In The Characterization Of The Newsvendor Demand Model It Is Stated That The Pro

In the characterization of the Newsvendor demand model, it is stated that the profit maximization problem is equivalent to the minimizing of the following cost function:

C(Q) = E [Cu x (D-Q)+  + Co x (Q-D)+]  or      C(Q) = Cu x E[Short] + Co x E[Left]

Assuming that the demand is normally distributed with mean u and standard deviation  sigma. By using the expression for the optimal order quantity, Q*, show that the optimal cost can be expressed as C(Q*) = A (Cu, Co) x sigma, where A(Cu, Co) is a constant which is a function of the cost parameters Cu and Co but not of the parameters (u, sigma) of the demand distribution D.  What can you infer for the maximum profit that the newsvendor can gain by ordering the optimal quantity?

σ

σ

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