Supreme Cola is a supplier of fountain equipment to restaurants, bars and cafeterias.
The fountain equipment is manufactured at their York PA plant site. A national distribution center (DC) for the fountain equipment is also maintained adjacent to the plant. Supreme has one common platform design to which they add various features and accessories to create 10 different product options. The lead time for manufacturing and delivering a batch of products to the distribution center is 2 weeks. They review inventory and order weekly. For product ACola, Supreme uses a Normal distribution with mean 25 and standard deviation 20 to model weekly demand. Demands across weeks are independent. ACola sells for $15,000 and they enjoy a 50% gross margin. The annual holding cost for inventory in the DC is 25% of the product's cost. In the event that a customer order cannot be filled from the warehouse due to an out-of-stock situation, Supreme expedites the manufacture and delivery of the item. It estimates that such expediting increases their cost by $770 per unit.
a. What order upto level should Supreme choose to minimize their inventory for ACola while achieving at least a 99.25% in-stock probability?
b. Supreme uses an order up-to policy with a base stock level equal to 250 for ACola. What is the probability that Supreme will have more than 40 units on order of that product at the start of any given week?