The Norwich Company has a policy, accepted by all its customers, of being allowed up to 1 week to satisfy each demand. Norwich wishes to use a P2 service measure with a specified P2 value. Consider an item controlled by an (s, Q) system with Q prespecified. Suppose that the lead time L was equal to the grace period.

a. Under these circumstances, what s value is needed to give P2 = 1.00?

b. More generally, consider an item with a desired P2 = 0.99 and a Q value of 500 units.

Other (possibly) relevant characteristics of the item are D = 1,000 units/year (the average is relatively level throughout the year)

v = $5/unit r = 0.20 $/$/year L = 5 weeks

σ1 = 10 units (for a 1-week period); σt = σ1t 1/2 How would you modify the logic for computing the s value to take into account of the 1-week “grace” period? Illustrate with this item.

c. For the item of part (b), how would you estimate the annual cost savings of having the grace period?