1. When buyers purchase new houses, they are frequently responsible for installing their own landscaping. The PERT/CPM network shown in the accompanying figure represents a landscaping project for a new home in Jackson, Mississippi. The times are in days.
a. What are the expected completion time and the critical path for the landscaping project?
b. What are the earliest and latest start and finish times for activity C?
c. How long can activity A be delayed without delaying the minimum completion time of the project?
d. If activities A, C, and F are each delayed three days, how long will the landscaping project be delayed?
2. Virtual Golf, Inc. (VGI) is contemplating introducing a new virtual reality golf experience that would, if successful, be located in many amusement parks and entertainment centers throughout the country. If the project gets the "go ahead", it must be completed within 20 weeks (140 days) to be installed in the Mall of America in Bloomington, Minnesota, for test marketing. The table below gives cost and time estimates (in days) for the activities of the project.
Activity
Immediate Predecessors
A. Feasibility study
-
B. Input from golf professionals
A
C. Conceptual design
B
D. Professional Feedback
C
E. Final design
D
F. Manufacture of unit
E
G. Software development
E
H. Equipment/software coordination
F,G
I. In-house unit testing
H
J. Operator training
H
K. Construct unit in mall store
I, J
L. Testing of unit in mall store
K
Activity
Normal Days
Crash Days
Normal Cost
Crash Cost
A. Feasibility study
14
12
$15,000
$17,500
B. Input from golf professionals
14
11
$55,000
$64,000
C. Conceptual design
8
8
$50,000
$50,000
D. Professional Feedback
12
9
$40,000
$50,000
E. Final design
18
16
$50,000
$65,000
F. Manufacture of unit
20
16
$40,000
$55,000
G. Software development
14
10
$55,000
$70,000
H. Equipment/software coordination
21
19
$25,000
$65,000
I. In-house unit testing
10
8
$25,000
$32,000
J. Operator training
21
21
$50,000
$50,000
K. Construct unit in mall store
9
6
$25,000
$40,000
L. Testing of unit in mall store
15
10
$10,000
$40,000
a. What is the minimum project cost that will allow the project to be completed within 21 weeks?
b. What is the minimum project cost that will allow the project to be completed within 19 weeks?
3. Consider the project facing VGI in Problem 2. If the company allocated a maximum of $450,000 to this project, what is the minimum time it would take to complete the project?
4. Universal Travel is planning to move its headquarters from Cincinnati to Columbus, Ohio. The table below details the steps that must be taken. Times are in weeks.
Immediate Predecessors
Optimistic Time
Most Likely Time
Pessimistic Time
A. Select a site
-
8
12
20
B. Refurbish building
A
9
10
12
C. Determine which staff will transfer
-
2
2
3
D. Hire staff replacements in Columbus
C
3
6
8
E. Pack boxes in Cincinnati
A,C
1
2
5
F. Move equipment
B
2
3
4
G. Move files
B,E
1
2
5
H. Set up equipment/files in Columbus
F,G
3
4
5
I. Occupancy
D,H
5
6
10
a. What is the expected completion time of the project? What is the critical path?
b. What is the probability the project will be completed within 36 weeks?
c. Suppose Universal will be charged for both sites if it is not completely moved in within 36 weeks. This will cost the company $5,000.
The company is considering two options to improve its chances to meet this deadline.
- For $1,000, additional movers can be hired to move the files. This would cut each of the three time estimates for that activity in half.
- Additional movers can be hired for $1,000 to assist in moving the equipment. This would cut the three time estimates for that activity by one week each.
The company can pursue either OR BOTH of these options. What is your recommendation?