Question

13.7 Table EX 13.7 shows the precedence relationships among the activities to complete a project.

Table EX 13.7

Activity	Predecessor	Duration (Weeks)
A	–	6
B	–	2
C	A	4
D	B	5
E	B	2
F	C, D	4
G	C, D	7
H	E, G	5
I	F	4

1. Construct an activity on node network for the project.
2. Identify the paths and path project durations.
3. Determine the critical path and the expected project completion time.
4. Find the ES, LS, EF, LF, and slack time for each activity.

Answer 1

Construct an activity on node network for the project.

Identify the paths and path project durations.

Path	Duration(Weeks)
A-C-G-H	6+4+7+5 = 22
A-C-F-I	6+4+4+4 = 18
B-D-F-I	2+5+4+4 = 15
B-E-H	2+2+5 = 9
B-D-G-H	2+5+7+5 = 19

Determine the critical path and the expected project completion time.

Critical path is the longest path and here the critical path is A-C-G-H with duration 22 weeks

Expected project completion time is duration of critical path = 22 weeks

Find the ES, LS, EF, LF, and slack time for each activity.

	ES	LS	EF	LF	Slack
A	0	0	6	6	0
B	0	3	2	5	3
C	6	6	10	10	0
D	2	5	7	10	3
E	2	15	4	17	13
F	10	14	14	18	4
G	10	10	17	17	0
H	17	17	22	22	0
I	14	18	18	22	4

Forward Pass

Early Start of A = 0

Early Finish of A = Early Start of A + Duration of A = 0+6 = 6

Early Start of C = Early Finish of A = 6

Early Finish of C = Early Start of C + Duration of C = 6+4 = 10

Early Start of G = Early Finish of C = 10

Early Finish of G = Early Start of G + Duration of G = 10+7 = 17

Early Start of F = Early Finish of C = 10

Early Finish of F = Early Start of F + Duration of F = 10+4 = 14

Early Start of B = 0

Early Finish of B = Early Start of B + Duration of B = 0+2 = 2

Early Start of D = Early Finish of B = 2

Early Finish of D = Early Start of D + Duration of D = 2+5 = 7

Early Start of E = Early Finish of B = 2

Early Finish of E = Early Start of E + Duration of E = 2+2 = 4

Early Start of H = Max(Early Finish of E, Early Finish of G) = Max(4,17) = 17

Early Finish of H = Early Start of H + Duration of H = 17+5 = 22

Early Start of I = Early Finish of F = 14

Early Finish of I = Early Start of I + Duration of I = 14+4 = 18

Backward pass

Late Finish of H = 22

Late Start of H = Late Finish of H - Duration of H = 22-5 = 17

Late Finish of I = 22

Late Start of I = Late Finish of I - Duration of I = 22-4 = 18

Late Finish of G = Late Start of H = 17

Late Start of G = Late Finish of G - Duration of G = 17-7 = 10

Late Finish of C = Late Start of G = 10

Late Start of C = Late Finish of C - Duration of C = 10-4 = 6

Late Finish of D = Late Start of G = 10

Late Start of D = Late Finish of D - Duration of D = 10-5 = 5

Late Finish of F = Late Start of I = 18

Late Start of F = Late Finish of F - Duration of F = 18-4 = 14

Late Finish of E = Late Start of H = 17

Late Start of E = Late Finish of E - Duration of E = 17-2 = 15

Late Finish of A = late start of C = 6

late Start of A = Late finish of A - Duration of A = 6-6 = 0

Late Finish of B = Min (Late start of D , and Late start of E) = Min(5,15) = 5

Late Start of B = Late Finish of B - Duration of B = 5-2 = 3

Slack = Late Start - Early Start = Late Finish - Early Finish