In 1997 Egghead Computers ran a chain of 50 retail stores all over the United States. Consider one type of computer sold by Egghead. Demand for this computer at each store on any given week was independently and normally distributed with a mean demand of 200 units and a standard deviation of 30 units. Inventory at each store is replenished directly from a vendor with a 10-week lead time. At the end of 1997, Egghead decided it was time to close their retail stores, put up an Internet site, and begin filling customer orders from a single warehouse.
a. By consolidating the demand into a single warehouse, what will be the resulting standard deviation of weekly demand for this computer faced by Egghead? Assume Egghead’s demand characteristics before and after the consolidation are identical.
b. Egghead takes physical possession of inventory when it leaves the supplier and grants possession of inventory to customers when it leaves Egghead’s shipping dock. In the consolidated-distribution scenario, what is the pipeline inventory?