Rainbow Colors paint store uses a continuous review to control its stock levels. For a popular eggshell latex paint, historical data show that the distribution of monthly demand is approximately Normal, with a mean of 28 and a standard deviation of 8. The replenishment lead time for this paint is about 14 weeks. Each can of paint costs the store $6. Although excess demands are back ordered, each unit of stockout costs about $10 due to bookkeeping and loss of goodwill. The fixed cost of replenishment is $15 per order and holding costs are based on a 30% annual interest rate (assume simple interest). Rainbow Colors is not sure whether the $10 estimate for the shortage cost is accurate. Hence, they decided to use a service-level approach. [Assume 52 weeks in 1 year, 12 months in a year]

What is the optimal reorder level if they want to achieve no stock-outs in 90% of the order cycles?

What is the expected inventory level just before an order arrives?

What is the optimal order size?