Weekly demand of packs of AAA batteries in BVE store is normally distributed with a mean of 1,000 and standard deviation of 50. The fixed ordering cost is $130 per order. The inventory holding cost is $1.5 per pack of batteries per year. The replenishment lead time is 2 weeks. The company uses a continuous review policy with order size of 3,000. BVE makes a profit of $1.7 per pack of batteries. Currently, demand during stockout is lost.
(a) What is the optimal CSL?
(b) BVE is considering a plan to backlog customer demand and mail the batteries to customers when the inventory is replenished. It does not offer any discount but the mailing cost is estimated to be $1 per pack of batteries. What is the optimal CSL under this plan?