Forecasting tonight's covers

How does a chef decide how much to prepare for a night nobody can predict?

At four in the afternoon a chef has to commit. Portion the fish, braise the short rib, pick the herbs, blanch the greens. By seven the decision is irreversible, and the number of guests who will actually walk in is genuinely unknown — reservations are only part of it, walk-ins are weather-dependent, and a fifth of the book might not show.

The obvious framing is: predict the number, then prepare that much. But watch what a good chef actually does, and she does not prepare the number she expects. She prepares more of some things than she expects to sell, and less of others. If forecasting were the whole job, that would be a mistake. It is not a mistake, so the framing must be wrong.

Start with what can be known. Ask what predicts tonight's covers, and the answer is mostly the same night last week. Day of week dominates almost everything else in restaurant demand; a Saturday resembles Saturdays far more than it resembles yesterday. Layer on seasonality, then the reservations already on the book, then a walk-in estimate, then subtractions for expected no-shows, then local adjustments — weather, a match, a conference in town, a holiday.

Notice something about that list. The reservation count is not the forecast; it is an indicator of the forecast. What converts it is a ratio learned from history: on a Thursday in this season, booked covers have historically been about such-and-such a share of total covers. So the chef is not counting, she is inferring — using an observable proxy plus a historical relationship to estimate an unobservable quantity.

Now push on the honest limit. Even a good forecast is not a number; it is a distribution. Two hundred is the centre of a range that might realistically run from a hundred and sixty to two hundred and forty. Any procedure that treats the centre as the answer is discarding the very thing that makes the decision hard.

So ask the better question: given a distribution, how much should you prepare? And here the asymmetry appears. What does running out cost? A guest who came for the signature dish is told no, the server absorbs it, and the damage is to reputation and to the evening. What does over-preparing cost? Food cost on the surplus — but crucially, only if it cannot be held. A braise, a stock or a mirepoix keeps and reappears tomorrow. Portioned raw fish and dressed salad do not.

Those two costs are not equal, and they are not equal in the same way for every item. That is why the chef prepares above her expectation for some dishes and below it for others. She is not forecasting different amounts. She is choosing a different point in the same distribution.

This has a formal name, and it is worth having. The newsvendor problem asks how much perishable stock to commit before demand is known, and its answer is not the mean — it is the quantile of the demand distribution set by the ratio of the shortage cost to the sum of the shortage and overage costs. High cost of running out and low cost of surplus pushes you well above the expected demand; the reverse pushes you below it.

Should you imagine chefs computing that fraction? Almost never. What they carry instead are par levels — standing prep quantities per station, tuned over time by what ran out and what got thrown away. That feedback loop converges on roughly the same place the formula points to, without anyone writing it down. I would not want to claim the two land in exactly the same spot; the honest claim is that the par level is an empirically fitted version of the same trade-off.

One more move, and it is the one that rescues the whole evening. Not every decision has to be made at four o'clock. Some things can be finished to order in minutes, others need hours. A well-designed prep plan pushes the irreversible commitments as late as the cooking allows, so that decisions can use information that only exists at seven — the actual arrival rate, the no-shows already visible, how the dish mix is running tonight rather than historically.

The misconception to shed is that prep is a two-step process — forecast, then match. It is one decision made under a distribution, and the shape of the loss matters as much as the centre of the forecast.

A second, subtler one: a chef who never runs out of anything is not therefore excellent. Never running out means the prep sits far up the distribution on every item, which for perishable dishes is simply expensive waste chosen quietly. The same goes for the mirror image. Some running out and some waste, on the right items, is what a correctly tuned kitchen looks like.

And a limit worth stating plainly. Better history narrows the forecast but does not close it. Whether a particular table of six shows up is not a knowable fact at four o'clock, and no amount of data makes it one. The residual uncertainty is irreducible, which is exactly why the response has to be a hedging strategy rather than a better guess.

• How cross-utilisation of ingredients across dishes changes the calculation by making surplus recoverable somewhere else.
• Why no-show rates respond to deposits and confirmation messages, and what that does to the width of the forecast.
• How the same newsvendor logic reappears in hotel overbooking, with an opposite-signed asymmetry.

Every term the collection defines is gathered in the glossary.