×

An approximation of the activity duration distribution in PERT. (English) Zbl 1080.90531

Summary: PERT is widely used as a tool for managing large-scale projects. The traditional PERT approach uses the beta distribution as the distribution of activity duration and estimates the mean and the variance of activity duration based on the ”pessimistic”, ”optimistic” and ”most likely” time estimates. Several authors have modified the original three point PERT estimators to improve the accuracy of the estimates. This article proposes new approximations for the mean and the variance of activity based on ”pessimistic”, ”optimistic” and ”most likely” time estimates. By numerical comparison with actual values, the proposal is shown as more accurate than the original PERT estimates and its modifications. Another advantage of the proposed approximation is that it requires no assumptions about the parameters of the beta distribution as in the case of existing ones.

MSC:

90B50 Management decision making, including multiple objectives
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Malcolm, D. G.; Rooseboom, J. H.; Clark, C. E.; Fazer, W., Application of a technique for research and development program evaluation, Operations Research, 7, 646-669 (1959) · Zbl 1255.90070
[2] Clark, C. E., The PERT model for the distribution of an activity time, Operations Research, 10, 405-406 (1962)
[3] Grubbs, F. E., Attempts to validate certain PERT statistics or ‘picking on PERT’, Operations Research, 10, 912-915 (1962)
[4] Sasieni, M. W., A note on PERT times, Management Science, 32, 1652-1653 (1986)
[5] Littlefield, T. K.; Randolph, P. H., An answer to Sasieni’s question on PERT times, Management Science, 33, 1357-1359 (1987)
[6] Gallagher, C., A note on PERT assumption, Management Science, 33, 1360 (1987)
[7] Donaldson, W. A., The estimation of the mean and variance of a PERT activity time, Operations Research, 13, 382-385 (1965)
[8] Keefer, D. L.; Verdini, W. A., Better estimation of PERT activity time parameters, Management Science, 39, 1086-1091 (1993) · Zbl 0800.90575
[9] Farnum, N. R.; Stanton, L. W., Some results concerning the estimation of beta distribution parameters in PERT, Journal of the Operations Research Society, 38, 287-290 (1987) · Zbl 0605.62123
[10] Golenko, D. I., (Ginzburg), On the distribution of activity time in PERT, Journal of the Operations Research Society, 39, 767-771 (1988) · Zbl 0644.90051
[11] Meredith JR, Mantel SJ. Project management: a managerial approach, 2nd ed. New York: Wiley, 1989.; Meredith JR, Mantel SJ. Project management: a managerial approach, 2nd ed. New York: Wiley, 1989.
[12] Pearson, E. S.; Tukey, J. W., Approximate means and standard deviations based on distances between percentage points of frequency curves, Biometrics, 52, 533-546 (1965) · Zbl 0151.24102
[13] Megill RE. An introduction to risk analysis. Tulsa, OK: Petroleum publishing company, 1977.; Megill RE. An introduction to risk analysis. Tulsa, OK: Petroleum publishing company, 1977.
[14] Lukaszewicz, J., On the estimation of errors introduced by standard assumptions concerning the distribution of activity duration in PERT calculations, Operations Research, 13, 326-327 (1965)
[15] Welsh, D. J., Errors introduced by a PERT assumption, Operations Research, 13, 141-143 (1965)
[16] Moder, J. J.; Rodgers, E. G., Judgement estimates of the moments of PERT type distributions, Management Science, 15, B76-B83 (1968)
[17] Johnson NL, Kotz S, Balakrishnan N. Continuous univariate distributions, vol. 2, 2nd ed. New York: Wiley, 1994. pp. 210-76.; Johnson NL, Kotz S, Balakrishnan N. Continuous univariate distributions, vol. 2, 2nd ed. New York: Wiley, 1994. pp. 210-76.
[18] MacCrimmon, K. R.; Ryavec, C. A., An Analytical study of the PERT assumptions, Operations Research, 12, 16-37 (1964)
[19] Perry, C.; Grieg, I. D., Estimating the mean and variance of subjective distributions in PERT and decision analysis, Management Science, 21, 1477-1480 (1975)
[20] Lau, A. H.; Lau, H.; Zhang, Z., A simple and logical alternative for making PERT time estimates, IIE Transactions, 28, 183-192 (1996)
[21] Alpert M, Raiffa H. A progress report on the training of probability assessors. In: Kahneman D, Solvic P, Tversky A, editors. Judgement under uncertainty: heuristics and biases. New York: Cambridge University Press, 1982. pp. 294-305.; Alpert M, Raiffa H. A progress report on the training of probability assessors. In: Kahneman D, Solvic P, Tversky A, editors. Judgement under uncertainty: heuristics and biases. New York: Cambridge University Press, 1982. pp. 294-305.
[22] Selvidge, J. E., Assessing the extremes of probability distributions by the fractile method, Decision Science, 11, 493-502 (1980)
[23] Davidson, L. B.; Cooper, D. O., Implementing effective risk analysis at Getty oil company, Interfaces, 10, 62-75 (1980)
[24] Littlefield, T. K.; Randolph, P. H., PERT duration times: mathematics or MBO, Interfaces, 21, 92-95 (1991)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.