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. The new manager desires a service level of 90 percent. Lead time is 3 days, and the dairy is open seven days a week. (Hint: Work in terms of weeks.)

If we use periodic inventory system, the time from delivery of an order until next review is 11 days (note: this is reported in days).

- What is the corresponding z-value for the desired service level? (keep three decimal places)

- How long is the lead time (in fractions of a week)?

- How much is the average demand during a week?

- How much is the standard deviation of the demand during the week?

- If we use continuous inventory system, what safety stock is consistent with the desired service level?

- If we use continuous inventory system, what ROP is consistent with the desired service level?

- If we use periodic inventory system, what safety stock is consistent with the desired service level?

- If we use periodic inventory system, what is the quantity to order when the supply at hand is 8 gallons?

Answer 1

a) Service level is 90%

z value for 90% service level using NORMSINV function is 1.282

b) Lead time in weeks (LT) = 3/7 = 0.429

c) Average demand during a week (D) = 21

d) standard deviation (s) = 3.5

e) Safety stock = z*s*sqrt(LT) = 1.282*3.5*sqrt(0.429) = 2.939

f) ROP = D*LT + Safety stock = 21*0.429 + 2.939 = 11.948