Weekly demand for Vespa at a retail store is normally distributed, with a mean of 12 and a standard deviation of 5. As this is the only Vespa retailer , any unmet demand is backordered. The store manager follows a periodic review policy with an inventory review period of one week and targets for a customer service level (CSL or instock probability) of 95%. The manufacturer of Vespa currently takes three weeks to fill an order. The store operates 52 weeks per year.

(a) What should the store's order-up-to (OUT) level be?

(b) What is the expected backorder?

(c) What is the expected on-order inventory? (Recall, your on-order inventory is also called pipeline inventory). (5 points)

(d) What is the expected on-hand inventory?

(e) What fill rate (FR) does the store achieve?

(f~g) The purchasing cost is 1,500 per vehicle, while the store manager has estimated that the penalty per unit backordered is 100 and the annual inventory carrying cost is around 25%.

(f) If the manager wishes to minimize holding and backorder penalty costs, what should be her target in-stock probability (CSL)?

(g) What should its OUT level be in this case?