Monthly demand for an inventory item is a normally distributed random variable with a mean of 20 units and a variance of 4. Demand follows this distribution every month, 12 months a year. When inventory reaches a predetermined level, an order for replenishment is placed. The fixed ordering cost is $60 per order. The items cost $4 per unit, and the annual inventory holding cost is 25 percent of the average value of the inventory. The replenishment lead time is exactly 4 months.
a. Determine the EOQ.
b. Assume that a 10 percent "all units" discount will be given if the order quantity is greater than or equal to 100 units. What order quantity would you recommend with this offer?
c. Determine the necessary reorder point and safety stock to achieve a 90 percent service level.