Weekly Demand d = 31 gallon
SD pf Weekly Demand = 4
Service Level = 90%
Z = 1.28
Lead Time LT = 3 days = 3/7 week
a.
ROP = d*LT + Z*Sd of Demand*(LT)^(1/2)
ROP = 31*(3/7) + 1.28*4*(3/7)^(1/2)
ROP = 16.64 gallons
ROP = 17 gallons
b.
Order Interval P = 7 days = 1 week
On Hand Inventory I = 10
Order Quantity Q = d*(LT+P) + Z*Sd of Demand*(LT+P)^(1/2) - I
LT +P = 3/7 + 1 = 10/7 weeks
Q = 31*(10/7) + 1.28*4*(10/7)^(1/2) - 10
Q = 50.41 - 10
Q = 40.41
Q = 40 gallons
c.
Stock on Hand = ROP - Used Stock = 17 - 7 = 10 galoon
Expected Receiving day = 2 days = 2/7 weeks
Now, we will treat 10 gallon as ROP with 2 days lead time and we will find the value of Z. After that we will find the service level basiz Z value and after that wwe will find the stock out probabiity bu subtractting service level from 1.
10 = 31*(2/7) + Z*4*(2/7)^(1/2)
10 = 8.8571 + Z*2.1381
Z = (10-8.8571)/2.1381
Z = 0.5345
Service Level = 0.7035
Stock out Probability = 1 - Service Level
Stock out Probabiity = 1 - 0.7035
Stock out Probability = 0.2965
Stock out Probability = 0.30
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