Critical Path Analysis: Step 6

You now have a fair amount of data about your project, but I haven't really explained what it all means.

Earliest Time Of Arrival: This indicates that if you were very quick and worked hard, then this is the earliest time that you could get to that event.

Latest Time Of Arrival: This is more important as far as the analysis goes. The value you have for the event indicates the latest time of arrival while still completing the project on time. Take event (1) for example, you could get there by day 14, yet you could put it off until day 62. If you start it before day 14 any other dependencies won't be ready (therefore it's impossible). If we start after day 62 the project will be delayed; yet we can start on any day between 14 and 62 and not hold the project up at all.

Those people that are working quickly today will have realised what the pattern means – the pattern where the Earliest time and Latest time are the same. All it really indicates is that you must be at that event by that day or the project will be delayed. If you only get to event (5) on day 26 the whole project will be delayed by 2 days, meaning that you cannot complete it until day 85.

You have a further calculation for this called the float and the slack. Float is for activities and slack is for events.

Float = Dest_Max – Src_Min – Activity_Length

Slack = Latest_Time – Earliest_Time

If the alack and/or the float is equal to 0 it is a critical event/activity; a critical activity must be completed on time and in order to avoid delays to the project.

A slack at any event means that if a person has completed the activity(s) prior to the event (and is ready to go onto the next event) they can rest/pause for that much time. A slack of 0 would mean that they can't pause at all and must carry on, but a slack of 10 means that they could spend 10 days spinning around in their chair. Later on when we look at scheduling we'll examine the possibility that instead of letting him/her spin around in their chair we get them working on another activity.

The float is similar, but it indicates how much extra time you can take, if it's a 10 day task and has a float of 3 then you can take up to 13 days to complete the task without delaying the project. It therefore makes sense that critical activities have a float of 0, because that activity must be done in the specified time period (or the project is delayed).

The revised table now shows the slack for each event. You can straight away see that events 0, 2, 5, 6, 7, and 8 are all critical events, and are said to be on the critical path. We can use this to find out what the critical activities are, those activities between 0-2, 2-5, 5-6, 6-7, 7-8. It's not always that simple, so we'll do it the proper way – work out the float for each activity: A = 14 – 0 – 14 = 0
B = 24 – 14 – 5 = 5
C = 24 – 9 – 5 = 10
D = 24 – 14 – 10 = 0
E = 55 – 24 – 31 = 0
F = 62 – 55 – 7 = 0
G = 62 – 0 – 14 = 48
H = 83 – 14 – 21 = 48
I = 19 – 0 – 14 = 5
J = 19 – 0 – 9 = 10
K = 83 – 62 – 21 = 0

I've made all the critical activities bold, and you can see what sort of float the other activities have. Combining this information you can calculate the critical path from start to finish:

This critical path indicates that you must complete these tasks back-to-back with no delay:

A – Graphics Engine
D – Input Engine
E – General Programming
F - Physics
K – Level Design

Makes sense really, and it is quite likely that you would have come up with something similar without using the algorithm. But this is only a simple example.

However, that doesn't mean that you can skip the other activities. They're still just as important in the overall plan. The key point is that the critical activities and events must be reached by the designated time, or the project will be delayed.

Step 7