Question

A network for a project is shown below. Activity times, in days, are indicated by the figure that appears under the activity. 3 6 6 5 2 3 6 8 10 2 3 5 2 2 3 2 (i) Analyze the network and determine the earliest and latest EVENT times and the duration of the project.

Answer 1

ACTIVITY	TIME LIMIT
1-2-3-6-8-9-10	18
1-2-3-6-8-10	17
1-2-3-6-10	11
1-4-6-10	15
1-4-6-8-10	21
1-4-6-8-9-10	22
1-5-7-9-10	10
1-7-9-10	8

From the time limit obtained, it is clear that the shortest event for the network diagram will be the path 1-7-9-10 and the longest path will be 1-4-6-8-9-10 for which their time limit 8 and 22 respectively. Thus inorder to clarify the shortest event as the earliest event :

1 $\rightarrow$ 7 $\rightarrow$ 9 $\rightarrow$ 10

(0,_) (2,1) (5,7) (8,9). These are the nodes given for start point and finish point for each activity where 8 as the total duration

1   $\rightarrow$ 4 $\rightarrow$ 6 $\rightarrow$    8 $\rightarrow$ 9 $\rightarrow$    10

(0,_)    (6,1) (12,4) (16,6) (19,8) (22,9). These are the nodes given for the start point and finish point for each activity where 22 as the total duration

Since 1 -7 -9 - 10 is the earliest event, with a total duration of 8

1 - 4 - 6 - 8 - 9 - 10 is the latest event with a total duration of 22

So the duration for the project will be 8.