Question

Summer Manufacturing Company uses an average of 30 gallons of cleaning fluid a day. Usage tends to be normally distributed with a standard deviation of 3 gallons per day. Lead time is normally distributed averaging 7 days with a standard deviation of 4 days. The company hopes to keep the desired service level is 90 percent. What amount of safety stock is appropriate if a fixed order size of 600 gallons is used?

Answer 1

Safety Stock = 153.94
`\approx` 154 gallons

Solution:

Average Demand =
`D_(avg) = 30 gallons/day`

Standard deviation of demand =
`\sigma_(d) = 3 gallons`

Average Lead Time =
`LT_(avg) = 7 days`

Standard deviation of Lead Time=
`\sigma_(LT) = 4 days`

Service Level = 90%

For Service Level 90%, Z-Score = 1.28

Z-score is called Service Factor

Calculation of Safety Stock:

Safety Stock =
`Z * \sqrt{[(LT_(avg)* \sigma_(d)^2)+(\sigma_(LT)* D_(avg))^2]}`

Safety Stock =
`1.28 * √([(7* 3^2)+(4* 30)^2])`

Safety Stock =
`153.94 \approx 154 gallons`