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.

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Answer #1

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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