It is your responsibility, as the new head of the automotive section of Nichols
ID: 354468 • Letter: I
Question
It is your responsibility, as the new head of the automotive section of Nichols Department Store, to ensure that reorder quantities for the various items have been correctly established. You decide to test one item and choose Michelin tires, XW size 185 × 14 BSW. A perpetual inventory system has been used, so you examine this as well as other records and come up with the following data:
Because customers generally do not wait for tires but go elsewhere, you decide on a service probability of 99 percent. Assume the demand occurs 365 days per year.
Cost per tire $ 45 each Holding cost 35 percent of tire cost per year Demand 1,240 per year Ordering cost $ 20 per order Standard deviation of daily demand 7 tires Delivery lead time 8 daysExplanation / Answer
From the given statement, we understand that we have to determine the Reorder quantity since it is mentioned that “….to ensure that reorder quantities of various items have been correctly established”
Given are the following data :
Standard deviation of daily demand = Sd = 7 tires
Delivery lead time = L = 8 days
Therefore , Standard deviation of demand during lead time = Sd x Square rot ( L ) = 7 x Square root ( 8 ) = 7 x 2.828 = 19.796
Z value corresponding to service probability of 99 percent = NORMSINV ( 0.99) = 2.326
Therefore , Safety stock
= Z value x Standard deviation of demand during lead time
= 2.326 x 19.796
= 46.04
Therefore ,
Reorder Quantity
= Average daily demand x Lead time + Safety stock
= Annual demand/ 365 days x Lead time ( days ) + Safety stock
= ( 1240/365) x 8 + 46.04
= 27.18 + 46.04
= 73.22 ( 73 rounded to nearest whole number )
REORDER QUANTITY = 73 TIRES
REORDER QUANTITY = 73 TIRES
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