Answer:
Safety Stock = 153.94 [tex]\approx[/tex] 154 gallons
Solution:
Average Demand =[tex]D_{avg} = 30 gallons/day[/tex]
Standard deviation of demand = [tex]\sigma_{d} = 3 gallons[/tex]
Average Lead Time = [tex]LT_{avg} = 7 days[/tex]
Standard deviation of Lead Time= [tex]\sigma_{LT} = 4 days[/tex]
Service Level = 90%
For Service Level 90%, Z-Score = 1.28
Z-score is called Service Factor
Calculation of Safety Stock:
Safety Stock = [tex]Z \times \sqrt{[(LT_{avg}\times \sigma_{d}^2)+(\sigma_{LT}\times D_{avg})^2]}[/tex]
Safety Stock =[tex]1.28 \times \sqrt{[(7\times 3^2)+(4\times 30)^2]}[/tex]
Safety Stock = [tex]153.94 \approx 154 gallons[/tex]
