# PROJECT MANAGEMENT Network or Critical Path Analysis

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PROJECT MANAGEMENT Network or Critical Path Analysis
IB BUSINSS & MANAGEMENT – A COURSE COMPANION (p238-p291)

Network or Critical Path Analysis
Network or Critical path analysis was designed to help project managers plan complex projects that have multiple interrelated tasks. It is a mathematical tool. It can be a great help in breaking down a complicated production process into clearly manageable units.

What is the aim of Critical Path Analysis?
The aim is to identify which tasks are so “critical” that they cannot be altered without having an impact on how long it tasks to complete the whole process OR by extension the likely effect of a change in any inputs such as HR or finance.

What do we need to know to create a network diagram?
The number and order of tasks The dependencies of each task (which one cannot be started until another has finished) The time that each task takes.

Conventions The process is drawn starting on the left of the page and working towards the right. A task is identified by a start and a finish that looks like the figure below.

CONVENTIONS A task is shown by drawing a line between the two nodes.
We put the code for the task above the line and the duration below it. This is shown below.

CONVENTIONS More than one task can start at the same node as shown in figure 5.23 More than one task can finish as the same node as shown in figure 5.24

This means that task B cannot start until Task A has been completed.
This means that neither task B nor C can start until task A has been completed. This means that task C cannot start until either task A OR Task B has been completed. This means that that neither task C nor D can start until task A and B have been completed.

DIAGRAMS YOU CANNOT DRAW
Drawing a diagram like this is not allowed as the task starting at the same time may have different durations so they cannot finish at the same node too. In this case there has to be at least a different start or finish node for the tasks.

CALCULATIONS Each mode is split into different quadrants. This is because we can fill these in with numbers that show the starting time and finishing time of the task and these will depend on what comes before the task, how long that task tasks and what will follow on from the task.

Understanding Calculations
Every task has two nodes attached that will look like the figure below. The very first node on the diagram – the start of the whole process always has an EST and LFT of 0. The very last node in the diagram has as EST and LFT equal to the total duration of the whole project. Again the two numbers will always be the same. We calculate the ESTs by working from left to right and finding when is the earliest time that we can start each task in the process. We calculate the LFTs, by working from right to left and finding out when is the latest time each task can be finished by.

Example 1 Imagine it is the last lesson of the school day.
The teacher won’t let you go until you have finished your work and the class has tidied up. Code Task Preceded by Duration (Minutes) A Finish Work - 30 B Tidy Up 7

Example 2 Now imagine that the teacher says, that after finishing your work, some of you should tidy up and the rest push away the laptops. After tidying up, those students should put all the chairs on top of the desks. Nobody can leave until all tasks are completed. Code Task Preceded by Duration (Minutes) A Finish Work - 30 B Tidy Up 7 C Put away laptops 15 D Put chairs on top of desks. 6

Example 2 At node 1, it will be zero, node 2 will be 30 and node 3 will be 37 (30 + 7) minutes. However, for node 4 we have to make a decision. We can’t leave the school until both tasks C and D have been completed. So the rule is that when there is more than one task at a node the EST always takes the higher number.

In this case the EST for node will be 45 (30 + 15 > 37 + 6)
As with our earlier example, we work from node 4 for our LFTs. They will start at 45 and then node 3 will be 39 (45-6) but again when we have a node at which there is more than one LFT we must make a decision. We take the lowest number. So for node 2, the LFT will be 30 (because < (is less than) 39-70

We can distinguish between a task that is critical (that cannot be altered without affecting the other tasks) from tasks that are not critical. We can show the critical path, which is all the linked tasks that cannot be altered without affecting the whole process – by adding these symbols. Note: All critical tasks will have ESTs equal to their LFTs.

FLOATS Spare time is known as a float and is important because it may be useful to know how much time a task can be delayed without having an impact on the whole process. There are two main floats. Free Float Total Float

Free Float This is the amount of time a task can be delayed without having an impact on the following task. It is calculated by the following formula: EST of next task – duration of the task – EST of this task

Total Float It is calculated by the following formula:
This is the amount of a time a sequence of tasks can be delayed without having an impact on the whole process. It is calculated by the following formula: LFT of this task – duration of task – EST of this task

Total Float vs Free Float
As the total float is for the whole process and the free float immediately effects the next activity alone, the total float will always be at least the same as the free float and often times it will be a bigger number. Total Float ≥ Free Float

Float - Example Critical Tasks always have 0 floats
Code Task Preceded by Duration (minutes) A Finish Work B Tidy Up 2 C Put Away Laptops D Put Chairs on top of Desks Critical Tasks always have 0 floats Task B, cannot be delayed as long as the next task (D) starts after 37 minutes; that is directly after the task has been completed. But also if we were to delay task B by two minutes this would delay everyone leaving school. Task D, cannot be delayed by more than two minutes as this will affect the whole process as it is the last activity.

Sometimes it is necessary to include in the network a task that is doe not actually exist. It is needed though to make sure that the whole process is completed logical.

Imagine that the teacher decides that the students putting away the laptops must sing their favorite pop songs as they do it. Remember when drawing the network we can’t have two tasks taking the same time starting and finishing from the same nodes. So we will have to another intermediate node in the network.

Example – Dummy & Variable Task (Table)
Code Task Preceded by Duration (minutes) A Finish Work - 30 B Tidy Up 7 C Put Away laptops 15 D Put Chairs on Top of Desks 6 E Sing Pop Songs F Dummy Task

As the task does not physically exist we cannot allocate time to it – its duration is therefore zero and we need not put this on to the network. The task is shown by a dotted line – with the arrow to show the direction necessary. The EST for the task following it will be EST start + 0 = EST start.

The point of the network diagram is to show those tasks that are so critical the manager has to focus on them as any delay will have an immediate impact. Critical paths therefore have some important characteristics They must have EST equal to LFT at the start and finish nodes. They must therefore have zero floats. They cannot be altered without affecting the whole process.

What are the benefits of critical path analysis for project managers?
By distinguishing between critical and non-critical tasks the manager can decide on which task to focus attention. The manager can calculate the effect of diverting resources from non-critical activities to critical ones and so reduce the overall time of the whole process. The manager can factor into calculations, the effect of delays to specific tasks and the impact on the whole process.

What are the benefits of critical path analysis for project managers?
The manager can also cost the various tasks and so be able to calculate the most efficient funding for the process. This is very important for complex projects that may require funding over a long period of time. The manager can therefore determine an effective cash flow for the whole process and identify critical points in the whole process

What are the benefits of critical path analysis for project managers?
The manager can test crash the process to see the effect of a change in circumstances. There are many computer programs that can run the process for speedy calculations.

Limitations of Critical Path Analysis
Critical path analysis focuses only on quantitative data and it ignores the qualitative aspects of production. It can be confusing to create the network diagram, especially if dummy activities are required. The assumption is that all activities are sequential with a definite start and end to the whole process. In reality many business tasks are continuous and independent of each other. Sometimes projects can be really complex and involve too many different jobs to be easily broken down into a clear diagram. The network is dependent on reliable data and this may be inaccurate or wrong.

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