Question

Jim Sweet, a project manager at Clover Health in San Francisco, is assigned to the team that is developing the process for implementing a new database management system at corporate headquarters. The corporate planning group in Waltham, Massachusetts has contacted him and has asked how confident the design group is about completing the project in 60 days. He has developed these estimated time durations in days for the project:

Activity	Immediate Predecessor Activities	Optimistic Time (to)	Most Likely Time (tm)	Pessimistic Time (tp)
A	--	10	12	15
B	A	6	10	14
C	A	8	16	18
D	A	6	12	20
E	B	5	6	8
F	C,E	10	12	13
G	B	12	14	16
H	D	18	21	24
I	D	10	15	20
J	F.G.H	8	10	14

1. Compute the expected time and variance for each activity.
2. Determine the critical path and the expected duration of the project.
3. What is the probability that the project will take longer than 58 days to complete?
4. Which path in the project network offers the greatest risk of overrunning a new deadline of 56 days?

Answer 1

Solution:-

Given that

Jim Sweet, a project manager at Clover Health in San Francisco, is assigned to the team that is developing the process for implementing a new database management system at corporate headquarters.

The design group is about completing the project in 60 days.

1) Compute the expected time and variance for each activity.

Mean	Std dev	Variance	Activity
12.16667	0.833333	0.694444	A
10	1.333333	1.777778	B
15	1.666667	2.777778	C
12.33333	2.333333	5.444444	D
6.166667	0.5	0.25	E
11.83333	0.5	0.25	F
14	0.666667	0.444444	G
21	1	1	H
15	1.666667	2.777778	I
10.33333	1	1	J

2) Determine the critical path and the expected duration of the project.

The critical path is:

A-D-H-J

Expected duration = 55.83
3) What is the probability that the project will take longer than 58 days to complete?

= 0.76

The probability is 0.2238.

4) Which path in the project network offers the greatest risk of overrunning a new deadline of 56 days?

A-D-H-I-J

The calculations are:

Data  

Results:-

Activity	Early Start	Early Finish	Late Start	Late Finish	Slack
A	0	12.16667	0	12.16667	0
B	12.16667	22.16667	17.5	27.5	5.333333
C	12.16667	27.16667	18.66667	33.66667	6.5
D	12.16667	24.5	12.16667	24.5	0
E	22.16667	28.333333	27.5	33.66667	5.333333
F	28.33333	40.16667	33.66667	45.5	5.333333
G	22.16667	36.16667	31.5	45.5	9.333333
H	24.5	45.5	24.5	45.5	0
I	24.5	39.5	40.83333	55.83333	16.33333
J	45.5	55.83333	45.5	55.83333	0
	Project	55.83333

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