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Goal programming
The LPP models discussed so far are based on the
optimization of a
single
objective function. There
are situations where multiple objectives are to be
met. We now present the goal programming
technique for solving multi objective models. The
principle idea is to convert the original multiple
objectives into a single goal. The resulting model
usually gives an efficient solution because it may
not meet all the objectives.
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View Full Document Formulation of Goal Programming problems
(problem 2 problem set 8.1A page 349)
The NW shipping model conducts special events to
attract potential patrons. The two most popular events
that seem to attract teenagers, the young/middleaged
group, and senior citizens are band concerts and art and
craft shows. The costs per presentation of the band and
art show are $1500 and $3000 respectively. The total
(strict) annual budget allocated to the two events is
$15000. The mall manager estimates the attendance of
the events as follows:
Number attending per presentation
Event
Teenagers
Young/middle age
Seniors
Band concert
200
100
0
Art show
0
400
250
The manager has set the minimum annual goals
of 1000,1200 and 800 for the attendance of
teenagers, the young/middleaged group, and
seniors, respectively. Formulate the problem as a
goalprogramming model.
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View Full Document Solution
1
x
Let
= number of band concerts to be held per year
2
x
= number of art shows to be held per year
Thus the goals are
1000
200
1
≥
x
1200
400
100
2
1
≥
+
x
x
800
250
2
≥
x
(attendance of teenagers)
(attendance of
young/middleaged group)
(attendance of seniors)
Subject to
15000
x
3000
x
1500
2
1
≤
+
0
2
,
1
≥
x
x
+
+
+
2
1
1
400
100
200
x
x
x
We now convert the goals into equalities by adding slack/
surplus variables
G1:
G2:
+
2
250
x
G3:
1000
=
1200
=
800
=

+

1
1
s
s

+

2
2
s
s

+

3
3
s
s
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+
i
i
s
s
,
+
i
s
are called
deviational variables
. They measure the
amount by which a goal is underachieved or over
achieved. For example

i
s
is positive(& so
will be 0)
means the attendance of teenagers fall short of the desired
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This note was uploaded on 02/23/2011 for the course MATH 112 taught by Professor Ritadubey during the Spring '11 term at Amity University.
 Spring '11
 ritadubey

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