PERT Chart Tutorial

Also see Gantt Practice

Also see real Gantt/PERT questions and solutions in these previous exams... 2001, 2002, 2003

Knowledge of Gantt and PERT is not required for the VCE IT course 2011-2014

Yes - it was not drawn very well, but it's late and I'm tired.

Here are the questions to ponder before we discuss the answers.

EXAM QUESTION 1: Which tasks are on the critical path of the PERT chart above? (1 mark)

EXAM QUESTION 2: What is the slack time for tasks C, D and G? (1 mark)

EXAM QUESTION 3: the person working on task C tells the project manager he can't start work until one day after the scheduled starting date. What impact would this have on the completion date of the project? Why? (2 marks)

EXAM QUESTION 4: Task A will be delayed by 2 days because some equipment has arrived late. If the project manager still wants to finish the project within the original time frame, he will need to shorten the time for one or more of the tasks. What steps can he take to reduce the number of days allocated to a task? (2 marks)

EXAM QUESTION 5: The project manager decides to reduce the time needed for tasks D and F by one day each. How effective will this reduction be in achieving his aim of maintaining the original finish time for the project? (2 marks)

The CIRCLES mark the beginnings and ends of TASKS to be done in the project. Also called NODES.

The ARROWS are the tasks themselves. They are identified by letters A to I. In a real PERT chart, the actual names of tasks would be used instead of letters. The lengths of the arrows does not relate to their length in time.

The NUMBERS after the task names are the DURATIONS of the task. The time interval may be anything from picoseconds to years. Let's assume these timings are in days.

Important point to remember: the ARROWS are tasks, not the circles (nodes).

When a node has two or more tasks branching from it, it means those tasks can be done concurrently (at the same time.)

When a node has incoming arrows, it means the incoming task must be completed before progress may continue to any arrows heading away from the node. e.g. Task A must be completed before tasks B or G may begin.

You need to be able to examine and interpret charts like this PERT. Let's examine it in English.

Task A is the first task and takes 2 days. When it is done, tasks B and G can begin. If we follow the task G line, it takes 2 days to reach task H which takes 5 days. Task H leads to the final task, I. Total time for following this path is 2 + 2 + 5 + 3 = 12 days. The path would be described as A,G,H,I.

When task G began, so did task B (with another team of workers). When task B finished, after 3 days, there is another opportunity to run some tasks concurrently. So after B, tasks C and D began at the same time.

If we follow task C, it takes 1 day to reach task E, which leads to the final task I. Total time for this path was 2 + 3 + 1 + 4 + 3 = 13 days.

If we followed task D, which takes 3 days, it leads to task F (also 3 days) before reaching the final task, I. Total time for this path is 2 + 3 + 3 + 3 + 3 = 14 days.

Note that tasks E, F and H must all be finished before task I can begin.

You will have noticed that there are several paths through from task A to task I. Each of these paths takes a different amount of time.

What is the shortest possible time for the project to take (without leaving any tasks out)?

14 days (the longest possible path). Yeah, it sounds odd that the shortest time is the longest path, but consider another example. You are getting ready for school. At the kitchen table, you have to have breakfast while you finish your maths homework. You have to finish both before you can leave. Breakfast takes 12 minutes. Maths takes 20 minutes. What's the shortest time you would need to leave? Twenty minutes, because both tasks must be finished. Just because one task finishes before the other, you can't leave yet. So in the chart above, the shortest project time would be 14 days.

That is the CRITICAL PATH of the project: the sequence of tasks from beginning to end that takes the longest time. No task on the critical path can take more time without affecting the end date of the project. In other words, none of the tasks on the critical path has any SLACK.

SLACK is the amount of extra time a task can take before it affects a following task. In the breakfast example above, the breakfast could take another eight minutes before it affected the leaving time, so it has eight minutes' slack.

Tasks on the critical path are called CRITICAL TASKS. No critical task can have any slack (by definition).

EXAM QUESTION 1: Which tasks are on the critical path of the PERT chart above? (1 mark)

ANSWER: A,B,D,F,I

EXAM QUESTION 2: What is the slack time for tasks C, D and G? (1 mark)

a. Slack time for task C: let's isolate that bit of the PERT chart.

