Question

Problem 5-7

The following activities are part of a project to be scheduled using CPM:

ACTIVITY	IMMEDIATE PREDECESSOR	TIME (WEEKS)
A	—	7
B	A	6
C	A	2
D	C	4
E	B D	3
F	D	4
G	E F	6

b. What is the critical path?

	A-C-D-F-G
	A-C-D-E-G
	A-B-E-G
	A-B-D-F-G

c. How many weeks will it take to complete the project?

Number of weeks            

d. How much slack does activity B have?

Slack of activity B             week(s)

Answer 1

step 1	find early start, and early finish from the start of the project for each activity
step 2	Find Maximum EF and keep it as the LF of last activities. Max of EF's is 23

Activity	Duration, D	Early start, ES=Max of early finish of preceding activities	Early finish, EF = ES + D	Late finish, LF= Min of LS of successor activities	Late start, LS= LF - D	Total slack= LF-EF	Critical activity, activities with 0 slack time
A	7	0	7
B	6	7	13
C	2	7	9
D	4	9	13
E	3	13	16
F	4	13	17
G	6	17	23	23

step 3

calculate LS for each activity after calculating its EF

Activity	Duration, D	Early start, ES=Max of early finish of preceding activities	Early finish, EF = ES + D	Late finish, LF= Min of LS of successor activities	Late start, LS= LF - D	Total slack= LF-EF	Critical activity, activities with 0 slack time
A	7	0	7	7	0	0	Yes
B	6	7	13	14	8	1	No
C	2	7	9	9	7	0	Yes
D	4	9	13	13	9	0	Yes
E	3	13	16	17	14	1	No
F	4	13	17	17	13	0	Yes
G	6	17	23	23	17	0	Yes

b: A-C-D-F-G is the critical path.

c: it will take 23 weeks

d: B has 1 week of slack