Demand for walnut fudge ice cream at a grocery store can be approximated by a normal distribution with a mean of 35 kg per week and a standard deviation of 4 kg per week. The new department manager desires a service level policy that has a 98% probability of not stocking out. Lead time from the producer is two days. The store is open seven days a week.
a) If a fixed quantity model is used, what ROP would be consistent with the desired service level?
b) If a fixed-period model is used instead of a fixed quantity model, what order size would be needed for the 98% service level with an order interval of 5 days and a supply of 14 kg on hand at the order time?
c) Suppose that the department manager is using the fixed quantity model described in part a. One day after placing an order with the supplier, the manager receives a call from the supplier that the order will be delayed because of problems with the supplier's plant. The supplier promises to have the order in there in TREE days. After hanging up, the manager checks the supply of the walnut fudge ice cream and finds that 3 kg have been sold since the order was placed. Assuming the supplier's promise is valid, what is the probability that the store will run out of this flavour before the shipments arrives?