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Question about delayed tasks in PERT important

There is just one thing about PERT that is confusing me - when more than one task on a path is delayed.

Here's an example of what is confusing me:

Say Path 1 takes 20 weeks, and the critical path takes 22 weeks.
Task 1 on Path 1 has a slack time of 1 week, and task 2 has a slack time of 2 weeks.

How can this be possible? If task 2 is delayed by 2 weeks, the project duration wont be affected, but path 1's duration will increase by 2 weeks, and be the same as the critical paths duration.
All of task 2's slack has been used up now, but what happens if task 1 is then delayed by 1 week? Task 1 has a slack time of 1 week, yet if path 1s duration is increased by 1 week, it will exceed the critical path duration. How can this be so?

I'm not sure if this has been worded very clearly, but I'd be very greatful for any help you can give me - I've asked lots of other people I know and none seem to know the answer.

Thanks in advance.

Reply 1

Né Stig

1st off - Are you putting the PERT in a Gantt Chart?
If so make sure the settings are correct. Sometimes the dates can be altered if the timing structure is not in sequence.

I can't give an answer to your question as I need to see a digraph. Please follow instructions below and you'll get the answer why.

Regarding CPA, there are normally 5 stages to come to the conclusion.
Break the PERT down into phases such as Time Analysis and other tasks.

Once you have broken your project into manageable pieces or into the methodolgy they suit you can now start working out what phase relies on what being finished.
Make sure every task is analyzed. If one task doesn't rely on another, then theoretically you can start that phase straight away.

You should have set an approximate time that the task can be completed in (in days, weeks etc).

Design a digraph with a start and finish. Each task should be characterized, and joined by its predecessor and the next task. The task that doesn't have any reliances may go straight from the start to finish. Put the days in brackets of each phase next to each line which it represents. You must also complete each digraph with the most immediate task situated at the top (the line which represents the task). This would then be your 1st job to do in the project. Put 1 at the end of that task (the line).

When you have done that, slack times, Maximum Days (Ei) and Latest possible allocation time (Li) can be worked out.

Ei = Maximum Days. As you have worked out your approximate days, and have also completed what tasks rely on what, a calculation can now be made from the digraph on how long it takes to get to stage 1. Do this for all stages.

Li = Is a reverse. Do this back to front deducting the last phase amount of days. So this sum would be the maximum time it takes to get to that stage subtracting the following phases amount of time.

Slack = A few sums may need to be devised in order to get the slack.
You already have how long it takes to get to stage 1 in maximum days. In theory there could be many taks following task 1 which is where the sum comes in.
1. At stage 1 you have X amount of days to complete. (Ei)
2. The following stage (Number 2 or how ever your graph is designed in accordance with your stages reliance on others), that figure should be taken (Ei) and then you should subtract the last task in order to get back to stage 1. So stage 2 (or whatever stage follows it) MINUS the previous task to get back to stage 1.
There could be many sums, and only the sum which has the least value should be taken. This may more than likely equate to Ei (Maximum Days). If it does, you have 0 days slack time. If you have 225 days Ei, and your lowest value on slack is 227 days, you have 2 days slack.

Its hard to explain, but I hope you kind of understand it. To do a full CPA will probably take you about a day. PERT (Program Evaluation and Review Technique) can be a phase in its own right. A Gantt chart is part of PERT and should also be included in your budgeting for time allowance. CPA is part of PERT as well as its evaluating and reviewing the time constraints of your project. Otherwise CPA would be slotted into the Preliminary Phase or Project proposal phase (waterfall methodology) if PERT was not a single phase.

I swear I've just done an essay. Any questions, just ask. I can safely say I'm an expert in this field :smile: