Tim & John Craft shop in Boston, MA sells a variety of quality handmade items to
ID: 420847 • Letter: T
Question
Tim & John Craft shop in Boston, MA sells a variety of quality handmade items to local tourist. T & J sells 500 hand-carved miniature replicas of a colonial soldier each year, the demand pattern during the year is uncertain. The replicas sell for $50 each, and T & J 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.
A. What is the recommended order quantity?
B. If the company desires no more than 5% chance to stock-out, what reorder point would you recommend?
C. What are the safety sotck and annual safety stock costs for this products?
Explanation / Answer
Average lead-time demand, d = 20
Standard deviation of lead time demand = 10 (it is not given in the question, so considered as 10 for sake of demonstrating the calculation)
Annual demand, D = 500
Unit cost, C = $ 50
Inventory holding cost, H = 50*3%*12 = $ 18 per unit per year
Ordering cost, S = $ 10
A) Recommended order quantity, Q = SQRT(2DS/H) = SQRT(2*500*10/18) = 23.6 ~ 24
B) Service level = 1 - chance of stockout = 1 - 5% = 0.95
z = NORMSINV(0.95) = 1.645
Safety stock = z * s = 1.645*10 = 16.45
Reorder point = Mean lead time demand + Safety stock = 20 + 16.45 = 36.45
C) Safety stock = 16.45 (as calculated in part B)
Annual safety stock cost = 16.45*18 = $ 296