Tim & John Craft shop in Boston, MA sells a variety of quality handmade items to

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

Annual demand, D = 500

Ordering cost, S = $ 10

Holding cost, H = 50*3% = $ 1.5

A) Recommended order quantity, Q = SQRT(2DS/H) = SQRT(2*500*10/1.5) = 82

B) Service level = 1 - stockout chance = 1 - 5% = 95 %

z = NORMSINV(0.95) = 1.645

Reoder point = Lead time demand + z * Std deviation of lead time demand = 20 + 1.645*10 = 36.45 (considering std deviation of lead time demand as 10)

C) Safety stock = z * Std deviation of lead time demand = 1.645*10 = 16.45

Annual safety stock costs for this product = 16.45*50 = $ 822.5

Annual Inventory carrying cost of safety stock = 822.5*3% = $ 24.68

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