An ice-cream parlor sells 9 flavors. By implementing postponement, they keep a g

Question

An ice-cream parlor sells 9 flavors. By implementing postponement, they keep a generic vanilla flavor in stock and then create the 9 flavors on the spot when ordered. Based on the costs of underage and overage, the in-stock probability before postponement is set at 90%, and after postponement is set at 95% so more customers will get served. The standard deviation of each flavor of ice cream is 20 gallons per week, and the lead time is one week as well. Determine the reduction in safety stock that postponement can achieve.

1.   Before postponement: safety stock of each flavor = 17 gallons, so 153 gallons in total. After postponement: 51 gallons of safety stock in total. Thus: a reduction of 102 gallons

2.   Before postponement: safety stock of each flavor = 26 gallons, so 234 gallons in total. After postponement: 99 gallons of safety stock in total. Thus: a reduction of 135 gallons

3.   There would be no reduction: the in-stock probability has increased, so sigma will be greater, so the safety stock will be greater after postponement!

4.   The reduction will be exactly 2/3: we go from 9 flavors to 1 flavor with a standard deviation in demand of the square root of 9, which is 3. So: from 9 different flavors to "3" different flavors is a reduction of 2/3!

Explanation / Answer

1.   Before postponement: z for 90% in-stock prob = NORMSINV(0.90) = 1.28

Safety stock of each flavor = z*std dev = 1.28*20 = 26 for each flavor. Total safety stock for 9 flavors = 26*9 = 234 gallons

After postponement: standard deviation of all the flavors combined = 20*SQRT(9) = 60

z for 95% in-stock prob = NORMSINV(0.95) = 1.645

Safety stock = 1.645*60 = 99 gallons

Reduction in safety stock as a result of postponement = 234-99 = 135 gallons

ANSWER: 2.   Before postponement: safety stock of each flavor = 26 gallons, so 234 gallons in total. After postponement: 99 gallons of safety stock in total. Thus: a reduction of 135 gallons

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