An automotive warehouse stocks parts that are sold at nearby dealers. One particular part, a popular brand of oil filter, is purchased by the warehouse for $1.50 each. The fixed setup cost (of order processing and receipt) is $100 per order. The inventory carrying charge is based on a 28% annual interest rate. Assume that if a filter is demanded when the warehouse is out of stock, then the demand is backordered, and the cost assessed for each backordered demand is $1.28.

The monthly demand for the filter follows a normal distribution with mean 280 and standard deviation 77. Order lead time is assumed to be five months.

Note:

Round intermediary results to the second decimal place, while, for the optimal order quantity (i.e., Q) and reorder level (i.e., R), round the results to the closest integers.

When using the L(Z) table, choose the value that is closest to your z-score obtained.

a) Find the mean and standard deviation of the demand during the order lead time

b) Determine the optimal values of the order quantity and the reorder level (note: use EOQ approximation for Q*).

c) Calculate the average annual cost of stockout associated with this item, assuming that the optimal policy (i.e., Q and R) is used.

The manager of the warehouse decides that the estimation of the stockout cost of $1.28 may not be very accurate. The manager wants to set the reorder level so that the probability of no stockout is 90%. d) Determine the reorder level to achieve the 90% probability of no stockout

The probability of no stockout is sometimes referred to as the Type 1 service level. Another commonly used service level, namely, the Type 2 service level or the fill rate, measures the proportion of demands that are met from stock. Specifically, Type 2 service level (fill rate) = 1 Expected number of shortages in a year/The average annual demand

e) Calculate the fill rate as defined above, assuming the reorder level of part d) is used.