# Newsvendor model

Last updated August 17, 2023

## What is the Newsvendor model?

The Newsvendor model is a classical inventory management model that helps companies determine the optimal order quantity for an item that has a random demand and a fixed selling price.

By determining the of an item to order, it is possible to maximize profit while minimizing the risk of or overstocking. The model assumes that the demand for the product is uncertain and follows a probability distribution, and that the company incurs a cost for each unit of the item that is not solid.

## The Newsvendor model in action

To calculate the optimal order quantity using the Newsvendor model, the company must estimate the expected demand for the item, the cost of ordering the item, the cost of holding the item in inventory, and the profit margin per unit of the item sold. The optimal order quantity is then determined by finding the quantity that maximizes the expected profit, which takes into account the probability of selling all of the ordered units versus the probability of unsold units.

F(Q*) = CU / CU + CO,

- CU: cost of being one unit short (typically the margin per unit)
- CO: cost of an unsold unit of inventory
- Q: Number of units stocked (the decision quantity, with the optimal quantity Q*)

## FAQ

Increasing the service level (probability of meeting demand) results in higher order quantities and reduced risk of stockouts. However, it also increases carrying costs due to higher inventory levels.

If the cost ratio (CR) is high, it indicates that understocking costs are significantly higher than overstocking costs. In this case, the optimal order quantity will be closer to the mean demand. If CR is low, indicating that overstocking costs are higher, the optimal order quantity will be closer to the maximum demand.

The model is based on the concept of a newsvendor who purchases newspapers at a wholesale price and sells them at a retail price, but is unable to return any unsold newspapers to the wholesaler.