Question

Frank’s Fine Floats is engaged in the business of building exquisite parade floats. Frank has a new float to build and hopes to use PERT/CPM to help them manage the project. The following table shows the activities that make up the project, as well as the estimated completion time (in days) and immediately preceding activities for each activity. Frank wants to know the total time to complete the project, which activities are critical, and the earliest and the earliest for each activity The latest start and finish date.

Activity	Immediate Predecessor	Duration (days)
A	-	20
B	-	18
C	-	12
D	A	10
E	B	15
F	B	5
G	C	10
H	B,D	8
I	G,H	10

problem:
(1) Draw a single-code network plan
(2) Assuming that the project start time is the first day and the project end time is the 100th day, determine the immediate activities of each activity and calculate the six time parameters of each activity, complete the following table:
Latest End Time Total Time Difference Single Time Difference

Event	Immediate Predecessor	Earliest Start Time	Earliest End Time	Latest Start Time	Latest End Time	Total Time Difference	Single Time Difference
A
B
C
D
E
F
G
H
I

(3) Determine the key activities and key routes of the project
(4) Determine the project duration

Answer 1

(1) Single node network plan-----

2) Six time parameters of each activity------

Events	Immediate predecessor	Earliest start time (Es))	Earliest end time (Ef) Es+t	Latest starttime (Ls) Lf-t	Latests Endtime (Lf)	Total time difference total float((Lf-Ef)
A		0	20	0	20	0
B		0	18	0	33	15
C		0	12	0	28	16
D	A	20	30	20	30	0
E	B	18	33	33	48	15
F	B	18	23	43	48	25
G	C	12	22	28	38	16
H	B,D	30	38	30	38	0
I	G,H	38	48	38	48	0

(3) Key activities and key routs of the project----

Key Activities	Key Routs	Duration
C-G-I	1-2-5-7	12+10+10=32
A-D-H-I	1-3-6-5-7	20+10+8+10=48*
B-H-I	1-4-6-5-7	18+8+10=36
B-F	1-4-7	18+5=23
B-E	1-4-7	18+15=33

(4). Project duration is------ 48 days

As we find in above table that critical path is what which has longest duration,so project duration is 48 days.