## Critical Path Analysis

This is a way of demonstrating how a complex project can be completed in the shortest possible time.  It identifies the critical path, these are the activities that must be completed on time in order to delay the whole project.

Constructing a Network

We will use the example of the tasks involved producing an advertising campaign, they are:

• A  plan the advertising campaign;
• B  make a TV video;
• C  design a poster;
• D  test market the TV video;
• E  test the suitability of the poster;
• F  present campaign to the board of directors;
• G  communicate the campaign to all company personnel.

The estimated length of time for each task and the order, i.e., the tasks that depend upon others being completed are shown below.

 Tasks Order/dependency Estimated time (hrs) A Must be done first 4 B Can only start when A is completed 6 C Can only start when A is completed 7 D Can only start when B is completed 8 E Can only start when C is completed 10 F Can only start when D and E are completed 9 G Can only start when D, E and F are completed 5

These activities can be shown on a network; a generalised network is shown overleaf followed by a network for the advertising campaign.

The advertising network shows the order in which the tasks can be completed.

EARLIEST START TIME

If we assume that the earliest start time for A is 0, then B and C can not start for 4 hours (0+4), these figures are shown in the top right hand corner of nodes 1 and 2.  Task D cannot start until A and B have been completed, this takes 10 hours (0+4+6), which is shown in node 3.  Task E cannot start until A and C have been completed, this takes 11 hours (0+4+7), which is shown in node 3.  Task F cannot start until E and D are completed, the EST for task F is 21 (0+4+7+10).  It is important to choose the longest route when calculating the ESTs.  The route A, B, D is only 18 (0+4+6+8), the EST of the longer route is shown in node 5.

LATEST FINISH TIME

The next step is to calculate the latest finish time (LFT) of each task without extending the whole project.  We must start at node 7 and work back.  Task G must be completed by the 35th hour and this is shown in node 7.  To calculate the LFT for task F, we subtract the time it takes to complete task F from the previous LFT (35-5=30) and place it in node 6.  When choosing between two LFTs, such as for task A we choose the route that gives the lowest LFT, in this case 4 (11-7) rather than 7 (13-6).

THE CRITICAL PATH

Once all of the LFTs have been identified it is possible to outline the critical path.  This can be drawn through all of the nodes where the ESTs and the LFTs are the same.  This means that there can be no delays between completing the previous tasks and starting the next one without prolonging the advertising campaign.  The critical path in this case is A, C, E, F, G is shown by striking two short lines across the critical activities.  If the manager sees that there is a possibility of a task on the critical path overrunning he or she can considering shifting labour across from a non-critical task.

THE FLOAT

B and D could be delayed for up to 3 hours without affecting the total time of the task, this is called the float.  The total float is found by subtracting the EST and the duration from the LFT, so for task B it would be 3 (13-6-4), this is the total float up to that activity.  The free float is found by subtracting the EST at the start of the task and the duration from the EST at the end, so for task B it would be 0 (10-6-4).  This is the free float for the task, i.e., its delay will interfere with other tasks, in this case D.

 Task Duration EST LFT Total Float Free Float A 4 0 4 0 0 B 6 4 13 3 0 C 7 4 11 0 0 D 8 10 21 3 3 E 10 11 21 0 0 F 9 21 30 0 0 G 5 30 35 0 0

• Reduce lost time between tasks, ensuring a smooth running of projects.
• By identifying projects that can be carried out simultaneously it should reduce the overall time of the project.
• The resources needed for each activity should be ordered for no earlier than the EST for that task.  This should reduce the cash outflows and ensure the working capital tied up in the project is minimised.  This will also assist JIT production if used.
• If the project is delayed, the network is a good starting point for working out the implications.