A firm is faced with the attractive situation in which it can obtain immediate d
ID: 406927 • Letter: A
Question
A firm is faced with the attractive situation in which it can obtain immediate delivery of an item it stocks for retail sale. The firm has therefore not bothered to order the item in any systematic way. However, recently profits have been squeezed due to increasing competitive pressures, and the firm has retained a management consultant to study its inventory management. The consultant has determined that the various costs associated with making an order for the item stocked are approximately $70 per order. She has also determined that the costs of carrying the item in inventory amount to approximately $27 per unit per year (primarily direct storage costs and forgone profit on investment in inventory). Demand for the item is reasonably constant over time, and the forecast is for 16,500 units per year. When an order is placed for the item, the entire order is immediately delivered to the firm by the supplier. The firm operates 6 days a week plus a few Sundays, or approximately 320 days per year. Determine the following: a. Optimal order quantity per order b. Total annual inventory costs c. Optimal number of orders to place per year d. Number of operating days between orders, based on the optimal ordering.Explanation / Answer
a. Optimal order quantity per order = [(2*annual demand*order cost)/carrying cost]^0.5
annual demand = 16,500 units. order cost = $70. carrying cost = $27.
optimal order quantity = [(2*16,500*70)/27]^0.5 = [2,310,000/27]^0.5
= 85,555.56^0.5 = 292.50 orders or 292 orders rounded off.
b. Total annual inventory costs = holding cost+ordering cost
holding cost = (order quantity/2)*holding cost per unit = 292/2*27 = $3,942
ordering cost = (annual demand/order quantity)*cost per order
=(16500/292)*70 = $3,955.48
Total cost = $3,942+$3,955.48 = $7,897.48
c. optimal number of orders = annual demand/optimal order quantity = 16,500/292 = 56.51 or 57 rounded off
d. number of operating days between orders = number of working days per year/number of orders
= 320 days/57 = 5.61 days or 6 days rounded off
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