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A clothing franchise currently has 25 retail stores in Istanbul. Weekly demand for bootcut jeans at each store is normally distributed with a mean of 100 and a standard deviation of 8. Weekly demand for wool coats at each store is normally distributed with a mean of 15 and a standard deviation of 10. Each pair of jeans costs the company $20 and each wool coat costs $100. The holding cost rate for jeans is 25%, whereas that for the wool coats is 40%. The management is considering starting to sell some of the merchandise through the online channel; they have to decide which products to carry at the retail stores and which products to carry at the central warehouse to be sold only via the online channel. For both products: the average supply lead-time is 5 weeks, with a standard deviation of 1 week, normally distributed; the targeted cycle service level is 97.5% (z=1.96); and the fixed cost of orders from the supplier is $150 per order. While the company manages all store inventories using a continuous review policy, the central warehouse uses a periodic review policy with T = 6 weeks. Furthermore, in case of online sales, it costs the company $1/item on average to ship from the central warehouse to the customers.

a) Answer for each product (jeans and coats) if the company sells them in retail stores.

i) What is the optimal order quantity to replenish inventory at each retail store?

ii) What is the safety stock used at each retail store?

iii) What is the total annual inventory holding and ordering costs? ,

b) Answer for each product (jeans and coats) if the company moves them to the central warehouse for online channel.

i) What is the optimal order up-to level at the central warehouse?

ii) What is the safety stock used at the central warehouse?

iii) What is the total annual inventory holding and ordering costs?

iv) Considering the additional transportation cost to deliver the items to the customers from the central warehouse, comment whether it makes sense to move the product to central warehouse for online channel.

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