Question

Period	Forecast
1	200
2	500
3	300
4	400
5	200
6	200

Regular time: $20 per unit (maximum of 280 units per period)

Overtime:    $30 per unit (maximum of 40 units per period)

Subcontracting:    Not available

Beginning inventory:   None

Carrying cost: $10 per unit per period

Backorder cost: $50 per unit per period

What is the total regular time cost for the plan which minimizes total cost?

Round answer to nearest dollar. Do not use a thousands separator or a dollar sign in your answer.

Answer 1

Period	Forecast	Regular time production	Overtime production	Backorder fulfillment
1	200	280	40	0
2	500	280	40	60
3	300	280	40	0
4	400	280	40	60
5	200	200	0	0
6	200	200	0	0
TOTAL	1800	1520	160	120

Total number of regular time production = 1520

Cst per unit of production in regular time = 20

Total cost of production in regular time = 1520 * 20 = 30400

How much to produce in each month and fulfill through backordering can be decided on the basis of the following criteria:

1.) Producer will want to produce as much as possible in regular time as much possible to fulfill requirements of current month as well as month to avoid backorder costs as much as possible.

2.) Current month regular time production cost to fulfill requirements of coming month is equal to overtime cost of production per unit in coming month and less than backorder cost per unit in coming month but both regular time production units and overtime production units is limited so in case of high demand without backordering demand can not be fulfilled.

3.) Current month overtime production cost per unit to fulfill requirements of coming month is less than backorder cost per unit in coming month.