Question

1. A sporting goods store is planning to open an outlet in a college town. The activities consist of the hiring of the manager of the outlet and his/her employees. Also it is necessary to coordinate the renovation of a building that previously was a fast food restaurant. To schedule this project using PERT, the following time estimates (in weeks) are gathered:

What is the critical path and expected completion time for this project?   (15 pts)

Which activity has the largest slack, and how large is that slack? (5 pts)

1. What is the probability that the project is completed in 26 weeks and 24 weeks? (15 pts)

Activity	Description	Opt. time	Likely time	Pess. time	Predecessors
A	Interview at college for new manager	4	10	16	None
B	Renovate building	4	6	20	None
C	Purchase new equipment for new outlet	1	4	7	B
D	Check references for new manager and make final selection	2	4	6	A
E	Place ad for new employees & interview applicants	3	3	3	D
F	Install new equipment	2	4	6	C
G	Make final selection for employees	3	3	3	E
H	Hold orientation meetings for employees	2	2	2	F,G

Answer 1

We first calculate the expected time using the formula

Expected time = (opt + 4*likely + pess)/6

And then calculate the variance using the formula

Variance = [(pess – opt)/6]^2

Then we calculate the early start, early finish, late start, late finish and slack based on the expected time.

The calculated table is shown below

Opt. Likely Pess. Predecessors Expected Variance time LS 0 Slack 0 1 Activity Description time ES time time 16 20 time 10 12 16 14 17 10 10 None 10 Interview at college for new manager Renovate building Purchase new equipment for new outlet Check references for new manager and make fina2 Place ad for new employees & interview applican 3 Install new equipment Make final selection for employees Hold orientation meetings for employees 3 A None 12 10 14 16 17 20 14 17 16 40.4444410 14 12 17 20 0 0.44444 6 D 0 0 9 G 10 H 12 14 15 16 17 18 19 20 23 24 +115% Sheet920 Sheet92 Sheet922 Sheet923Sheet924

a.

The critical path is A-D-E-G-H and the expected completion time is 22 weeks

b.

The activities B,C, and F has the largest slack of 4 each.

c.

The project variance (along the critical path) is 4.44. The standard deviation is sqrt(4.44) = 2.1

26 weeks:

For 26 weeks, the z value is (26 – 22)/2.1 = 1.90

The probability at z = 1.90 is 0.9712 or 97.12%

24 weeks:

For 24 weeks the z value is (24-22)/2.1 = 0.95

The probability at z = 0.95 is 0.8289 or 82.89%