Inventory and Annual Holding Cost

Your firm uses a continuous review system and operates 52 weeks per year. One of the SKUs has the following characteristics. Demand (D) = 20,000 units/year
Ordering cost (S) = $40/order

Holding cost (H) = $2/unit/year
Lead time (L) = 2weeks
Cycle-service level = 95%
Demand is normally distributed with a standard deviation of weekly demand of 100 units. The current on-hand inventory is 1.040 units with no scheduled receipts and no backorders. 1. Calculate the item’s EOQ. What is the average time, in weeks between orders? EOQ = (2DS)/H

EOQ = (2*20000*40)/2
EOQ = 800000
EOQ = 894.43894
TBO = (EOQ/D)*52weeks
TBO = (894/20000)*52weeks
TBO = (0.0447)*52weeks
TBO = 2.32442.32weeks

2. Find the safety stock and reorder point that provides a 95% cycle-service level. Safety stock = Z*(standard deviation of demand during the lead time) Z for 95% service level is 1.64

Safety stock = 1.64*(2*100)
Safety stock = 328 units

Reorder point = (Average demand during lead time) + (Safety Stock) Reorder point = ((20000/52weeks)*2) + 328 = 1097.23 1097
3. For these policies, what are the annual costs of holding the cycle inventory and placing orders?
Annual holding cost = (Average cycle inventory)*(Unit holding cost)
Annual holding cost = (Average Lot size/2)*(Unit holding cost)

Annual holding cost = ((20000/52weeks)*2.32weeks)/2 * 2
Annual holding cost = (892.30 892/2)*2
Annual holding cost = 446*2 = $892
Annual ordering cost = (Number of orders/year)*(Ordering cost)
Annual
ordering cost = (Demand/Average lot size)*(Ordering cost)
Annual ordering costs = (20000/892)*(40)
Annual ordering costs = 22.42*40 = $896.8

4. Withdrawal of 15 units just occurred. Is it time to reorder? If so, how much should be ordered?
Inventory position = on hand inventory + schedule receipts – backorders Inventory position = 1040+15+0=1055
IP (1055) < R (1097) so new order must be placed
Order quantity: Target inventory level – Inventory position
Target inventory level = Average demand during the protection interval + Safety stock Target inventory level = (Demand/52weeks)*((EOQ/Demand)*52weeks)*(Lead time) + Safety Stock Target inventory