Demand for walnut fudge ice cream at the Sweet Cream Dairy can be approximated b

Question

Demand for walnut fudge ice cream at the Sweet Cream Dairy can be approximated by a normal distribution with a mean of 21 gallons per week and a standard deviation of 3.5 gallons per week. Lead time is two days, and the dairy is open seven days a week.

Now an order is place when there is a supply of 8 gallons on hand. One day after placing an order with the supplier, the manager receives a call from the supplier that the order will be delayed because of problems at the supplier’s plant. The supplier promises to have the order there in two days.

After hanging up, the manager checks the supply of walnut fudge ice cream and finds that 2 gallons have been sold since the order was placed. Assuming the supplier’s promise is valid, what is the probability that the dairy will run out of this flavor before the shipment arrives?

0.1423

0.4168

0.5832

0.8577

0.1423

0.4168

0.5832

0.8577

Explanation / Answer

The new lead time one day after placing the order = 2 days = 2/7 weeks

Average demand during this lead time, m = 21*(2/7) = 6 gallons

Std dev of demand during this lead time, s = 3.5*SQRT(2/7) = 1.871

Stocks on hand = 8-2 = 6 gallons

z = (x-m)/s = (6-6)/1.871 = 0

F(z) = NORMSDIST(0) = 0.5

Therefore, probability that the dairy will run out of this flavor before shipment arrives in 2 days = 1-0.5 = 0.50

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