Bargues, and E. Pellicer. 2019b. “Earned schedule min-max: Two new EVM metrics for monitoring and controlling projects.” Autom. Constr. 103 (Apr): 279–290. https://doi.org/10.1016/j.autcon.2019.03.016.
Ballesteros-Pérez, P., E. Sanz-Ablanedo, R. Soetanto, M. C. González-Cruz, G. D. Larsen, and A. Cerezo-Narváez. 2020c. “Duration and cost variability of construction activities: An empirical study.” J. Constr. Eng. Manage. 146 (1): 04019093. https://doi.org/10.1061/(ASCE)CO.1943-7862.0001739.
Barrientos-Orellana, A., P. Ballesteros-Pérez, D. Mora, M. C. González-Cruz, and M. Vanhoucke. 2021. “Stability and accuracy of deterministic project duration forecasting method in earned value management.” Eng. Constr. Archit. Manage. 29 (3): 1449–1469.
Batselier, J., and M. Vanhoucke. 2015a. “Construction and evaluation framework for a real-life project database.” Int. J. Project Manage. 33 (3): 697–710. https://doi.org/10.1016/j.ijproman.2014.09.004.
Batselier, J., and M. Vanhoucke. 2015b. “Empirical evaluation of earned value management forecasting accuracy for time and cost.” J. Constr. Eng. Manage. 141 (11): 05015010. https://doi.org/10.1061/(ASCE)CO.1943-7862.0001008.
Chen, S.-P. 2007. “Analysis of critical paths in a project network with fuzzy activity times.” Eur. J. Oper. Res. 183 (1): 442–459. https://doi.org/10.1016/j.ejor.2006.06.053.
Chudley, R., and R. Greeno. 2016. Building construction handbook. Abingdon, UK: Routledge.
Clark, C. E. 1961. “The greatest of a finite set of random variables.” Oper. Res. 9 (2): 145–162. https://doi.org/10.1287/opre.9.2.145.
Clark, C. E. 1962. “Letter to the editor–The PERT model for the distribution of an activity time.” Oper. Res. 10 (3): 405–406. https://doi.org/10.1287/opre.10.3.405.
Colin, J., and M. Vanhoucke. 2014. “Setting tolerance limits for statistical project control using earned value management.” Omega 49 (Dec): 107–122. https://doi.org/10.1016/j.omega.2014.06.001.
Colin, J., and M. Vanhoucke. 2015. “A comparison of the performance of various project control methods using earned value management systems.” Expert Syst. Appl. 42 (6): 3159–3175. https://doi.org/10.1016/j.eswa.2014.12.007.
Colin, J., and M. Vanhoucke. 2016. “Empirical perspective on activity durations for project-management simulation studies.” J. Constr. Eng. Manage. 142 (1): 04015047. https://doi.org/10.1061/(ASCE)CO.1943-7862.0001022.
de Koning, P., and M. Vanhoucke. 2016. “Stability of earned value management: Do project characteristics influence the stability moment of the cost and schedule performance index.” J. Mod. Project Manage. 4 (1): 9–25.
Demeulemeester, E., M. Vanhoucke, and W. Herroelen. 2003. “RanGen: A random network generator for activity-on-the-node networks.” J. Scheduling 6 (1): 17–38. https://doi.org/10.1023/A:1022283403119.
Dodin, B., and M. Sirvanci. 1990. “Stochastic networks and the extreme value distribution.” Comput. Oper. Res. 17 (4): 397–409. https://doi.org/10.1016/0305-0548(90)90018-3.
Fan, S.-L., I.-C. Yeh, and W.-S. Chi. 2021. “Improvement in estimating durations for building projects using artificial neural network and sensitivity analysis.” J. Constr. Eng. Manage. 147 (7): 04021050. https://doi.org/10.1061/(ASCE)CO.1943-7862.0002036.
Flyvbjerg, B. 2011. “Over budget, over time, over and over again.” In Oxford handbook of project management, edited by P. W. G. Morris, J. Pinto, and J. Söderlund. New York: Oxford University Press.
Hajdu, M. 2013. “Effects of the application of activity calendars on the distribution of project duration in PERT networks.” Autom. Constr. 35 (Nov): 397–404. https://doi.org/10.1016/j.autcon.2013.05.025.
Hajdu, M., and O. Bokor. 2014. “The effects of different activity distributions on project duration in PERT networks.” Procedia Soc. Behav. Sci. 119 (Mar): 766–775. https://doi.org/10.1016/j.sbspro.2014.03.086.
Hamzah, N., M. A. Khoiry, I. Arshad, N. M. Tawil, and A. I. Che Ani. 2011. “Cause of construction delay—Theoretical framework.” Procedia Eng. 20 (Jan): 490–495. https://doi.org/10.1016/j.proeng.2011.11.192.
Herrerías-Velasco, J. M., R. Herrerías-Pleguezuelo, and J. R. van Dorp. 2011. “Revisiting the PERT mean and variance.” Eur. J. Oper. Res. 210 (2): 448–451.
Keane, P. J., and A. F. Caletka. 2008. Delay analysis in construction contracts. Oxford, UK: Wiley-Blackwell.
Kelley, J. E., and M. R. Walker. 1959. “Critical-path planning and scheduling.” In Proc., Eastern Joint Computer Conf., 160–173. New York: Macmillan.
Kelley, J. E., and M. R. Walker. 1989. “The origins of CPM: A personal history.” PMnetwork 3 (2): 7–22.
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.
Khamooshi, H., and D. F. Cioffi. 2013. “Uncertainty in task duration and cost estimates: Fusion of probabilistic forecasts and deterministic scheduling.” J. Constr. Eng. Manage. 139 (5): 488–497. https://doi.org/10.1061/(ASCE)CO.1943-7862.0000616.
