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ATENEO DE MANILA UNIVERSITY
Graduate School of Business
MBA MIDDLE MANAGER PROGRAM
MANAGEMENT SCIENCE
Integer/Binary Programming
Submitted by:
Cenon Oriel
David Viray
Rodolfo Milan Jr.
02 December 2009
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In a project selection model involving seven projects (P
1
, P
2
, P
3
, P
4
, P
5
, P
6
7
), write
constraints to satisfy each of the following conditions:
1.
Exactly one project from the set (P
1
, P
4
, P
5
) has to be selected;
2.
At most four projects can be invested in ;
3.
If investment in P
3
is made, P
6
must also be selected;
4.
Projects P
2
and P
5
must both be selected or both be rejected;
5.
If investment is made both in P
1
and P
2
, then project P
7
must also be chosen;
6.
If project P
6
is selected, then project P
7
cannot be selected
1. P1 + P4 + P5
=
1
2. P1 + P2 + P3 + P4 + P5 + P6 + P7
=
4
3.
P3 <
P6
4.
P2
=
P5
5.
P1 + P2
<
P7 + 1
6.
P6 = P7
<
1
2.
A research administrator in the Federal Science Foundation is trying to decide which
projects to fund for the coming year. She has received the eight proposals listed
below. After careful study, she has made a subjective estimate of the value of each
project on a scale of 0 to 100. The research administrator wants to find a mix of
projects having the greatest total value. However, there are several limitations. First,
she has a budget of $320,000. Second, she must either accept or turn down a
project (i.e. no partial funding). Third, certain projects are related. She does not wish
to fund both projects G & H; further, project D shout not be funded unless A is also
funded (but A can be funded without D)
PROJECT COST ($000s) VALUE
A 80 40
B 15 10
C 120 80
D 65 50
E 20 20
F 10 5
G 60 80
H 100 100
Let
A be a binary such that A=1 if project A is selected; A= 0 if project is not selected
B be a binary such that B=1 if project B is selected; B= 0 if project is not selected
C be a binary such that C=1 if project C is selected; C=0 if project is not selected
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 Spring '09
 RaulRuiz

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