A store has collected the following information on one of its products:

Demand = 6,760 units/year
Standard deviation of weekly demand = 18 units
Ordering costs = $40/order
Holding costs = $2/unit/year
Cycle-service level = 90%
Lead-time = 3 weeks
Number of weeks per year = 52 weeks

If the firm uses the continuous review system to control the inventory, what would be its order quantity and reorder point?

Assume that the firm decided to change to the periodic review system to control the item’s inventory. The time between reviews, P, is calculated using the EOQ model. For the most recent review, an inventory clerk checked the inventory of this item and found 500 units. There were no scheduled receipts or backorders at the time. Determine how many units should the firm order.

The firm should order about 420 units.

Explanation:

From the question given, let us recall the following statements

D=  The Demand = 6760 Unit/year,

Co =The ordering cost  = $40 order,

Ch =the holding cost Ch =$2/unit

Then

The EOQ = √ (2*D*Co/Ch)  which is = ( 2*6760*40/2)

= √270400 = 520 units

The number of orders in an years = 6760/520  which is = 13 orders

The Cost of Order = 13*$40= $520

The Cost of Holding = Average stock * Cost of holding = (520/2)*$2 = $520

The Total of   cost of  handling inventory = $520+$520 =$ 1040

Thus,

It is shown that, the lead time is 3 weeks, means once an order has been done, it will get there in 3 weeks, which is an instruction given , when you have a stock for 3 weeks an order should be placed.

The Average stock required for a week = 6760/52 =130 units

The required stocks for 3 weeks = 130*3 = 390  this is known as safety stock

Under 90% cycle time  of reordering = Safety stock + Z*Standard Deviation (Where Z is the standard normal distribution value when probability is 90%,and Z=1.645)

The point of re-ordering  = 390+1.645*18 = 419.61 units = 420 units.

Therefore  the stock that is examined  is 500, when it gets to  420 an order should be doe,