D1: D1: Event Event TimesTimes

D1: Earliest Or Early Event Time

The earliest event time is the earliest time that an event can be completed.

You are looking to find the earliest time that all the activities leading into an event could be completed.

If you think about this carefully you will see that the early event time must, in fact, be the value of the ‘longest’ or ‘heaviest’ route to the event.

Let’s show this with an example.

D1: Earliest Or Early Event Time

The early event time for the source node is always 0.

The early event time for event 1 is 9; for event 2 it is 6.Event 3 has two edges leading into it but both give 12.The early event time for event 4 is 15.

Events 5 and 6 both have two edges leading into them that would give different early event times… the early event times are 18 and 25 respectively.

D1: Earliest Or Early Event Time

Finding early event times is an example of a forward scan. Forward scans go from the source node to the sink node.

Once all the early event times for the events of an activity network are found, the early event time at the sink node is the minimum time it will take to complete the project.You can then start to find the latest or late event times. This is an example of a backward scan, as it goes from the sink node to the source node.

Finding both the early and late event times is essential in critical path analysis. Look at the activity network again.

D1: Latest Or Late Event Time

To calculate late event times it will be useful to introduce two more definitions.

4 5F (7)

As you know, activities connect

two events.

At the beginning of the activity, you have the tail event.

Tail Tail EventEvent

At the end of the activity, you have the head event.

Head Head EventEvent

D1: Latest Or Late Event Time

Event Earliest Event Time Latest Event Time

0 0 0

1 9 9

2 6 7

3 12 16

4 15 16

5 18 18

6 25 25

The late event time for the sink node is the same as the early event time.For the other events, find:

Late event time at head event

SUBTRACT

Activity Duration

D1: Event Times Notes• The early event time is the biggest weight

going into the event. The late event time is the smallest possible value of

Latest event time at head event minus activity duration

This is true!

• Most exam questions on this topic ask you to fill in the early and late event times on the activity network (see next slide).

• Beware of dummies! If you calculate all the possible event times in both directions, you are sure to find the right one.

D1: Early And Late Event Times