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In the formal presentation of the Newsvendor problem, we have shown that the profit maximization problem is equivalent to the minimizing of the following cost function:
C(Q) = E[Cu · (D - Q)+ + Co · (Q - D)-] or,
C(Q) = CuE[short] + CoE[left]
Assume that the demand is normally distributed with mean μ and standard deviation σ. By using the characterization (i.e., expression) for the optimal order quantity, Q*, show that the optimal cost can be expressed as C(Q ∗) = A(Cu, Co) × σ, where A(Cu, Co) is a constant which is a function of the cost parameters C? and C? but not of the parameters (μ, σ) of the demand distribution D. What can you infer for the maximum profit that the newsvendor can gain by ordering the optimal quantity?
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