The Norwitch Company uses a continuous review (s, Q) system for inventory control.  Weekly demand for an item, Pressure Valve #5 (PV5), is distributed Normally with a mean and standard deviation of 20 and 10 respectively.  Norwitch uses an order quantity of 200 units for PV5 and its supplier takes 5 weeks to fill an order.  Each unit of PV5 costs $50 and carrying charges are $0.20/$/yr.  Norwitch uses a 99% fill rate as a target service measure.

(a) Compute the reorder point, s, that will satisfy Norwitch's target fill rate.  What is the likelihood that Norwitch has stocked out of PV5 when a new shipment arrives from its supplier?
 
 (b) Suppose Norwitch has worked out a new contract, accepted by all its customers, of being allowed up to one week to satisfy each demand.  Norwitch still uses a 99% "fill rate" as a target service measure.  However, stockouts satisfied within a week is considered as good as demand satisfied from the on-hand inventory.  
 
How would you modify the logic of computing the re-order point, s, to take account of the one-week grace period?  Sketch the average behavior of the (s,Q) system to illustrate your reasoning.
 
(c) Compute the reorder point for the new contract.  What is the safety stock?  On an average, how much inventory Norwitch has on hand when a new shipment of PV5 arrives?  
 
(d) Estimate the annual cost savings due to the one-week grace period.

(e) What will be the impact of one-week grace period on Norwitch's customers? Should Norwitch and its customers make the inventory status of PV5 known to each other?   What good will that do?