A purchased product, sold in a retail store, has a normally distributed daily demand, with a mean of 8 units/day and a variance of 4 (units)^{2}. Its supply lead time is 6 days and the store is open 365 days a year. Currently, this item's inventory replenishment policy is based on a periodic review system with a review period of 30 days (dictated by the supplier) and an order-up-to level, i.e. maximum inventory position, of 250 units. The purchase cost of this product is $16 per unit, its ordering cost is $50 per order and the store's inventory carrying cost rate is $0.25/$/year. It is also estimated that the cost of not having sufficient stock to satisfy this item's demand routinely off the shelf is $40 per stockout incident.
(a) What is this item's cycle service level under the current ordering policy? Also, compute the average number of days between consecutive stockouts and the annual expected total relevant cost for this product.
(b) Based on a reassessment of current policy, management has specified that it is willing to tolerate an average of no more than one stockout per year for this item. How would you modify the current ordering policy to satisfy this requirement and what would be the resulting annual expected total relevant cost?