A paint store in Rolla sells a specific paint. The monthly demand of this paint follows a normal distribution with mean of 100 and variance of 144. The excess demand can be backordered. It takes the paint store one month to receive the order it placed to the manufacturer. The unit purchase price the paint store will pay is $16. The holding cost is estimated based on the annual rate of 8%. The fixed cost per ordering is $20. The store reviews it inventory continuously and will place order with size Q when the inventory level hits R. The owner of this paintstore decides to use a service level model to determine its inventory strategy. The target service level is that there is no stock-out in 90% of the cycles.
1) Find the resulting order size (Q) and reorder point (R).
2) If the owner of the store wants to satisfy 90% of the demand from the stock (achieve a 90% fill rate), what is reorder point R?
3) If the lead time is two months, what will be the Q and R if the store still hopes to achieve the target of service level that 90% of the cycles should not have any stock-outs?