UVac Industries makes a robotic vacuum cleaner for home use. The vacuum cleaners remain docked near a wall plug until put into use, so the robotic vacuums are designed in several different colors to coordinate with home décor. Until recently, UVac made its vacuums in numerous colors in a US factory for its European market. This resulted in a large number of stock-keeping units (SKUs) with uncertain demand.

Recently, UVac modified its product design and production process so that the outer shell of the vacuum can be made separately and shipped to Europe, and the final product can thus be assembled in the European warehouse for each local market.

a. Under the old production process, UVac produced robotic vacuums in 10 different colors. Weekly demand for each color in the European market is normally distributed independently, with a mean of 6,000 and a standard deviation of 300 units. The production plus shipment lead time from the US factory to the European warehouse is five weeks, and shipments are sent once every week. UVac maintains a target in-stock rate of 98% (assume a z value of 2.05) with sufficient safety stock so that the chance of a stock-out is only 2% on average. What is the total finished goods inventory required by UVac in this supply chain to achieve a 98% in-stock rate? Keep in mind that total inventory includes inventory in transit as well as inventory at the European warehouse.

b. With the new design and production process, UVac makes plain robotic vacuums and ships them to Europe. Workers at the European warehouse assemble vacuum cleaners as needed from the plain SKUs and colored shells. The lead time is five weeks, the length of the review cycle is one week, and the target in-stock rate is 98%, as before. How much reduction in total finished goods inventory is achieved at UVac by implementing this new process?