Profit Function
The standard newsvendor profit function is
where is a random variable with probability distribution representing demand, each unit is sold for price and purchased for price, is the number of units stocked, and is the expectation operator. The solution to the optimal stocking quantity of the newsvendor which maximizes expected profit is:
where denotes the inverse cumulative distribution function of .
Intuitively, this ratio, referred to as the critical fractile, balances the cost of being understocked (a lost sale worth ) and the total costs of being either overstocked or understocked (where the cost of being overstocked is the inventory cost, or so total cost is simply ).
Read more about this topic: Newsvendor Model
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