1. General Foundry, Inc., a metal works plant in Milwaukee, has long been trying to avoid the expense of installing air pollution control equipment. The local environment protection group has recently given the foundry 16 weeks to install a complex air filter system on its main smokestack. General Foundry has been warned that it may be forced to close unless the device installed in the allotted period. Lester Harky, the managing partner, wants to make sure that installation of the filtering system progressed smoothly and on time.
General Foundry has identified the following eight activities that need to be performed and their sequential relationship.
|
Activity
|
Description
|
Time
(weeks)
|
Immediate
Predecessors
|
|
A
|
Build internal components
|
2
|
--
|
|
B
|
Modify roof and floor
|
4
|
--
|
|
C
|
Construct collection stack
|
2
|
A
|
|
D
|
Pour concrete and install frame
|
4
|
A, B
|
|
E
|
Build high-temperature burner
|
4
|
C
|
|
F
|
Install pollution control system
|
3
|
C
|
|
G
|
Install air pollution device
|
5
|
D, E
|
|
H
|
Inspect and test
|
2
|
F, G
|
a. Construct the appropriate network diagram.
b. Which jobs can be delayed without delaying the project completion time?
c. Can General Foundry complete the project on time? Why or why not?
d. Suppose Lester wants to shorten the completion time and his options are:
(1) Reduce activity D by one week, which costs $700/week;
(2) Reduce activity E by one week, which costs $800/week;
(3) Reduce activity G by one week, which costs $1000/week;
If General Foundry will save $2000 for each week that the earliest completion time is reduced, which single option, if any, should Lester choose?
2. The following table represents a plan for a project:
|
|
Time Estimates (days)
|
|
Job No.
|
Predecessor Job(s)
|
Optimistic
|
Most likely
|
Pessimistic
|
|
A
|
-
|
1
|
2
|
3
|
|
B
|
-
|
2
|
3
|
4
|
|
C
|
A
|
4
|
5
|
6
|
|
D
|
B
|
8
|
9
|
10
|
|
E
|
C, D
|
2
|
5
|
8
|
|
F
|
D
|
4
|
5
|
6
|
|
G
|
E
|
1
|
2
|
3
|
a. Construct the appropriate network diagram.
b. What is the critical path?
c. What is the expected completion time for the project and what is the variance of project completion time?
d. Is the probability that the project will take less than 18 days to complete larger than 50% or smaller than 50%?