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Suppose you serve demand in a set of six cities with a single product, where each city has weekly demand for the product that
Suppose you serve demand in a set of six cities with a single product, where each city has weekly demand for the product that is normally distributed with mean 250 units and standard deviation 85. Assume that city demands are pairwise independent. You replenish stock weekly with negligible lead time and use an order up to policy with an order up to level that meets a Type I service level of 0.94. You are considering two options: (a) each city's stock is held in a separate warehouse; (b) the stock for all six cities is held in one warehouse. The inventory holding cost per unit per year, h, equals $150. If we compute safety stock cost as equal to h multiplied by the average safety stock level, what is the difference in average annual safety stock cost between these two options?
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