Practice questions for OEM DMOR Final Exam
Question 1.
A company is pursuing a project that requires three phases:
(i) data
collection, (ii) model development, and (iii) implementation.
Phases i and ii can be done
simultaneously by the team.
After those phases are complete, phase (iii) can begin.
We
anticipate that phase (i) will require 20 weeks, phase (ii) will require 22 weeks, and phase
(iii) will require 16 weeks.
We have three adhoc teams, A, B, and C, that can work on phases i, ii, and iii,
respectively.
Every week that team A works reduces the number of weeks required by
phase (i) by 0.7.
Every week that team B works reduces the number of weeks required
by phase (ii) by 0.8, and every week that team C works reduces the number of weeks
required by phase (iii) by 0.6.
However, there are three restrictions that govern the team assignment process:
1:
The total amount of weeks worked by these three teams is no more than
20.
2:
Due to project accounting limits, we cannot allocate more than $80,000 to
teams A, B, and C, combined.
Team A gets paid $5,000 per week, Team
B gets paid $8,000 per week, and Team C gets paid $6,000 per week.
3:
Because of overlaps in team members, the sum of weeks worked by Team
B and Team C must be no more than 8.
The objective is to minimize the time that the entire project is finished.
The following is
the model:
Minimize
t
subject to
t
–
t
1
–
t
3
≥
0
(Constraint 1)
t
–
t
2
–
t
3
≥
0
(Constraint 2)
t
1
+ 0.7
x
A
= 20
(Constraint 3)
t
2
+ 0.8
x
B
= 22
(Constraint 4)
t
3
+ 0.6
x
C
= 16
(Constraint 5)
x
A
+
x
B
+
x
C
≤
20
(Constraint 6)
5000
x
A
+ 8000
x
B
+ 6000
x
C
≤
80000
(Constraint 7)
x
B
+
x
C
≤
8
(Constraint 8)
t
,
t
1
,
t
2
,
t
3
,
x
A
,
x
B
,
x
C
≥
0
Part a:
Give a brief (one line) interpretation of each variable.
t
is the time at which the entire project finishes
t
1
is the time at which phase i finishes (similarly for
t
2
and
t
3
)
x
A
is the number of weeks that team A works on this project (similarly for
x
B
and
x
C
).
Part b:
Modify the problem as follows.
Team C can also be assigned to help out in phase
(ii) if required.
Every week of Team C’s effort on phase (ii) reduces the number of
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View Full Documentweeks required for that phase by 0.5.
Team C can work on a combination of phase (ii)
and phase (iii).
(You may need an extra variable, perhaps two, for this modification.)
Now, we need to know not just how many weeks team C works, but how many hours
team C works on phase ii, and how many they work on phase iii.
Remove variable
x
C
,
and replace it with two new variables:
x
C
2
(weeks worked on phase ii by team C) and
x
C
3
(weeks worked on phase iii by team C).
t
2
+ 0.8
x
B
+ 0.5
x
C
2
= 22
(New constraint 4)
t
3
+ 0.6
x
C
3
= 16
(New constraint 5)
x
A
+
x
B
+
x
C
2
+
x
C
3
<= 20
(New constraint 6)
5000
x
A
+ 8000
x
B
+ 6000
x
C
2
+ 6000
x
C
3
<= 80000
(New constraint 7)
x
B
+
x
C
2
+
x
C
3
<= 8
(New constraint 8)
Also, both new variables are nonnegative.
The next few parts are all independent of all other questions.
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 Fall '09
 VLADIMIRLBOGINSKI
 chance, Extra Point, Twopoint conversion

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