Activity on Edge For the graph in Figure 2, please calculate the earliest and la
ID: 3874553 • Letter: A
Question
Activity on Edge
For the graph in Figure 2, please calculate the earliest and latest time for all activities and events and write them down in a table. Also, please mark critical activities and answer what is the shortest possible duration of the whole project. Once again, please use edge weights to denote edges (activities).
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Solution :
Let us consider 0 as A, 1 as B, 2 as C, 3 as D, 4 as E and 5 as F for simplicity of this problem.
Now after applying Distance Vector Algorithm, tables claculated are as follows
For Node A
To Node
Cost
Via Node
A
0
-
B
1
-
C
4
-
D
9
-
E
6
C
F
11
C,E
For Node B
To Node
Cost
Via Node
A
-
-
B
0
-
C
-
-
D
-
-
E
6
-
F
11
E
For Node C
To Node
Cost
Via Node
A
-
-
B
-
-
C
0
-
D
-
-
E
2
-
F
7
E
For Node D
To Node
Cost
Via Node
A
-
-
B
-
-
C
-
-
D
0
-
E
-
-
F
3
-
For Node E
To Node
Cost
Via Node
A
-
-
B
-
-
C
-
-
D
-
-
E
0
-
F
5
-
For Node F
No nodes can be reached from Node F as it is the last node of this directed graph, so no table for node F.
From the above tables it is clear that the first table that is table for node A is the shortest possible time required complete the activities from Node A to F.
Two orders that can be used to complete the whole project are:-
1. A to C to E to F
2. A to B to E to F
Total cost in the 1st link is 11 units.
Total cost in the 2nd link is 12 units.
So, the shortest possible duration to complete the whole project is 11 units and the link is A to C to E to F.
Thank You
To Node
Cost
Via Node
A
0
-
B
1
-
C
4
-
D
9
-
E
6
C
F
11
C,E
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