|
Secondly, we have to work out the latest finish time (lft) for each task. This is worked out similar to the est's except we subtract figures and work from right to left on the diagram. The lft is then placed inside the bottom right hand segment of the node. Ignore the red line for now, this will be explained later. Remember - from right to left.
Now the est's and the lft's have been calculated, we can determine the critical path. This is found by recognizing those nodes where the est = lft.
By looking at the above diagram, all the nodes have equal est and lft except for number 4. By acknowledging this, we can identify the critical path as:
A - B - D - F - G (highlighted by the red line)
In other words, there must be no delays in completing these tasks, otherwise the project completion time will be also be delayed beyond the expected 11 weeks. This is not true for the tasks that do not lie on the critical path, as explained below. So, what can we determine from those tasks that do not lie on the critical path - C and E? Well, either task C or E can be delayed by 1 week without affecting the completion time of the project. This is called the float. There are two types of float - the total float and the free float. Only those tasks that are not on the critical path will have a float, as you will see.
| Total Float The total float is the accumulated float up to the specific task. This is worked out by subtracting the est and the duration from the lft: i.e. Total Float = LFT - EST - Duration | 
|
| Task | Duration | Est | Lft | Total Float (wks) | Free Float (wks) (refer back to diagram - click here) | | A | 1 | 0 | 1 | 0 : (1 - 0 - 1) | 0 : (1 - 0 - 1) | | B | 3 | 1 | 4 | 0 : (4 - 1 - 3) | 0 : (4 - 1 - 3) | | C | 2 | 1 | 4 | 1 : (4 - 1 - 2) | 0 : (3 - 1 - 2) | | D | 3 | 4 | 7 | 0 : (7 - 4 - 3) | 0 : (7 - 4 - 3) | | E | 3 | 3 | 7 | 1 : (7 - 3 - 3) | 1 : (7 - 3 - 3) | | F | 2 | 7 | 9 | 0 : (9 - 7 - 2) | 0 : (9 - 7 - 2) | | G | 2 | 9 | 11 | 0 : (11 - 9 - 2) | 0 : (11 - 9 - 2) |
E.g. For task C, the total float = 4 - 1 - 2 = 1 (week)
Free Float
| The free float is worked out by subtracting the est at the start of the task and the duration, from the est at the end of the task: i.e. Free Float = End EST - Start EST - Duration | 
|
So, again for task C, the free float = 3 - 1 - 2 = 0 This is showing that task C can be delayed (like all tasks), but it will have an effect on the start time of the next task. All tasks that calculate zero has the same rule applying. But, what about those tasks that calculate a figure other than zero? If we work out the free float for task E, we get: Free Float = 7 - 3 - 3 = 1 week Now, this means that task E can be delayed by 1 week without having an effect on the start time of the next task (F). Any delays over this time would only then affect the proceeding task. For example, if task E was delayed by 2 weeks, it would delay the start time of task F by 1 week - 1 week compensated by the float, and the other causing 1 week delay.
Finally, let's now look at the floats for all the tasks.
By looking at the table, those tasks without a 'total float' (i.e. zero) are considered 'critical' and coincidentally are found on the critical path. It is therefore important that these tasks are not delayed in order to complete the project on time as planned (11 weeks). Acknowledging and integrating float is very important. For example, those tasks that do carry float may have resources (labour, capital, equipment, etc) that could be used elsewhere to complete other tasks quicker. Also, for those tasks that do carry float, any delays can be accepted unless it is sufficient enough to eliminate the float completely. In such case, at sometime previous to the current task, a major problem or issue has occurred - investigate and act immediately.
I'm Lost! We do accept that this area can be confusing in places, and so if you are unsure that you can now go and complete a similar analysis for your project, visit the following link: A new window will open and you will be directed away from this web-site. Here, you can enter your details for the project on-line and let the computer calculate the appropriate figures.
Further Reading
This article went through the basics of the critical path analysis (believe it or not!) and so, if you believe that such a tool can be useful in your business, why not read further.
Critical Path Calculator
Article Index
1 Introduction
2 Critical Path Analysis Part 2
|
