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Problem 5: An important quantity in inventory models is the lead time demand, demand that arises...

Question:

Problem 5: An important quantity in inventory models is the lead time demand, demand that arises over the time it takes for a replenishment order to be delivered (we will go into why this is the case in the class; trust me for now!). Suppose weekly demand for an item has been determined to follow a Gamma distribution with a mean of 1000 units and a standard deviation of 300 units, and the replenishment lead time is 3 weeks. Demand in each week is statistically independent of demand in other weeks. a) Compute the parameters of the Gamma distribution that yield the specified mean and standard deviation.

Problem 5: An important quantity in inventory models is the lead time demand, demand that arises over the time it takes for a replenishment order to be delivered (we will go into why this is the case in the class; trust me for now!). Suppose weekly demand for an item has been determined to follow a Gamma distribution with a mean of 1000 units and a standard deviation of 300 units, and the replenishment lead time is 3 weeks. Demand in each week is statistically independent of demand in other weeks. a) Compute the parameters of the Gamma distribution that yield the specified mean and standard deviation.

Answers

a)

E(X) = 1000

Var (X) =-= 3002-90000 82

Divide and get beta and substitute to get alpha

alpha = 100/9

eta = 1/90

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