Weekly demand per store for a particular item at The Gap is normally distributed with mean 8 and standard deviation 2. The delivery lead time to each store is 3 weeks. The items cost $27 each and sell for $42. The shipping and administrative costs are $20 per store order. There are 2000 stores across the nation. Assume a 35% annual inventory carrying charge. a) If they choose to stock the item with a 95% service level in every store, how much safety stock must they keep for the item, summed over all the stores? b) Suppose they choose to stock the item in a central location (and pay for overnight shipping to the customers). Assume that demand at the central location will be the sum of demands from all the individual stores. i.How much average safety stock must they hold for that item if they want to provide a 95% service level? ii. Shipping and administrative costs are $100 per order to the central location. What is the percentage savings in average cycle stock for the centralized system relative to the decentralized system?
Weekly demand per store for a particular item at The Gap is
a) If they choose to stock the item with a 95% service level in every store, how much safety stock must they keep for the item, summed over all the stores?
b) Suppose they choose to stock the item in a central location (and pay for overnight shipping to the customers). Assume that demand at the central location will be the sum of demands from all the individual stores.
i.How much average safety stock must they hold for that item if they want to provide a 95% service level?
ii. Shipping and administrative costs are $100 per order to the central location. What is the percentage savings in average cycle stock for the centralized system relative to the decentralized system?
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