Uncertainty in Task Duration and Cost Estimates: Fusion of Probabilistic Forecasts and Deterministic Scheduling
Publication: Journal of Construction Engineering and Management
Volume 139, Issue 5
Abstract
A model for project budgeting and scheduling with uncertainty is developed. The traditional critical-path method (CPM) misleads because there are few, if any, real-life deterministic situations for which CPM is a great match; program evaluation and review technique (PERT) has been seen to have its problems, too (e.g., merge bias, unavailability of data, difficulty of implementation by practitioners). A dual focus on the distributions of the possible errors in the time and cost estimates and on the reliability of the estimates used as planned values suggests an approach for developing reliable schedules and budgets with buffers for time and cost. This method for budgeting and scheduling is executed through either simulation or a simple analytical approximation. The dynamic buffers provide much-needed flexibility, accounting for the errors in cost and duration estimates associated with planning any real project, thus providing a realistic, practical, and dynamic approach to planning and scheduling.
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Appendix. Mathematical Underpinning of USM Approach
Assume that the planning department or the estimators are asked to provide the following information on each task or work package:where = actual duration needed for the task or work package; = estimated duration needed for the task or work package; = potential error in the time estimate; and = reliability of the duration estimate stated as a probability by the estimator.where = actual cost or the budget needed to do the task ; = estimated cost or the budget needed to do the task ; = potential value for the error in the cost estimate; and = reliability of the cost estimate stated as a probability by the estimator.
(1)
(2)
(3)
(4)
Although the reliability of each estimate is not necessarily the same for all the elements in a project, usually there is a level of learning and experience in each organization that provides some consistency in the accuracy level of the estimates. The range of these reliability estimates will be larger for more-complex, innovative, and research-and-development types of projects and smaller for more-established and repeated types of project. As discussed in the paper, average reliability for time and cost estimates were used:where = number of tasks on the network’s critical path.where = number of tasks in the project.
(5)
(6)
So the average probability for each of the duration estimates to go over its value is , and that of the cost estimates is . If the completion of each task or work package is considered to be the same as one trial in a binomial experiment, the number of tasks that will finish on time and of those that will possibly be delayed should be determined. For the duration of the project, the focus should be on the activities on the critical path; for the cost of the project, all the work package tasks in the network, presented by , should be considered. If a binomial distribution for the occurrence of the delays and cost overruns is assumed, the probability of exactly out of tasks being delayed and out of activities needing more money can be determined from the following representations of the binomial distribution, respectively:where and = number of occurrences, or successes, in a binomial experiment of or trials, respectively.
(7)
(8)
The size of the total delay is a function of the number of activities on the critical path, , the probability of duration overrun for each activity, , the potential extension or delay (size of the error, for which a point estimate is assumed; this assumption is relaxed later) and management’s level of confidence. For a predefined confidence level, e.g., 0.99, is found by solving the following probability equation:
(9)
If a distribution for the value of the error is assumed—normal, , negative exponential, right-angle triangular, or any other suitable distribution—then, according to the central-limit theorem, the distributions for and will be normal. That is, if
(10)
(11)
Then,
(12)
(13)
To set an amount for contingency, a confidence level has to be set, say . Then the buffer or contingency value has to be solved such that
(14)
Using Eqs. ( 12) and ( 13) and based on central-limit theorem,where = probability found from a standard normal distribution. For the cost contingency, if a level of confidence of is assumed, there is a contingency value such that
(15)
(16)
(17)
(18)
The sums are over to for durations and to for cost contingency. The probability of being less than or equal to or being less than or equal to could be assumed, for example, to be 99%. Then, by using the central-limit theorem and the normal distribution, and could be determined.
The previous mathematical exercise is not practical for two reasons. First, the calculation is not straightforward for practitioners; second, the data from which the needed distributions can be developed are not available. The computational problem could be resolved for advanced practitioners by using simulation, but the lack of reliable data is a serious problem that cannot be overcome easily. Instead, a binomial distribution can be used for setting the contingencies.
A binomial distribution for the duration of a task is assumed, and the total delay is found by adding the first errors, ranked in descending order:
(19)
The cost overrun at a given certainty level (e.g., 0.99) is the sum of deviations over overruns from the activities composing the project:
(20)
(21)
References
Back, W. E., Boles, W. W., and Fry, G. T. ( 2000). “ Defining triangular probability distributions from historical cost data.” J. Constr. Eng. Manage., 126( 1), 29– 37.
