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Newsvendor Problem.

Order a perishable stock quantity before revealing tomorrow’s uncertain demand.

Interactive experimentintuitiveField note ·
INTERACTIVE EXPERIMENT / P56

Newsvendor Problem

Order a perishable stock quantity before revealing tomorrow’s uncertain demand.

PLAY & EXPLAIN

Stock a one-day kiosk. Each unit costs 6, sells for 10 and returns 2 as salvage. Tomorrow’s demand is one of five known possibilities; unsold stock does not carry forward.

0120
Declared demand distribution
DemandProbabilityProfit with selected order
200.1-80
400.280
600.4240
800.2240
1000.1240
Expected profit under stated distribution
176.00
Overage / underage cost
4 / 4

This newsvendor model uses invented prices and probabilities. Expected-profit optimisation is not a guarantee for a single day, and missing demand data or stockout effects can change the answer.

Prices and probabilities are invented and demand is independent of availability. Multiple products, uncertain distributions, lead times and customer substitution are omitted.

THE SHORT VERSION

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.

01 / THE MECHANISM

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.

02 / FOLLOW IT THROUGH

A worked example

Order against a declared five-point demand distribution

  1. Choose quantity sixty with unit cost six, selling price ten and salvage value two.

  2. Inspect the profit ledger and expected profit one hundred seventy-six before revealing demand.

  3. 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.

03 / BEYOND THE EXPERIMENT

Where this idea is useful

A practical use

Separate a good inventory policy under a distribution from a lucky realised sales day.

CHECK YOUR INTUITION

A common misconception

THE TEMPTING CONCLUSION

“The order with the best expected profit wins on every realised day.”

THE MORE USEFUL DISTINCTION

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.
ONE MORE QUESTION

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.

TAKE THE IDEA WITH YOU

Which demand distribution and shortage-versus-excess costs justify your order?

Associated thinkers

Associated withKenneth Arrow ↗

Associations marked provisional are awaiting source review.

Further reading

Explore the original research or the teaching reference behind this experiment.