To work out the slack time for a task, backtrack from the task to the node where the task split off from other concurrent tasks. In our case, it is the node directly before task C. Also look forward to the node where task C and the other concurrent tasks (D,F) join up again with C.

In the picture below, the beginning node is marked red and the ending node is marked green...

The top pair of tasks (C,E) is being done at the same time as the bottom pair of tasks (D,F). Together, C and E take 1 + 4 = 5 days. Together, D and F take 3 + 3 = 6 days, so tasks C,E will finish 1 day before D, F finish. Therefore, either task C or task E could take one extra day to finish without disturbing the task that comes after the green node.

That is the SLACK time for task C (it equally applies to task E: but remember the slack time is shared between them. They can't both take another day without causing delays.)

So, the slack time available to task C is ONE DAY.

b. Good. Let's try the next question: what is the slack time for task D? This is easy, when you remember that task D is on the critical path. By definition, critical tasks HAVE NO SLACK: they cannot run overtime without affecting the ending date of the project. So, the easy answer for this is THERE IS NO SLACK for task D.

c. Finally, what is the slack time for task G? Let's isolate the relevant bits of the chart again...

Once again, I have gone back from task G to the (red) node where it branches off from a concurrent task. We look ahead to where task G's path rejoins its concurrent brothers (the green node).

Tasks G,H take a total of 7 days. Meanwhile, tasks B,C,E take 3 + 1 + 4 = 8 days and tasks B,D,F take 3 + 3 + 3 = 9 days. So, task G could run an extra 2 days before it caused delays, since it had to wait for tasks B,D,F to finish anyway.

So the answer would be, The slack time for task G is 2 days.

EXAM QUESTION 3: the person working on task C tells the project manager he can't start work until one day after the scheduled starting date. What impact would this have on the completion date of the project? Why? (2 marks)

Let's look at the whole PERT chart again...

Task C starting one day late is not significant to the ending date of the project. It would cause task E to start a day late (because task E is dependent on task C finishing first), but remember earlier we found that task C had ONE DAY OF SLACK. Therefore, if task C started a day late, it would merely use up its day of slack and no disruption would be felt by the time task E finished and the other concurrent tasks joined up to begin task I. So the answer is: task C finishing one day late would have no impact on the completion date of the project because it has one day of slack it could use.

EXAM QUESTION 4: Task A will be delayed by 2 days because some equipment has arrived late. If the project manager still wants to finish the project within the original time frame, he will need to shorten the time for one or more of the tasks. What steps can he take to reduce the number of days allocated to a task? (2 marks)

This is not really a PERT question at all: it is a common sense question. How can you finish a job more quickly? You could put more people to work on it, you could work more hours in a day or you could increase the efficiency of work (e.g. automating a manual task). Always remember common sense is your most valuable tool in an exam!

EXAM QUESTION 5: The project manager decides to reduce the time needed for tasks D and F by one day each. How effective will this reduction be in achieving his aim of maintaining the original finish time for the project? (2 marks)

Have a think: what has changed?

YES! Reducing tasks A,B,D,F,I by a total of 2 days (to 12 days) means it is no longer the critical path! It is no longer the longest route from start to finish. In other words, it has been demoted.

What is the new critical path?

Right: Path A,B,C,E,I is now the longest at 13 days so it becomes the new critical path.

So - the project manager has reduced the old critical path from 14 to 12 days, but the new critical path still takes 13 days. So, the project will now finish ONE day earlier than originally.

Reducing both tasks D and F by one day each was unnecessary because after a 1 day reduction, the tasks were no longer critical. To reduce the overall project time further, the manager would have had to shift his attention to the new critical path, and try to reduce the times of the new critical tasks.

So, an answer could be: Reducing tasks D and F each by one day would only shorten the project by one day since after a 2 day reduction, tasks D and F are no longer on the critical path. To further shorten the project time, the project manager would have to shorten tasks on the new critical path A,B,C,E,I.

PERT Diagram using Activity On Arrow (AOA) convention 

• The critical path is through activities C, F, H, J (can you prove it?)
• The expected project duration is 21 weeks (7+5+5+4)

Here are some neat pages I've found on Gantt and PERT.

Covers WBS, CPM, PERT, Gantt