# Difference between revisions of "Newsvendor problem"

Authors: Morgan McCormick (mm3237), Brittany Yesner, Daniel Aronson, John Bednarek

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## Formulation

To formulate a standard newsvendor problem to determine profit, the function is

${\displaystyle E[profit]=E[s*min(n,R)]-wn}$
. In the formulation, s represents the price a unit is sold for, n represents the number of units in inventory, R is a random variable representing a probability distribution for the demand a given day, and w is the wholesale cost for the vendor to purchase materials. The goal is to optimize the profit to be a maximum. This is achieved by also maximizing the amount of inventory on hand to be able to sell while also minimizing the amount of unsold inventory that is void at the end of the day and considered a loss.

The balance of being understocked and losing potential sales with the potential loss from being overstocked can be represented by the critical fractile.  This is illustrated by formula ${\displaystyle n=F^{-}1({s-w \over s})}$ where F-1 is the inverses of the cumulative distribution function of R.

Demand for a given day can be represented using a variety of distributions. Most commonly, there are uniform, normal, or lognormal distributions.

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