Consider the following excerpts from a New York Times article (Kaufman, 2000): Despite its early promise . . . Restoration has had trouble becoming a mass-market player. . . . What went wrong? High on its own buzz, the company expanded at breakneck speed, more than doubling the number of stores, to 94, in the year and a half after the stock offering . . . Company managers agree, for example, that Restoration's original inventory system, which called for all furniture to be kept at stores instead of at a central warehouse, was a disaster. Let's look at one Restoration Hardware product, a leather chair. Average weekly sales of this chair in each store is Poisson with mean 1.25 units. The replenishment lead time is 12 weeks. (This question requires using Excel to create Poisson distribution and loss function tables that are not included in the appendix. See Appendix C for the procedure to evaluate a loss function table.)
a. If each store holds its own inventory, then what is the company's annual inventory turns if the company policy is to target a 99.25 percent in-stock probability?
b. Suppose Restoration Hardware builds a central warehouse to serve the 94 stores. The lead time from the supplier to the central warehouse is 12 weeks. The lead time from the central warehouse to each store is one week. Suppose the warehouse operates with a 99 percent in-stock probability, but the stores maintain a 99.25 percent in-stock probability. If only inventory at the retail stores is considered, what are Restoration's annual inventory turns?