(a) Worksheet 8.1 provides the solution to this problem and the corresponding aggregate
plan.
The total cost of the plan is $360,400,000.
(b) If the number of overtime hours per employee were increased from 20 to 40 it would
result in decreasing the total cost to $356,450,000.
So, it is advantageous to do it.
(c) If the number of employees is decreased to 1200 and the overtime hours per
employee are held at 20 and 40 then the total costs of the plan are $363,324,000 and
$357,422,000, respectively.
If the number of employees is increased to 1300 and the
overtime hours per employee are held at 20 and 40 then the total costs of the plan are
$358,790,000 and $356,270,000, respectively.
So, the value of additional overtime
increases as workforce size decreases.
(d) We add a new constraint:
12
,...
1
,
667
.
1291
=
≤
t
P
t
. The cost will be $363,049,982.
Problem 82
:
We now include the subcontract option in the model:
Minimize
∑
∑
∑
∑
∑
=
=
=
=
=
+
+
+
+
12
1
12
1
12
1
12
1
12
1
26000
20000
3000
30
3200
i
t
i
t
i
t
i
t
t
t
C
P
I
O
W
Subject to:
Inventory constraints:
12
,..,
1
,
1
=
=

+
+

t
D
I
C
P
I
t
t
t
t
t
50
12
0
=
=
I
I
Overtime constraints:
12
,...,
1
,
0
20
=
≤

t
W
O
t
t
Production constraints:
12
,...
1
,
0
1000
960
1000
6
=
≤


t
W
O
P
t
t
t
Workforce constraints:
12
,...,
0
,
1250
=
=
t
W
t
Worksheet 82 provides the solution to this problem.
(a) Without the subcontract option the total cost is $360,400,000 (from problem 81) and
the total number of units produced is 14,900,000.
Thus, the cost per unit is $24.19.