Question: Consider a situation where a particular product is produced and placed in in-process inventory until it is needed in a subsequent production process. The number of units required in each of the next 3 months, the setup cost, and the regular-time unit production cost (in units of thousands of dollars) that would be incurred in each month are as follows:
|
Month
|
Requirement
|
Setup Cost
|
Regular-time Unit cost
|
|
1
|
1
|
5
|
8
|
|
2
|
3
|
10
|
10
|
|
3
|
2
|
5
|
9
|
There currently is 1 unit in inventory, and we want to have 2 units in inventory at the end of 3 months. A maximum of 3 units can be produced on regular-time production in each month, although 1 additional unit can be produced on overtime at a cost that is 2 larger than the regular-time unit production cost. The holding cost is 2 per unit for each extra month that it is stored. Use dynamic programming to determine how many units should be produced in each month to minimize the total cost.