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.
Liu, Y., and Z. F. Wang. 2013. “Analysis of project schedule risk indexes in PERT network using Monte Carlo simulation.” Adv. Mater. Res. 760–762: 2205–2211. https://doi.org/10.4028/www.scientific.net/AMR.760-762.2205.
Lu, M. 2002. “Enhancing project evaluation and review technique simulation through artificial neural network-based input modeling.” J. Constr. Eng. Manage. 128 (5): 438–445. https://doi.org/10.1061/(ASCE)0733-9364(2002)128:5(438).
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.
Mahamid, I., A. Bruland, and N. Dmaidi. 2012. “Causes of delay in road construction projects.” J. Manage. Eng. 28 (3): 300–310. https://doi.org/10.1061/(ASCE)ME.1943-5479.0000096.
Malcolm, D. G., J. H. Roseboom, C. E. Clark, and W. Fazar. 1959. “Application of a technique for research and development program evaluation.” Oper. Res. 7 (5): 646–669. https://doi.org/10.1287/opre.7.5.646.
Martens, A., and M. Vanhoucke. 2018. “An empirical validation of the performance of project control tolerance limits.” Autom. Constr. 89 (May): 71–85. https://doi.org/10.1016/j.autcon.2018.01.002.
Nelson, R. G., A. Azaron, and S. Aref. 2016. “The use of a GERT based method to model concurrent product development processes.” Eur. J. Oper. Res. 250 (2): 566–578. https://doi.org/10.1016/j.ejor.2015.09.040.
Operations Research & Scheduling Research Group. 2022. “MTD dataset.” Accessed July 30, 2022. https://www.projectmanagement.ugent.be/sites/default/files/datasets/RCPSP/RCPLIB.zip.
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.
Sanz-Ablanedo, E., J. H. Chandler, P. Ballesteros-Pérez, and J. R. Rodríguez-Pérez. 2020. “Reducing systematic dome errors in digital elevation models through better UAV flight design.” Earth Surf. Processes Landforms 45 (9): 2134–2147.
Taylor, F. W. 1903. Shop Management. New York: Harper & Brothers.
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.
Trietsch, D., L. Mazmanyan, L. Gevorgyan, and K. R. Baker. 2012. “Modeling activity times by the Parkinson distribution with a lognormal core: Theory and validation.” Eur. J. Oper. Res. 216 (2): 386–396. https://doi.org/10.1016/j.ejor.2011.07.054.
Valadares Tavares, L., J. Antunes Ferreira, and J. Silva Coelho. 1999. “The risk of delay of a project in terms of the morphology of its network.” Eur. J. Oper. Res. 119 (2): 510–537. https://doi.org/10.1016/S0377-2217(99)00150-2.
Vanhoucke, M. 2008. “Measuring time using novel earned value management metrics.” In Vol. 1 of Proc., 22nd IPMA World Congress, 99–103. Rome, Italy: International Project Management Association.
Vanhoucke, M. 2010. Measuring time—Improving project performance using earned value management: International series in operations research and management science, 136. Dordrecht, Netherlands: Springer.
Vanhoucke, M. 2011. “On the dynamic use of project performance and schedule risk information during project tracking.” Omega 39 (4): 416–426. https://doi.org/10.1016/j.omega.2010.09.006.
Vanhoucke, M. 2013. Project management with dynamic scheduling. Berlin: Springer.
Vanhoucke, M. 2015. “On the use of schedule risk analysis for project management.” J. Mod. Project Manage. 2 (3): 108–117.
Vanhoucke, M., J. Coelho, and J. Batselier. 2016. “An overview of project data for integrated project management and control.” J. Mod. Project Manage. 3 (3): 7–21.
Vanhoucke, M., J. Coelho, D. Debels, B. Maenhout, and L. V. Tavares. 2008. “An evaluation of the adequacy of project network generators with systematically sampled networks.” Eur. J. Oper. Res. 187 (2): 511–524. https://doi.org/10.1016/j.ejor.2007.03.032.
Votto, R., L. L. Ho, and F. Berssaneti. 2021. “Earned duration management control charts: Role of control limit width definition for construction project duration monitoring.” J. Constr. Eng. Manage. 147 (9): 04021108. https://doi.org/10.1061/(ASCE)CO.1943-7862.0002135.
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.
Wilson, J. M. 2003. “Gantt charts: A centenary appreciation.” Eur. J. Oper. Res. 149 (2): 430–437. https://doi.org/10.1016/S0377-2217(02)00769-5.
Zidane, Y. J. T., and B. Andersen. 2018. “The top 10 universal delay factors in construction projects.” Int. J. Managing Projects Bus. 11 (3): 650–672. https://doi.org/10.1108/IJMPB-05-2017-0052.
Information & Authors
Information
Published In
Journal of Construction Engineering and Management
Volume 148 • Issue 11 • November 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Jan 26, 2022
Accepted: Jun 10, 2022
Published online: Aug 30, 2022
Published in print: Nov 1, 2022
Discussion open until: Jan 30, 2023
ASCE Technical Topics:
- Analysis (by type)
- Bibliographies
- Business management
- Construction engineering
- Construction management
- Engineering fundamentals
- Forecasting
- Information management
- Management methods
- Mathematics
- Practice and Profession
- Probability
- Project delay
- Project management
- Regression analysis
- Scheduling
- Statistical analysis (by type)
- Statistics
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited by
- Lili Zhang, Zhengrui Chen, Dan Shi, Yanan Zhao, An Inverse Optimal Value Approach for Synchronously Optimizing Activity Durations and Worker Assignments with a Project Ideal Cost, Mathematics, 10.3390/math11051178, 11, 5, (1178), (2023).