Baker, W. R. ( 1986). “ Handling uncertainty.” IJPM, 4, 205– 210.
Ballard, G. ( 1999). “ Improving work flow reliability.” Proc., 7th Annual Conf. of the Int. Group for Lean Construction, Univ. of California, Berkeley, CA, 275– 286.
Ballard, G. ( 2000). “ Phase scheduling.”, Lean Construction Institute, San Diego.
Britney, B. R. ( 1976). “ Bayesian point estimation and the PERT scheduling of stochastic activities.” Manage. Sci., 22( 9), 938– 948.
Buehler, R., Griffin, D., and Ross, M. ( 1994). “ Exploring the ‘planning fallacy’: Why people underestimate their task completion times.” J. Pers. Soc. Psychol., 67( 3), 366– 381.
Burt, C. D. B., and Kemp, S. ( 1994). “ Construction of activity duration and time management potential.” Appl. Cognit. Psychol., 8( 2), 155– 168.
Chan, D. W. M., and Kumaraswamy, M. M. ( 1997). “ A comparative study of causes of time overruns in Hong Kong construction projects.” Int. J. Proj. Manage., 15( 1), 55– 64.
Cioffi, D. F. ( 2006). “ Subject expertise, management effectiveness, and the newness of a project: The creation of the Oxford English Dictionary.” Proc., Project Management Institute Research Conf., Project Management Institute, Newtown Square, PA.
Cioffi, D. F., and Khamooshi, H. ( 2008). “ A practical method to determine project risk contingency budget.” J. Oper. Res. Soc., 60( 4), 565– 571.
Clark, C. E. ( 1961). “ The greatest of a finite set of random variables.” Oper. Res., 9( 2), 145– 162.
De Meyer, L. C. H., and Pitch, M. T. ( 2002). “ Managing project uncertainty: From variation to chaos.” MIT Sloan Management Review, Winter, 60– 67.
Eden, C., Williams, T., and Ackerman, F. ( 2005). “ Analysing project cost overruns: Comparing the ‘measured mile’ analysis and system dynamics modeling.” Int. J. Proj. Manage., 23( 2), 135– 139.
Emhejellen, M., Emhejellen, K., and Osmundsen, P. ( 2003). “ Cost estimation overruns in the North Sea.” Proj. Manage. J, 34, 23– 29.
Fente, J., Schexnayder, C., and Knutson, K. ( 2000). “ Defining a probability distribution function for construction simulation.” J. Constr. Eng. Manage., 126( 3), 234– 241.
Flyvbjerg, B. ( 2008). “ Curbing optimism bias and strategic misrepresentation in planning: Reference class forecasting in practice.” Eur. Plann. Stud., 16( 1), 3– 21.
Flyvbjerg, B., Garbuio, M., and Lovallo, D. ( 2009). “ Delusion and deception in large infrastructure projects, two models for explaining and preventing executive disaster.” Calif. Manage. Rev., 51( 2), 170– 193.
Flyvbjerg, B., Holm, M. S., and Buhl, S. ( 2002). “ Understanding costs in public works projects, error or lie?” J. Am. Plann. Assoc., 68( 3), 279– 295.
González, V., Alarcón, L. F., Maturana, S., Mundaca, F., and Bustamante, J. ( 2010). “ Improving planning reliability and project performance using the reliable commitment model.” J. Constr. Eng. Manage., 136( 10), 1129– 1139.
Gutierrez, G. J., and Kouvelis, P. ( 1991). “ Parkinson’s law and its implications for project management.” Manage. Sci., 37( 8), 990– 1001.
Herroelen, W., De Reyck, B., and Demeulemeester, E. ( 1998). “ Resource constrained project scheduling, a survey of recent development.” Comput. Ops. Res., 25( 4), 279– 302.
Herroelen, W., and Leus, R. ( 2004). “ The construction of stable project baseline schedules.” Eur. J. Opl. Res., 156( 3), 550– 565.
Herroelen, W., and Leus, R. ( 2005). “ Project scheduling under uncertainty—Survey and research potential.” Eur. J. Opl. Res., 165( 2), 289– 306.
Howick, S. ( 2003). “ Using system dynamics to analyze disruption and delay in complex projects for litigation: Can the modeling purposes be met?” J. Oper. Res. Soc., 54( 3), 222– 229.
