Problem 1: Personnel Scheduling
Decision Variables:
Let
T
i
be the number of trained employees available in month
i
(
i
=
1
,...,
6)
Let
UP
i
be the number of untrained employees engaged in production
in month
i
(
i
= 1
,...,
6)
Let
UT
i
be the number of untrained employees enrolled in training pro
gram in month
i
(
i
= 1
,...,
6)
Let
E
i
be the number of untrained employees required in month
i
. Note
that these are not variables but are known quantities:
E
1
= 100,
E
2
= 100,
E
3
= 115,
E
4
= 125,
E
5
= 140,
E
6
= 150.
Constraints:
Assume that
T
1
= 0, and start with 145 untrained workers.
UT
1
+
UP
1
= 145
.
For each month
i
= 1
,...,
6 :
The required number of employees is
UP
i
+ 1
.
2
T
i
≥
E
i
.
The number of trained employees is
T
i
=
T
i

1
+ 0
.
9
UT
i
.
The number of untrained employees is
UT
i
+
UP
i
= 0
.
95
UP
i

1
+ 0
.
1
T
i

1
.
1
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 Winter '07
 S.Furino,B.Guenin
 Optimization, LP, Line segment

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