Newsvendor model
Assumptions
1. Products are stocked only for a single period – highly perishable or vulnerable to
obsolescence quickly
2. Stock out cost known
3. Overstocking has a cost as well, and is known in advance.
If purely cost and price details are given, then the cost of overstocking and understocking can be
calculated as
Cost of overstocking (Co) = Cost Price per unit – Salvage value per unit
Cost of understocking (Cu) = Selling Price per unit – Cost price per unit
Steps to determine the stocking level
i.
ii.
iii.
Evaluate critical ratio (Cr) = Cu/(Cu + Co)
Find Z such that the area to the left of Z in the standard normal curve is the critical ratio
Cr. In other words, the cumulative probability of the standard normal distribution upto
point Z should be same as the critical ratio.
Stocking level = Mean demand + Z x std dev of demand
In this Z can even be negative, implying you stock less than the average demand – perfectly fine.
There is a risk that this calculation might give a negative stocking level; but that is a limitation of
normal distributional assumption of demand. In most practical cases, this will not occur.
Some metrics that can be defined
i.
ii.
iii.
iv.
Expected lost sales = standard deviation of demand X L(z);
Where z is the value you obtained from normal curve while determining the stocking
level. L(z) is the normal loss function
Expected lost sales + Expected sales = Average demand
Expected sales + Expected leftover inventory = Q
Expected Profit = (Selling Price – Cost Price) * Expected Sales – (Cost price – Salvage
value ) * Expected leftover inventory.