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An online clothing retailer sells men’s white undershirts. In each week, the demand for these undershirts has a normal distribution with mean 2,500 and standard deviation 600.
At the end of each week, the retailer observes its inventory position and decides whether or not to place an order, and if so, for how many units (so this is a periodic review system). When the retailer orders more shirts from its supplier, it receives them after a lead time of 3 weeks (don’t forget to add a week to get the e?ective lead time).
If the retailer doesn’t have enough inventory on hand to ful?ll a customer’s order, the order is backlogged and then ful?lled once the retailer has su?cient stock on hand. When an order is backlogged, the retailer compensates each a?ected customer with a discount of $1 per unit ordered (so, if a customer ordered 3 shirts, they would receive a discount of $3 on their order). The inventory holding/carrying cost for one unit is $5 per year.
a) What is the average lead time demand? b) What is the standard deviation of lead time demand?
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