IBM introduced the Winchester drive in 1973the precursor of todays terabyte drives. It remained the standard until 2011. Disk Drives Limited (DDL) produced a line of in-ternal Winchester disks for microcomputers. The drives used a 3.5-inch platter that DDL purchased from an outside supplier. Demand data and sales forecasts indicated that the weekly demand for the platters closely approximated a normal distribution with mean 38 and variance 130. The platters required a three-week lead time for receipt. DDL had been using a 40 percent annual interest charge to compute holding costs. The platters cost $18.80 each, order cost was $75.00 per order, and the company used a stock-out cost of $400.00 per platter. (Because the industry was so competitive, stock-outs were very costly.)

a. Because of a prior contractual agreement with the supplier, DDL purchased the platters in lots of 500. What would have been the reorder point?

b. If DDL renegotiated its contract with the supplier, what lot size should it have written into the agreement?

c. How much of a penalty in terms of setup, holding, and stock-out cost was DDL paying for contracting to buy too large a lot?

d. DDLs president was uncomfortable with the $400 stock-out cost and decided to substitute a 99 percent fill rate criterion. If DDL used a lot size equal to the EOQ, what would its reorder point have been? Also, find the imputed cost of shortage.