Problem :
A computer manufacturer is developing a production schedule for the next five months (say March -- July). Demands for this manufacturer's laptop computer in the next five months are forecasted to be 1200, 2100, 1500, 1000, and 800, respectively.
Assume that it costs this manufacturer $1200 to produce each laptop computer. At the end of each month, a holding cost of $300 per computer left in inventory is incurred. Increasing production from one month to the next incurs costs for hiring and training new employees. It is estimated that a cost of $2000 per computer is incurred if production is increased from one month to the next.
Decreasing production from one month to the next incurs costs for laying off employees, loss of morale, and so forth. It is estimated that a cost of $1800 per computer is incurred if production is decreased from one month to the next.
All demands must be met on time, and the units produced in one month can be used to meet demand for the current month as well as for future months. In the current month (February), 1500 laptop computers were produced.
Assume that at the beginning of March, there are 100 computers in inventory.
Questions:
Formulate a Linear Programming model for this problem and solve it via ASPE (Excel Solver).
Check Figure: ~$9.50million-9.55million. (I need help with the Increase/ Decrease Variables)
What is the optimal solution? Briefly explain it.
| Production Cost |
|
|
|
|
|
|
|
|
M o n t h |
|
|
March |
April |
May |
June |
July |
| Beginning Inventory |
|
100 |
500 |
0 |
0 |
0 |
| Units Produced |
1500 |
1,600 |
1,600 |
1,500 |
1,000 |
800 |
| Units Demanded |
|
1,200 |
2,100 |
1,500 |
1,000 |
800 |
| Ending Inventory |
|
500 |
0 |
0 |
0 |
0 |
|
|
|
|
|
|
|
| Unit Produced Increase Cost |
|
2,000 |
2,000 |
2,000 |
2,000 |
2,000 |
| Unit Produced Decrease Cost |
|
-1,800 |
-1,800 |
-1,800 |
-1,800 |
-1,800 |
| Unit Produced Change |
|
100 |
0 |
-100 |
-500 |
-200 |
|
|
|
|
|
|
|
| Unit Production Cost |
|
1,200 |
1,200 |
1,200 |
1,200 |
1,200 |
| Unit Carrying Cost |
|
300 |
300 |
300 |
300 |
300 |
| Unit Produced Change Cost |
|
200,000 |
0 |
180,000 |
900,000 |
360,000 |
|
|
|
|
|
|
|
| Monthly Production Cost |
|
$1,920,000 |
$1,920,000 |
$1,800,000 |
$1,200,000 |
$960,000 |
| Monthly Carrying Cost |
|
$150,000 |
$0 |
$0 |
$0 |
$0 |
| Monthly Production Change Cost |
|
$200,000 |
$0 |
$180,000 |
$900,000 |
$360,000 |
|
|
|
|
|
|
|
|
|
|
|
|
Total Cost |
$9,590,000 |