Demand for the vanilla ice cream at an ice cream store can be approximated by a Normal distribution with a mean of 21 litres per week and a standard deviation of 3.5 litres per week. The ice cream is purchased from an ice cream producer. The store manager desires a lead time service level of 90 percent. Lead time from the producer is two days. The store is open seven days a week.
a. [f the EOQ/ROP model is used for ordering the ice cream from tire producer, what ROP would be consistent with the desired lead time service level?
b. If a fixed order interval model is used instead, what order quantity' should be used if the order interval is 7 days and 8 litres are on hand in inventory at the time of order?
c. Suppose that the manager is using the EOQ/ROP model described in part a. One day after placing an order with the producer, the manager receives a call from the producer that the order will be delayed because of problems at the producer’s plant. The producer promises to have the order there in two days. After hanging up, the manager checks the inventory of vanilla ice cream and finds that 2 litres have been sold since the order was placed. Assuming that the producer’s promise is valid, what is tire probability that the store will run out of vanilla ice cream before the shipment arrives?