Both PERT and CPM Each arrow represents an activity & its precedence relationship(s); May Step 3 (a) (Continued): Calculate the Path Completion Times. The critical path method (CPM) aims at the determination of the time to complete a . The following are the time estimates and the precedence relationships. precedence relations for better modeling of overlapping activities ; the introduction management on float computation, and by introducing margin calculation .. CPM Schedule Summarizing Function of the Beeline Diagramming Method.
Consider the widget manufacturing example. To perform PERT analysis, you need to provide three estimates of activity duration: These three estimates are used to obtain a weighted average that is assumed to be a reasonable estimate of the activity duration.
- The CPM Procedure
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The time estimates for the activities must be independent for the analysis to be considered valid. Furthermore, the distribution of activity duration times is purely hypothetical, as no statistical sampling is likely to be feasible on projects of a unique nature to be accomplished at some indeterminate time in the future. Often, the time estimates used are based on past experience with similar projects.
To derive the formula for the mean, you must assume some functional form for the unknown distribution. The well-known Beta distribution is commonly used, as it has the desirable properties of being contained inside a finite interval and can be symmetric or skewed, depending on the location of the mode relative to the optimistic and pessimistic estimates.
A linear approximation of the exact formula for the mean of the beta distribution weights the three time estimates as follows: The DATA step also calculates the weighted average duration for each activity. The estimate of the mean project duration obtained in this instance always underestimates the true value since the length of a critical path is a convex function of the activity durations.
Their analysis relies on an implicit assumption that you may ignore all activities that are not on the critical path in the deterministic problem that is derived by setting the activity durations equal to the mean value of their distributions. And when the last activity on a network path is completed by its early finish, you have all the resources of those activities at your disposal to deploy on other high risk activities.
Always start with the critical path and then go with paths with descending order of their total duration.
How to Calculate Critical Path, Float, Early Start & Late Start, and Early Finish & Late Finish
Early start of first activity on critical path is always 1. Write it at the top left corner of that activity box see the image below.
Add its activity duration to this early start number and reduce it by one. Write the resulting number on the top right corner of activity box. Take the subsequent number of this early finish and write as early start for next activity. Continue this till you reach the end of critical path. Select the network path with second highest total duration, and calculate early starts and finishes.
PROC CPM: PERT Assumptions and Calculations -
If you find an activity with early start and finish already written do not overwrite them. Do the same for remaining network paths.
If you find two activities converging on a single activity say, activity-Git indicates that the activity-G will start only AFTER converging activities finish. So, you will take the largest value amongst the early finish of these two activities and write subsequent number as early start of the activity-G. Why add duration to early start and then reduce by one, to get early finish? Because the duration of an activity includes both start and finish days or any other unit of measurement you use.
That is 6 days including the start and finish days. Early start and finish As you noticed, early start number is written at the top left corner of activity box, and early finish on the top right corner. The critical path with early start and early finish days will look like this — Figure 7: Early start and early finish for critical path Late start and Late finish Indicates the latest time an activity on a network path can start and latest it can finish.