Livingston Tools, a manufacturer of battery-operated, hand-held power tools for consumer markets, has a problem. Its two biggest customers are “big box” discounters. Because the customers are fiercely price competitive, each wants exclusive products, thereby preventing consumers from making price comparisons. For example, Livingston will sell the exact same power drill to each retailer, but Livingston will use packing customized to each retailer (including two different product identification numbers). Suppose weekly demand for each product to each retailer is normally distributed with mean 5200 and standard deviation 3800. Livingston makes stocking decisions on a weekly basis and has a replenishment lead-time of three weeks. Because these two retailers are quite important to Livingston, it has set a target fill rate of 99.9 percent.

a. Based on the order up-to model, what is Livingston’s on-hand inventory of each of the two versions of the power drill?

b. A supply chain analyst at Livingston suggests that it stock drills without putting them into their specialized packing. As the orders are received from the two retailers, Livingston will fulfill those orders from the same stockpile of inventory, since it doesn’t take much time to actually package the tools. For simplicity, assume that the two demands are independent. By how much would this new system reduce inventory? Would you expect a higher or a lower savings if the two demands are negatively correlated?