Demand
Optional label first. Add * or "sold out" when you ran out, since real demand was higher. Use comparable seasons (same product type and selling window). Three or more; five or more is much better.
Guessed ranges are usually too narrow, so the spread is widened by the factor shown (1 = trust your range exactly).
Money
The whole order is priced at the tier it reaches. The first line's quantity is treated as the minimum order. A single number is a flat unit cost.
Enter demand and money, then click Find the best order.
Result
Expected profit by order quantity
The two orders compared
| Quantity | Expected profit | Chance of sell-out | Expected leftover | Chance of a loss | Bad-season profit (10th pct) | Cash in |
|---|
Best order inside each price tier
| From | Unit cost | Best quantity | Expected profit |
|---|
If demand turns out different
Expected profit of your recommended quantity if true demand is scaled, against the best quantity for that demand.
| Demand | Profit with your order | Best order then | Profit with that | Regret |
|---|
Back-test on your own seasons
| Season | Actual | Tool ordered | Profit | Average rule | Profit | Best-ever rule | Profit |
|---|
Cash-limited basket
Buying several products from one pot of cash? Analyse each one above and add it here. The tool spreads your cash to where each dollar earns most expected profit, and says what the limit costs you against ordering every best quantity. Heuristic: price breaks make the true optimum lumpy, so the upper bound shown is the best any plan could do.
| Product | Best order alone | Order within cash limit | Cash used | Expected profit |
|---|
How it is calculated
Demand: ln(demand) is treated as normal. From past seasons the mean and spread are fitted by EM so that a sold-out season counts as "demand was at least this". With few seasons the spread is uncertain, so demand is drawn from the Bayesian predictive (scaled inverse chi-squared spread, normal mean), truncated at 3.5 standard deviations. From a low / likely / high guess the median and spread come from your 10th and 90th percentiles, widened by your factor. 4,000 stratified, seeded draws are used, so a result is reproducible. Profit for an order q and demand D: price × min(q, D) + (leftover value − holding cost) × leftover − lost-sale cost × shortfall − unit cost at the tier reached × q − fixed cost. Every candidate quantity, including each price-break quantity and the one just below it, is scored on the same draws. The best order maximises the average; the cautious order maximises the average of the worst 10% of outcomes. The textbook newsvendor quantile is shown as a reference. Value of knowing demand is an upper bound from ordering exactly the demand each time. Back-test: for each season that did not sell out, demand is fitted from the other seasons, the tool's order is placed, and its profit on the actual demand is compared with ordering the average, and the best, of those other seasons.
Not modelled: trends between seasons, competitors, demand that depends on price or ad spend, partial reorders, staggered deliveries, and discounting during the season. Sold-out seasons not flagged are treated as true demand, which biases the answer down. Unverified: checked against the closed-form newsvendor answer and simulated data in unit tests, not against a published dataset or a commercial tool.
Common questions
How many units should I order for a seasonal or one-time product?
Order the quantity that maximises expected profit, not the one you expect to sell. The gain from one more unit (price minus cost) is usually different from the loss on a leftover unit (cost minus what leftovers fetch), and demand is uncertain. The best order is the point where the chance of selling out equals the ratio of those two costs, known as the newsvendor rule. This tool applies it to your own numbers and your own sales history.
What is the newsvendor model?
It is the classic inventory model for goods you buy once for a selling period and cannot reorder: fashion drops, holiday stock, event merchandise, perishables. With underage cost cu (profit lost per unit short) and overage cost co (loss per leftover unit), the best order is the demand quantile at cu divided by cu plus co. This tool goes beyond the formula by also handling supplier price breaks, minimum orders, fixed order costs and uncertain demand estimated from few seasons.
How does it estimate demand from past seasons?
It fits a lognormal distribution to your past seasons' units sold. A season that sold out is treated as demand of at least that many units, not as the true figure, using an EM fit for censored data. With only a few seasons the spread of demand is itself uncertain, so the forecast is widened by a Bayesian predictive, and tails are truncated at 3.5 standard deviations. Three seasons is the minimum; five or more make the answer sharper.
What if I have no sales history?
Use the low, likely and high mode. Enter your 10th-percentile, median and 90th-percentile guess for units demanded. People's ranges are usually too narrow, so the tool widens the spread by a factor you can change. A pre-order or waitlist is the best way to replace a guess with data, and the result shows an upper bound on what knowing demand in advance is worth.
How do supplier price breaks change the answer?
A cheaper unit cost at a higher quantity can make ordering more worthwhile even if you will probably not sell it all, because the saving applies to every unit. Because this is not a smooth formula, the tool evaluates the expected profit of every order quantity, including the exact quantity of each break, and shows the best order inside each price tier. Minimum order quantities are respected.
What is the cautious order?
The expected-profit order accepts bad outcomes in some seasons. The cautious order instead maximises the average of the worst 10% of outcomes (conditional value at risk), which protects cash at the cost of some expected profit. The page shows the chance of a loss, the 10th percentile profit and the cash you would put in for each.
How accurate is it, and is my data uploaded?
It is a statistical estimate from the seasons you enter and the assumption that demand is lognormal around a stable level; it cannot see trends, stock-outs outside the ones you flag, competitors or one-off events. A leave-one-out back-test compares its orders with two rules of thumb on your own history. Nothing you type is uploaded: the calculation runs in this browser tab.