SmartBeans is Canada’s largest online retailer of fair-trade organic coffee, and

Question

SmartBeans is Canada’s largest online retailer of fair-trade organic coffee, and imports coffee beans from several countries. SmartBeans operates 300 days a year and sells an average of 150 pounds of Harar (Ethiopia) Fair Trade Organic beans a day. After ordering, beans are always shipped from Ethiopia within exactly 11 days. Annual holding costs per pound are estimated to be 15% of the per pound cost of beans. The ordering cost is $35 per order. The cost of a pound of green coffee beans is $7.

The demand for the Harar Fair Trade Organic beans is assumed to be normally distributed with a variance of 400 pounds per day, and lead time is assumed to be normally distributed with a variance of 4 days. Assume that management has specified that no more than a 5% risk of a stockout is acceptable. What is the standard deviation of demand during lead time? What is the safety stock needed to attain a 5% risk of stockout during lead time? What is the demand during lead time? What should be the reorder point? What is the annual holding cost of maintaining the level of safety stock needed to support a 5% risk of a stockout?

Explanation / Answer

Service level = 95% ( it is at the 5% stock out risk)

Value of Z at 95% = 1.645

Standard deviation of demand (during lead time ) SDd = Variance^.5 = 400^.5 = 20

Safety stock = Z*(SDd^2 * L + SDl^2 * D^2)^.5

Safety stock = 1.645*(20^2 * 11 + 2^2* 150^2)^.5

Safety stock = 505.42

Demand during lead time = D*L = 150*11 = 1650

Reorder point = Demand during lead time+ safety stock = 1650 + 505.42 = 2155.42

Annual holding cost for the safety stock = 505.42*(15%*7)

Annual holding cost for the safety stock = $530.69

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