Don Washing is trying to determine how many gallons of lemonade to make each day

Question

Don Washing is trying to determine how many gallons of lemonade to make each day. Don needs to consider a single-period system because whatever lemonade is left over at the end of the day must be thrown out due to health concerns. Every gallon he mixes costs him $2.50 but will generate $10 in revenue if sold. Don knows from past experience that daily demand follows a normal distribution. To further complicate things, Don also knows that the mean and standard deviation for demand differ by day of the week (Monday-Friday, = 422 = 67; Saturday, = 719 = 113; and Sunday, = 528 = 85). a. What is the service level and target stocking level for Monday-Friday? b. What is the service level and target stocking level for Saturday? c. What is the service level and target stocking level for Sunday?

Explanation / Answer

Underage cost, Cu = 10-2.5 = $ 7.5

Overage cost, Co = $ 2.5

Critical value (target service level) = Cu/(Cu+Co) = 7.5/(7.5+2.5) = 0.75

a) Service level for Monday-Friday = 0.75 (as calculated above)

z value = NORMSINV(0.75) = 0.6745

Target stocking level = 422 + 0.645*67 = 467

b) Service level for Saturday = 0.75   (same as calculated in the beginning)

Target stocking level = 719 + 0.6745*113 = 795

c) Service level for Sunday = 0.75   (same as calculated in the beginning)

Target stocking level = 528 + 0.6745*85 = 585

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