Question

1. Tom Schriber, a director for personnel of Management Resources, Inc., is in the process of designing a program that its customers can use in the job-finding process. Some of the activities include preparing resumes, writing letters, making appointments to see prospective employers, researching companies and industries, and so on. Some of the information on the activities is shown in the following table:

	Days			Immediate Predecessors
Activity	a	m	b
A	8	9	10	__
B	6	7	8	__
C	3	3	5	A
D	10	20	30	B
E	6	8	8	B
F	9	10	12	C,D
G	6	8	10	E,C,D

1. Determine the expected time and variance for each activity.
2. Construct a network for this problem.
3. Determine ES, EF, LS, LF, and slack for each activity.
4. Determine the critical path and project completion time.
5. Determine the probability that the project will be finished in 40 days or less. (15 points)

Answer 1

(a)

Activity	a	m	b	te = (a + 4m + b)/6	s2 = (b - a)2/36
A	8	9	10	9	0.111
B	6	7	8	7	0.111
C	3	3	5	3.333	0.111
D	10	20	30	20	11.111
E	6	8	8	7.667	0.111
F	9	10	12	10.167	0.250
G	6	8	10	8	0.444

(b)

A F Start Finish B D G E

(c)

Forward Pass:

ES of the starting activities = 0
ES of all other activities = Max. (EF of their immediate predecessors)
EF of an activity = Its ES + Its 't_e'

Backward Pass:

LF of ending activities = Max. (All the EFs)
LF of all other activities = Min. (LS of their immediate successors)
LS of an activity = Its LF - Its 't_e'

Total slack (or, float) = LF - EF for each activity.

Activity	te = (a + 4m + b)/6	ES	EF	LS	LF	Slack
A	9	0.000	9.000	14.667	23.667	14.667
B	7	0.000	7.000	0.000	7.000	0
C	3.333	9.000	12.333	23.667	27.000	14.667
D	20	7.000	27.000	7.000	27.000	0
E	7.667	7.000	14.667	21.500	29.167	14.500
F	10.167	27.000	37.167	27.000	37.167	0
G	8	27.000	35.000	29.167	37.167	2.167

(d)

The critical path of a project is composed of activities with zero total slack.

So, the critical path is B-D-F. The expected completion time = 37.167 days.

(e)

Activity	te = (a + 4m + b)/6	s2 = (b - a)2/36
B	7	0.111
D	20	11.111
F	10.167	0.250
Totals	37.167	11.472

Project's mean duration = 37.167 days

Stdev = sqrt(11.472) = 3.387 days

Target = 40 days

So, z = (40 - 37.167)/3.387 = 0.837

So, F(z) = NORMSDIST(0.837) = 0.799

So, the probability that the project is completed by 40 days = 0.799