Question

Given the projected demands for the next six months, prepare an aggregate plan that uses inventory, regular time and overtime, and backorders. The plan must wind up with no units in ending inventory in Period 6. Regular time capacity is 150 units per month. Overtime capacity is 20 units per month. Overtime cost is $30 per unit, backorder cost is $20 per unit, inventory holding cost is $5 per unit, regular time cost of $20 per unit, and beginning inventory is zero.

Month             Forecast

1                      180

2                      170     

3                      140

4                      150

5                      130

6                      150

1.How should overtime capacity be utilized? (In what period, and how many units)

2.What are the total regular time costs?

3.What are the total backorder costs?

4.What is the total cost for this plan?

Answer 1

To solve this question first make the whole plan by using the following formula to calculate all the required feilds

Now there is no information about the minimum number of units allowed to be produced in the question. There are two possibilities depending upon the assumptions. Following are the assumptions and the corrrosponding answers to the question:

1. There is no obligation to produce the minimum production of 150 in a month and we are free to produce any number of units upto 150.

2. We are obliged to produce 150 units in a month if productio starts:

The answer to all the 4 sub parts can be obtained from the table above depending upon which solution satisfies your requirement.

According to me we should ideally go with assumption 1 for this question and thus the answers would be:

1. Full overtime capacity will be utilised in month 1 & 2 and no overtime production will be done post that.

2. $17600

3. $400

4. $19200