Question 12.8: Computing the ROP and Safety Stock When the Mean and Standar...
Computing the ROP and Safety Stock When the Mean and Standard Deviation of Lead Time Demand Are Given
Suppose that the manager of a construction supply house determined from historical records that demand for sand during lead time averages 50 tons. In addition, suppose the manager determined that demand during lead time could be described by a normal distribution that has a mean of 50 tons and a standard deviation of 5 tons. Answer the following questions, assuming that the manager is willing to accept a stockout risk of no more than 3 percent.
a. What value of z is appropriate?
b. How much safety stock should be held?
c. What reorder point should be used?
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Expected lead time demand = 50 tons
σ_{dLT} = 5 tons Risk = 3 percent
a. From Appendix B, Table B, using a service level of 1 − .03 = .9700, you obtain a value of z = +1.88.
b. Safety stock = zσ_{dLT} = 1.88(5) = 9.40 tons
c. ROP = Expected lead time demand + Safety stock = 50 + 9.40 = 59.40 tons