Craft Shop in Bennington, Vermont, sells a variety of quality handmade items to
ID: 420521 • Letter: C
Question
Craft Shop in Bennington, Vermont, sells a variety of quality handmade items to tourists. B & P sells 500 hand-carved miniature replicas of a Colonial soldier each year, but the demand pattern during the year is uncertain. The replicas sell for $50 each, and B & P uses 3% monthly inventory holding cost rate. Ordering costs are $10 per order, and the demand during the lead-time follows normal distribution with the mean of 20.
What is the recommended order quantity?
If the company desires no more than 5% chance of stock-out, what reorder point would you recommend?
What are the safety stock and annual safety stock costs for this product?
Explanation / Answer
Following data are provided :
Annual demand of replica of colonial soldiers = D = 500
Ordering cost = Co = $10 per order
Annual inventory holding rate = 3% x 12 = 36%
Sale price of replica = $50 / unit
Therefore ,
Annual unit inventory holding cost = Ch = 36% of $50 = $18
Recommended order quantity ( EOQ )
= square root ( 2 x Co x D / Ch )
= square root ( 2 x 10 x 500 / 18 )
= 23.57 ( 24 rounded to nearest whole number )
RECOMMENDED ORDER QUANTITY = 24 REPLICAS
Since maximum stock out is 5%, in stock probability will of 0.95
Corresponding Z value = NORMSINV ( 0.95 ) = 1.6448
Safety stock
= Z value x Standard deviation of demand during lead time
= 1.6448 x Standard deviation of demand during lead time
( Note : Data on standard deviation of demand during lead time has not been provided in the problem )
Annual safety stock cost for the product
= $50 / replica x Safety stock
= $50 x 1.6448 x Standard deviation of demand during lead time
= 82.24 x Standard deviation of demand during lead time
Reorder point
= Average demand during lead time + Safety stock
= 20 + Safety stock
RECOMMENDED ORDER QUANTITY = 24 REPLICAS