Question: The Gap has started selling through its online channel along with its retail stores. Management has to decide which products to carry at the retail stores and which products to carry at a central warehouse to be sold only via the online channel. The Gap currently has 1000 retail stores in the United States. Weekly demand for large Khaki pants at each store is normally distributed with a mean of 900 and a standard deviation of 100. Each pant costs $30. Weekly demand for purple Cashmere sweaters at each store is normally distributed with a mean of 60 and a standard deviation of 60. Each sweater costs $100. The Gap has a holding cost of 25 percent. The Gap manages all inventories using a continuous review policy and the supply lead-time for both products is 3 weeks. The targeted cycle service level is 98 percent. Assume demand from one week to the next to be independent and demand at one store is independent of the demand at other stores.

First complete the Excel spreadsheet below and then answer the following questions:

a) How much reduction in holding cost per unit sold can The Gap expect on moving each of the two products from the stores to the online channel? Which of the two products should The Gap carry at the stores and which at the central warehouse for the online channel? Why?

b) Now assume a correlation of 0.4 between the demands of all stores. Repeat (a) for this correlation.

c) Now assume a correlation of 0.8 between the demands of all stores. Repeat (a) for this correlation.

d) Plot correlation versus difference in percentage of product costs from moving to the online channel (with correlation on the x-axis.). What conclusion can you draw from this plot? Is this conclusion consistent with the lessons learned from the diversification of stocks? Explain. (I recommend varying correlation from 0.1 to 1.00 with an increment of \[0.\text{2}\] )