ABC Tools is a manufacturer of battery-operated, hand-held power tools for consumer market. Its two biggest customers are "big box" discounters. Because these customers are fiercely price competitive, each wants exclusive products, thereby preventing consumers from making price comparisons. For example, ABC will sell exact same power screwdriver to each retailer, but ABC will use packing customized to each retailer (including two different product identification numbers). Suppose weekly demand of each product to each retailer is normally distributed with mean 5,200 and standard deviation 3,800. ABC makes production decisions on a weekly basis and has a three-week replenishment lead time. Because these two retailers are quite important to ABC, ABC sets a target fill rate of 99.9%.

 

a)   Based on the order-up-to model, what is ABC's average inventory of each of the versions of this power screwdriver?

 

b)   Someone at ABC suggests that ABC stock power screwdrivers without putting them into their specialized packaging. As orders are received from the two retailers, ABC would fulfill those orders from the same stockpile of inventory, since it doesn't take much time to actually package each tool. Interestingly, demands at the two retailers have a slight negative correlation, -0.20. By approximately how much would this new system reduce ABC's inventory investment?