Question

The table below defines the activities and the normal time duration for each activities within a small project. You can decrease (crash) the durations at an additional expense. Table 1 summarizes the time-cost information for the activities to complete the project.

Table 1: The time-cost information for the activities

Activity	Normal Completion Time (weeks)	Immediate Predecessor	Crash Time (weeks)	Normal cost for activities	Crash cost for activities/week
A	2	-	1	1200	400
B	3	-	1	1400	500
C	4	A	4	1500	600
D	3	B, A	2	1600	1300
E	8	D	7	1400	1200
F	3	C	2	1100	1000
G	2	E	2	1400	1100
H	3	F, G	2	1200	400

Questions:

1. Draw the network diagram.
2. Find the earliest start time and earliest finish time for each activity.  
3. Find the latest start time and latest finish time for each activity.
4. Find the slack for each activity. Which of the paths is a critical path?
5. Project overhead cost is $300/week. Find the minimum possible time of the project and the cost associated with this.

Answer 1

a.

b.

Activity	ES	EF
A	0	2
B	0	3
C	2	6
D	3	6
E	6	14
F	6	9
G	14	16
H	16	19

c.

Activity	LS	LF
A	1	3
B	0	3
C	9	13
D	3	6
E	6	14
F	13	16
G	14	16
H	16	19

d.

Activity	ES	EF	LS	LF	Slack
A	0	2	1	3	1
B	0	3	0	3	0
C	2	6	9	13	7
D	3	6	3	6	0
E	6	14	6	14	0
F	6	9	13	16	7
G	14	16	14	16	0
H	16	19	16	19	0

Slack = LS-ES=LF-EF

Critical path = B-D-E-G-H which is the longest path and has slack = 0

e.