Question 12.p.5: ROP for constant demand and variable lead time. The motel in...

ROP for constant demand and variable lead time. The motel in the preceding example uses approximately 600 bottles of water each day, and this tends to be fairly constant. Lead time for water delivery is normally distributed with a mean of six days and a standard deviation of two days. A service level of 90 percent is desired.
a. Find the ROP.
b. How many days of supply are on hand at the ROP?

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d = 600 bottles per day
SL = 90 percent, so z = +1.28 ( from Appendix B, Table B2 )
\overline{LT} = 6 days
σ_{LT} = 2 days
a. ROP = d \overline{LT}   + z ( σ_{LT} ) d = 600 ( 6 )  + 1.28 ( 2 ) ( 600 )
= 5,136 bottles of water

b. \frac{ROP}{d}=\frac{5,136}{600}=8.56  days

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