Don Washing is trying to determine how many gallons of lemonade to make each day
ID: 371663 • Letter: D
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, m = 422 s = 67; Saturday, m = 719 s = 113; and Sunday, m = 528 s = 85).
What is the service level and target stocking level for Monday-Friday?
What is the service level and target stocking level for Saturday?
What is the service level and target stocking level for Sunday?
Explanation / Answer
Following are the given data :
Cost of lemonade per Gallon = C = $2.5 / Gallon
Price of Lemonade per Gallon = P= $10 / Gallon
Salvage value per Gallon = S = 0
Therefore,
Cost of underage = Cu = P – C = 10 – 2.5 = 7.5
Cost of overage = Co = C – S = 2.5
Therefore , Critical Ratio = Cu/ ( Cu + Co) = 7.5 / ( 7.5 + 2.5) = 7.5/10 = 0.75
Critical Ratio is the value of in-stock probability i.e. service level.
Since the values of Cu and Co do not change from day to day, critical ratio and hence in stock probability( and corresponding Z value ) will not change from day to day. Therefore constant service level will be = 0.75 x 100 = 75%
Z value corresponding to probability of 0.75 as derived from standard normal distribution table = 0.6745
SERVICE LEVEL ON ALL DAYS = 75%
Stocking level for any day = Zvalue x Standard deviation of demand during that day
Therefore,
Stocking level for Monday – Friday = Zvalue x Standard deviation of demand = 0.6745 x 67 = 45.19 Gallons
Stocking level for Saturday = Zvalue x Standard deviation of demand = 0.6745 x113 = 76.22 Gallons
Stocking level for Sunday = Zvalue x Standard deviation of demand = 0.6745 x 85 =57.33 Gallons
SERVICE LEVEL ON ALL DAYS = 75%
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