You are the manager of Splash Painting, a paint store which uses a continuous review inventory system to control its stock. For a popular eggshell latex paint, historical data show that the distribution of monthly demand is approximately Normal, with mean 28 and standard deviation 8. Lead time for this paint is about 14 weeks. Fixed cost of replenishment is $15 per order. It takes $6 per unit for Splash Painting to purchase it, and holding cost is estimated to be 30% of purchase cost. Assume 1 year is 50 weeks and 1 month is 4 weeks.
a. What is the optimal lot size (order quantity) and reorder point if Splash Painting wants to achieve no stock-outs in 90% of the order cycles (i.e, service level)?
b. What is the expected number of orderings per year?
c. What is the total expected cost of ordering per year?