Problem:
The Upton Corporation manufactures heavy duty air compressors for the home and light industrial markets. Upton is presently trying to plan its production and inventory levels for the next six months. Because of seasonal fluctuations in utility and raw material costs, the per unit cost of producing air compressors varies from month to month - as does the demand for air compressors. Production capacity also varies from month to month due to differences in number of working days, vacations, and scheduled maintenance and training. The following table summarizes the monthly production costs, demands, and production capacity Upton's management expects to face over the next six months.
|
Month
|
|
1
|
2
|
3
|
4
|
5
|
6
|
|
Unit Production Cost
|
$240
|
$250
|
$265
|
$285
|
$280
|
$260
|
|
Units Demanded
|
1,000
|
4,500
|
6,000
|
5,500
|
3,500
|
4,000
|
|
Maximum Production
|
4,000
|
3,500
|
4,000
|
4,500
|
4,000
|
3,500
|
Given the size of Upton's warehouse, a maximum of 6,000 units can be held in inventory at the end of any month. The owner of the company likes to keep at least 1,500 units in inventory as safety stock to meet unexpected demand contingencies. To maintain a stable workforce, the company wants to produce no less than one half of its maximum production capacity each month. Upton's controller estimates that the cost of carrying a unit inventory in any given month is approximately equal to 1.5% of the unit production cost in the same month. Upton estimates the number of units carried in inventory each month by averaging the beginning and ending inventory for each month.
There are 2,750 units currently in inventory.
Required:
Upton would like to identify the production and inventory plan for next six months that will meet the expected demand each month while minimizing production and inventory costs.
Solve the given numerical problem and illustrate step by step calculation.