Question

# Period Forecast 1 200 2 500 3 300 4 400 5 200 6 200 Regular time:...

 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 first period in which overtime should be scheduled in order to minimize total cost for the aggregate plan?

Forecast in period 1 = 200 units

Production in regular time = \$20 per unit

Overtime production cost = \$30 per unit

Carrying cost = \$10 per unit

Back order cost = \$50 per unit

Closing inventory = 80 units (regular time + 40 units (overtime)

=120 units

As cost of closing inventory for overtime period = overtime production cost per unit + carrying cost

= \$30+\$10 = \$40 which is less than back order cost which is \$50 per unit if order is not fulfilled.

As per forecast period 2 requirement is 500 units which can't be fulfilled in that period itself. Hence production overtime should e scheduled from very period 1 so that cost can be minimized for period 2.

Forecast in period 2 : 500 units

Production in regular time = 280 units

Overtime production = 40 units

Remaining units = 500-320 units = 180 units

Opening stock from period 1= 120 units (including overtime production units )

Orders not fulfilled = 60 units.

Due to overtime production in period 1 cost saving is = 40 units * (\$50-\$40) = \$400

Hence overtime should be scheduled from period 1.