Aggregate production in the next four quarters is set to be 300 units in each qu
ID: 371620 • Letter: A
Question
Aggregate production in the next four quarters is set to be 300 units in each quarter. Demand is 300, 250, 400, and 250 units respectively in each of the next four quarters. Beginning inventory is zero. If we are unable to meet the demand, it is not lost but backordered. Cost of holding one unit in inventory per quarter is $ 3, and the cost of having one unit of inventory backordered per quarter is $ 10. In the given production plan, what is the total cost of inventory (holding cost and backorder cost combined)? (For simplicity, assume that all shipments take place at the end of each quarter, not during the quarter)
Explanation / Answer
Following will be the status of inventory and backordered quantity for each quarter:
Quarter 1:
Demand = 300
Production = 300
Hence, Inventory ( Production – Demand ) = 0
Backordered quantity = 0
Quarter 2:
Demand = 250
Production = 300
Inventory ( Production – Demand ) = 50
Backordered quantity = 0
Quarter 3:
Demand = 400
Production = 300
Inventory = 0
Shortfall ( which should be backordered from next quarter production ) = 400 – 300 – 50 (inventory from previous quarter) = 50
Quarter 4:
Demand = 250
Production = 300
Backordered quantity for previous quarter = 50
Inventory = Production – Demand – Backordered quantity = 300 – 250 – 50 = 0
Inventory = 0
Thus:
Total inventory on quarterly basis = 50
Total backordered quantity on quarterly basis = 50
Thus,
Inventory holding cost = $3/unit x 50 units = $150
Backordering cost = $10/ unit x 50 units = $ 500
Thus , total cost of inventory = $150 + $500 = $650
TOTAL COST OF INVENTORY = $650
TOTAL COST OF INVENTORY = $650