An approximate solution to the pert problem

Sculli, D.; Shum, Yu-Su

doi:10.1016/0898-1221(91)90046-7

Cited by 16 publications

(16 citation statements)

References 17 publications

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“…Interesting, but certainly minority research has also been devoted to studying the possible effects of assuming independence versus the existence of (partial) correlation between activities (e.g., Banerjee and Paul (2008); Cho (2009); Mehrotra et al (1996); Sculli and Shum (1991)). Some of their principles will be used here in M-PERT too, and two brief examples are provided later in Figure 5.…”

Section: Review Of the Most Relevant Pert-related Extensionsmentioning

confidence: 99%

“…Finally, the case of the maximum from two Normal distributions (the durations of two activities) was coincidentally proposed by Clark (1961) but at that time it required intensive use of tables and did not allow for correlation (ρ) between both activities. In particular, the expression for the maximum was taken from Sculli and Shum (1991) and was also used by Cox (1995), whereas the expression for the minimum was taken from Nadarajah and Kotz (2008). Both expressions, despite looking long, are very easy to calculate.…”

Section: <Figure 3>mentioning

confidence: 99%

“…Then these expressions can be applied recursively until there is just one activity left, a moment in which the activity will be in series again and can keep being merged with its neighbor activities in series. This recursive merging procedure is not new either, as it was successfully applied by Cox (1995), Gong and Hugsted (1993) and Sculli and Shum (1991). However, it is also true that when more than two activities are merged, there is a small error in the final mean and variance calculation, which is also dependent (but to a minimum extent) on the exact merger order too.…”

Section: <Figure 3>mentioning

confidence: 99%

“…For solving these subnetworks that usually represent a small portion of the whole network, authors like Mehrotra et al (1996) and Sculli and Shum (1991) proposed a sequential recursive procedure that involves calculating all the variance and covariance values between the 'untangled' paths. Implementing this procedure basically requires identifying all the possible paths and then merging them, first, two of them, and then one by one with the already merged group.…”

Section: <Figure 5>mentioning

confidence: 99%

“…The only tricky part is to calculate the correct value of ρ between the paths. However, Sculli and Shum (1991) derived the generic expression for obtaining it, but since that expression is somehow difficult to understand for the beginner, the ρ expressions for up to four parallel paths (normally ordered from higher to lower mean duration µ k and sequentially named A, B, C and D) are given here:…”

Section: <Figure 5>mentioning

confidence: 99%

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M-PERT: Manual Project-Duration Estimation Technique for Teaching Scheduling Basics

Ballesteros‐Pérez

2017

J. Constr. Eng. Manage.

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The Program Evaluation and Review Technique (PERT) has become a classic Project Management tool for estimating project duration when the activities have uncertain durations. However, despite its simplicity and widespread adoption, the original PERT, in neglecting the merge event bias, significantly underestimated the duration average and overestimated the duration variance of real-life projects. To avoid these and other shortcomings, many authors have worked over the last 60 years at producing interesting alternative PERT extensions. This paper proposes joining the most relevant of those to create a new reformulated PERT, named M-PERT. M-PERT is quite accurate when estimating real project duration, while also allowing for a number of interesting network modelling features the original PERT lacked: probabilistic alternative paths, activity self-loops, minima of activity sets and correlation between activities. However, unlike similar scheduling methods, M-PERT allows manual calculation through a recursive merging procedure that downsizes the network until the last standing activity represents the whole (or remaining) project duration. Hence, M-PERT constitutes an attractive tool for teaching scheduling basics to engineering students in a more intuitive way, with or without the assistance of computer-based simulations or software. One full case study will also be proposed and future research paths suggested.

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