Newsvendor Problem, explained.
The newsvendor problem selects a one-period order quantity by balancing the expected costs of excess inventory and insufficient stock under a specified demand distribution.
Why it happens
Unit cost six, selling price ten and salvage two give equal underage and overage costs of four. Five demand levels with stated probabilities make a median demand of sixty an expected-profit optimum.
The newsvendor problem selects a one-period order quantity by balancing the expected costs of excess inventory and insufficient stock under a specified demand distribution.
Read the result
Expected profit weights all declared demand scenarios. The realised sales day supplies one payoff and cannot by itself establish the quality of the ordering policy.
A worked example
Order against a declared five-point demand distribution
Choose quantity sixty with unit cost six, selling price ten and salvage value two.
Inspect the profit ledger and expected profit one hundred seventy-six before revealing demand.
Commit the order and compare realised profit with its expectation, retaining the same probabilities rather than judging the policy only by luck.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
Unit cost six, selling price ten and salvage two give equal underage and overage costs of four. Five demand levels with stated probabilities make a median demand of sixty an expected-profit optimum.
Where this idea is useful
A practical use
Separate a good inventory policy under a distribution from a lucky realised sales day.
A common misconception
“The order with the best expected profit wins on every realised day.”
A distribution-based optimum balances overage and underage costs; another order can outperform it under a particular realised demand.
What this explanation leaves out
- Prices and probabilities are invented and demand is independent of availability. Multiple products, uncertain distributions, lead times and customer substitution are omitted.
Why does this example target a demand median?
Underage and overage costs are both four, giving critical fractile one-half under the declared one-period model.
Which demand distribution and shortage-versus-excess costs justify your order?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.