Question

Demand for walnut fudge ice cream at the Sweet Cream Dairy can be approximated by a normal distribution with a mean of 23 gallons per week and a standard deviation of 4.0 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 9 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

Z value for desired service level of 90 percent = NORMSINV ( 0.90 ) = 1.281

Lead time = 3 days = 3/7 week = 0.428 week

Average demand during a week = 23 Gallons

Standard deviation of demand during a week = 4 Gallons

Standard deviation of demand during lead time of 3 days

= standard deviation of weekly demand x Square root ( 3/7)

= 4 x Square root ( 3/ 7 )

= 4 x 0.654

= 2.616 days

Safety stock under continuous review system

= Zvalue x Standard deviation of demand during lead time

= 1.281 x 2.616

= 3.351 Gallons

ROP under continuous review system

= Average daily demand x Lead time ( days ) + safety stock

= 23/7 x 3 + 3.351

= 9.857 + 3.351

= 13.208 Gallons

Under periodic review system, The protection period = Review period + Lead time = 9 + 3 = 12 days

Standard deviation of demand during protection period

= Standard deviation of weekly demand x Square root ( 10/7)

= 4 x Square root ( 10/7)

= 4 x 1.195

= 4.78

Therefore , Safety stock

= Z value for 90 % service level x Standard deviation of demand during protection period

= 1.281 x 4.78

= 6.123 Gallons

Theoretical ROP under periodic review system

= Daily demand x Protection period ( days ) + safety stock

= 23/7 x 12 + 6.123

= 39.428 + 6.123

= 45.551

Quantity to order when supply at hand is 8 Gallons = 45.551 – 8 = 37.551 Gallons