Operations.

The Service Level

5 min read·Apply by lunch

The question

How much do you hold of the thing you can run out of — the stock, the spare seat, the standby shift — and could you say, in dollars, what one stockout costs you and what one unsold unit costs you? Until you can, that quantity is a matter of opinion, and the loudest opinion in the room is the one setting it.

The idea

Every argument about how much to hold is really an argument about a forecast, and a forecast is the one thing in the room nobody can settle. Kenneth Arrow, then a young economist at Stanford and later a Nobel laureate, moved the question somewhere it could be settled, in a 1951 Econometrica paper written with Theodore Harris and Jacob Marschak called Optimal Inventory Policy. The problem is older still: F. Y. Edgeworth had used probability to set a bank's cash reserve as far back as 1888. Textbooks call it the newsvendor, after the seller who buys his papers before he knows how many he'll sell, and the shape recurs everywhere. Commit too low and you pay the underage cost — the lost margin, the expedite fee, the customer who quietly goes elsewhere. Commit too high and you pay the overage cost — the write-down, the wage for the idle hour, the capital sitting still. The right service level is the first divided by the sum of both. If running out costs forty dollars and one too many costs five, the ratio is forty over forty-five, and you cover demand to the eighty-ninth percentile. The trap is treating this as a forecasting problem. It's a pricing problem, and both prices are already yours.

The framework

01
Price the stockout first — it's the number nobody has.
Most businesses can tell you to the cent what a unit costs to hold and have never once costed a unit they didn't have. So do it properly: the margin you forfeit, the expedite freight, the penalty clause, and — where it applies — the customer who buys somewhere else and doesn't come back. That last one is where the real money hides, and it's why running out of a repeat-purchase item costs multiples of running out of a one-off. You won't get either figure exactly right. An honest estimate still beats another meeting about the forecast.
02
Two prices in, one percentile out.
Divide the cost of running out by the sum of both costs and the answer is the fraction of demand you should cover. High margin with cheap storage pushes it towards ninety-nine per cent; thin margin on something perishable pushes it far lower, and running out becomes the correct decision rather than a failure. Then run it backwards on whatever target you're holding today. A ninety-five per cent service level is a statement that running out hurts you nineteen times more than holding one too many. Sometimes that's true. Mostly nobody's checked.
03
Does every line on your shelf deserve the same number?
One blanket service level across a whole catalogue is the most common way this gets implemented and the most expensive. The ratio is item by item, because both costs are item by item: the anchor product a customer will change supplier over sits at a very different percentile from the accessory they'll happily wait a week for. Sort your lines into three or four bands, compute the ratio for one representative line in each, then apply it across the band. The same logic runs your rosters, where an unfilled shift and one spare pair of hands are rarely priced the same.
04
The ratio picks the percentile; the spread picks the quantity.
Knowing you want to cover eighty-nine per cent of demand tells you nothing until you know what demand does. You need its spread, not just its average — everything you buy above the middle is the buffer you're pricing. So keep the history week by week across a year, including the weeks you'd rather forget, then sort those weeks low to high and count your percentile up the list: at eighty-nine per cent of fifty-two weeks, you're reading off the forty-sixth. Two products with identical average sales and different volatility land on very different figures there, and a monthly average hides that completely.

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