Suppose that you work in the inventory planning department of a large electronics store, and a (Q, R) inventory system is used to control the replenishment of a popular LCD computer monitor. The store pays $85 for each monitor when it purchases the monitors from its supplier in Asia; in addition, a fixed setup fee of $275 is charged for each order. Assume the annual holding rate is 15%. The penalty cost per shortage is $8. Monthly demand is normally distributed with mean 400 and standard deviation 35, and the order lead time is 1.5 months.
a. Calculate the order quantity (using EOQ approximation) and the optimal re-order point.
b. Calculate the service level, the safety stock level, and the expected number of shortages per cycle.
c. Calculate the expected annual setup cost, inventory holding cost, and shortage cost.
d. If the store wants to maintain a fixed service level of 97%, calculate the re-order point.
e. Compare your answer of part d) with your answers for part (a) and (b), which service level is higher and which re-order point is larger?