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Question 12.p.6: ROP for variable demand rate and variable lead time. The mot...

ROP for variable demand rate and variable lead time. The motel replaces broken glasses at a rate of 25 per day. In the past, this quantity has tended to vary normally and have a standard deviation of three glasses per day. Glasses are ordered from a Cleveland supplier. Lead time is normally distributed with an average of 10 days and a standard deviation of 2 days. What ROP should be used to achieve a service level of 95 percent?

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\overline{d} = 25 glasses per day            \overline{LT}= 10 days

σ_d = 3 glasses per day            σ_{LT}= 2 days

SL = 95 percent, so z = +1.65 (Appendix B, Table B2)

ROP = \overline{d}\overline{LT}+z \sqrt{\overline{LT}σ²_d +\overline{d²}σ²_{LT}}

= 25(10) + 1.65 \sqrt{10(3)^2 + (25)^2(2)^2} = 334  glasses

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