Hughes, M. W. ( 1986). “ Why projects fail: The effects of ignoring the obvious.” Ind. Eng., 18( 4), 14– 18.
Khamooshi, H. ( 1999). “ Dynamic priority—Dynamic programming scheduling method : A dynamics approach to resource constraint project scheduling.” Int. J. Proj. Manage., 17( 6), 383– 391.
Khamooshi, H., and Cioffi, D. F. ( 2009). “ A holistic approach to program risk contingency planning.” IEEE Trans. Eng. Manage., 56( 1), 171– 179.
Kirytopoulos, K., Leopoulos, V., and Diamantas, V. ( 2008). “ PERT vs. Monte Carlo simulation along with the suitable distribution effect.” Int. J. Proj. Organ. Manage., 1( 1), 24– 46.
Klingel, A. R., Jr. ( 1966). “ Bias in PERT project completion times calculations for a real network.” Manage. Sci., 13( 4), B-194– B-201.
Lee, H.-S., Shin, J.-W., Park, M., and Ryu, H.-G. ( 2009). “ Probabilistic duration estimation model for high-rise structural work.” J. Constr. Eng. Manage., 135( 12), 1289– 1298.
Lichtenberg, S. ( 1983). “ Alternatives to conventional project management.” Int. J. Proj. Manage., 1( 2), 101– 102.
MacCrimmon, K. R., and Ryanec, C. A. ( 1964). “ An analytical study of the PERT assumptions.” Oper. Res., 12( 1), 16– 27.
Parkinson, C. N. ( 1957). Parkinson’s law and other studies in administration, Random House, New York.
Pertmaster [Computer software]. 〈 www.pertmaster.com〉.
Peterson, C., and Miller, A. ( 1964). “ Mode, median, and mean as optimal strategies.” J. Exp. Psychol., 68( 4), 363– 367.
Pinto, J. K., and Mantel, S. J. ( 1990). “ The causes of project failure.” IEEE Trans. Eng. Manage., 37( 4), 269– 276.
Ritch, M. T., Loch, C. H., and De Meyer, A. ( 2002). “ On uncertainty, ambiguity and complexity in project management.” Manage. Sci., 48( 8), 1008– 1023.
Roy, M. M., Christenfeld, N. J. S., and McKenzie, C. R. M. ( 2005). “ Underestimating the duration of future events: Memory incorrectly used or memory bias?” Psychol. Bull., 131( 5), 738– 756.
Schonberger, R. ( 1981). “ Why projects are always late: Rationale based on manual simulation of a PERT/CPM network.” Interfaces, 11( 5), 66– 70.
Standish Group. ( 1998). “ CHAOS ‘98: A summary review.” A Standish Group Research Note, Standish Group International, Boston, MA, 1– 4.
Standish Group. ( 2009). “ CHAOS: A summary review.” A Standish Group Research Note, Standish Group International, Boston, MA.
Touran, A. ( 2010). “ Probabilistic approach for budgeting in portfolio of projects.” J. Constr. Eng. Manage., 136( 3), 361– 366.
Ward, S., and Chapman, C. ( 2003). “ Transforming project risk management into project uncertainty management.” Int. J. Proj. Manage., 21( 2), 97– 105.
Wayne, D., and Cottrell, P. E. ( 1998). “ Simplified program evaluation and review technique (PERT).” J. Constr. Eng. Manage., 125( 1), 16– 22.
Williams, T. M. ( 1995). “ What are PERT estimates?” J. Oper. Res. Soc., 46( 12), 1498– 1504.
Williams, T. M. ( 1999). “ The need for new paradigms for complex projects.” Int. J. Proj. Manage., 17( 5), 269– 273.
Williams, T. M. ( 2005). “ Assessing and moving on from the dominant project management discourse in the light of project overruns.” IEEE Trans. Eng. Manage., 52( 4), 497– 508.
Wook, S. J., and Rojas, E. M. ( 2011). “ Impact of optimism bias regarding organizational dynamics on project planning and control.” J. Constr. Eng. Manage., 137( 2), 147– 158.
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Published In
Journal of Construction Engineering and Management
Volume 139 • Issue 5 • May 2013
Pages: 488 - 497
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Oct 25, 2010
Accepted: May 29, 2012
Published online: Jul 24, 2012
Published in print: May 1, 2013
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