Question 1
Davidson was able to determine the activity times for the leadership training program. He would like to determine the total project completion time and the critical path. The activity time appears in the following table.
Activity Time (days)
A 2
B 5
C 1
D 10
E 3
F 6
G 8
35
Question 2
Tom Soon, a personnel director of Management Resource 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 a resume, writing letters, making appointments to see prospective employers, research companies and industries, and so on. Some of the information on the activities is shown in the following table.
Days
Activity a m b Immediate Predecessors
A 8 10 12 -
B 6 7 9 -
C 3 3 4 -
D 10 20 30 A
E 6 7 8 C
F 9 10 11 B, D, E
G 6 7 10 B, D, E
H 14 15 16 F
I 10 11 13 F
J 6 7 8 G, H
K 4 7 8 I, J
L 1 2 4 G, H
a) Construct a network for this problem.
b) Determine the expected time and variance for each activity.
c) Determine ES, EF, LS, LF and slack for each activity
d) Determine the critical path and project completion time.
e) Determine the probability that the project will be finished in 70 days or less.
f) Determine the probability that the project will be finished in 80 days or less.
g) Determine the probability that the project will be finished in 90 days or less.
Question 3: Case study - Moore Housing Contractors
Moore Housing Contractors is negotiating a deal with Countryside Realtors to build six houses in a new development. Countryside wants Moore Contractors to start in late winter or early spring, when the weather begins to moderate and build on through the summer and into the fall. The summer months are especially busy time for the realty company, and it believes it can sell the houses as soon as they are ready, and may be even before. The houses all have similar floor plans and are of approximately equal size; only the exteriors are noticeably different. The completion time is so critical for Countryside Realtors that it is insisting that a project management network accompany the contractor’s bid for the job, with an estimate of the completion time for a house. The realtor also needs to be able to plan its offerings and marketing for the summer. It wants each house to be completed within 45 days after it is started. If a house is not completed within this time frame, it wants to be able to charge the contractor a penalty. Mary and Sandy Moore, the president and vice president, respectively, of Moore Contractors, are concerned about the prospect of a penalty charge. They want to be very confident that they can meet the deadline for a house before they enter into any kind of agreement with a penalty involved. (If there is a reasonable likelihood that they cannot finish a house within 15 days, they want to increase their bid to cover potential penalty charges).
The Moores are experienced home builders, so it was not difficult for them to list the activities involved in building a house or to estimate activity times. However, they made their estimates conservatively and tended to increase their pessimistic estimates to compensate for the possibility of bad weather and variations in their workforce. Following is a list of the activities involved in building a house and the activity time estimates.
Time (days)
Activity Activity description predecessors a m b
a Excavation, pour footers - 3 4 6
b Lay foundation a 2 3 5
c Frame and roof b 2 4 5
d Lay drain tiles b 1 2 4
e Sewer (floor) drains b 1 2 3
f Install insulations c 2 4 5
g Pour basement floor e 2 3 5
h Rough plumbing pipes e 2 4 7
i Install windows f 1 3 4
j Rough electrical wiring f 1 2 4
k Install furnace, air conditioner c, g 3 5 8
l Exterior brickwork i 5 6 10
m Install plasterboard, mud, plaster j, h, k 6 8 12
n Roof shingles, flashing l 2 3 6
o Attach gutter downspouts n 1 2 5
p Grading d, o 2 3 7
q Lay sub-flooring m 3 4 6
r Lay driveway, walks, landscape p 4 6 10
s Finish carpentry q 3 5 12
t Kitchen cabinetry and sink q 2 4 8
u Bathroom cabinetry, fixtures q 2 3 6
v Painting (interior and exterior) t,u 4 6 10
w Finish wood floors, lay carpet v,s 2 5 8
x Final electrical light fixtures v 1 3 4
a) Develop a CPM/PERT network for Moore Housing Contractors and determine the probability that the company can complete a house within 45 days. Does it appear that the Moores might need to increase their bid to compensate for potential penalties?
b) Indicate which project activities Moore Housing Contractors should be particularly diligent to keep on schedule by making sure workers and materials are always available. Also indicate which activities the company might shift workers from as the need arises.