Most inventory decisions get made by feel. You notice the shelf looks light, you call the supplier, you order about what you ordered last time. It works, in the sense that you rarely run out and the business keeps moving. What it hides is a cost you never see itemized, because no invoice ever arrives for ordering wrong.
There are two questions underneath every reorder, and they have real answers. How much should you order at a time? And how low should you let stock fall before you place the order? Guess high on the first and your cash sits on a shelf as boxes. Guess low and you are paying to place orders you did not need. Guess wrong on the second and you are on the phone apologizing to a customer. The arithmetic that answers both has been settled for decades. Almost nobody runs it.
How much: the quantity that balances two opposite costs
Ordering has a fixed cost every time you do it. Somebody spends twenty minutes placing it, a delivery fee lands, an invoice gets processed. That cost is the same whether you order fifty units or five hundred, so the more you order at once, the fewer orders you place, and the less you spend on ordering across the year.
Holding stock has a cost too, and it runs the other way. Inventory takes up space you pay for. It ties up money that could be doing something else. Some of it spoils, expires, or goes out of style. The more you order at once, the more sits there waiting, and the more all of that costs you.
So the two costs pull against each other. Order in big batches and your ordering cost falls while your holding cost climbs. Order in small ones and the reverse. Somewhere between the extremes is the quantity where their sum is as low as it goes, and there is a formula that finds it. It has a satisfying property worth knowing as a sanity check: at exactly the right quantity, the two costs are equal. If your holding cost and your ordering cost for the year are wildly different, you are ordering in the wrong size.
When: cover the wait, then buffer for the bad weeks
The second question is about timing, and it has two pieces.
The first piece is easy. If delivery takes two weeks and you sell about 350 units a week, you burn roughly 700 units waiting for the truck. Let stock fall to 700 and reorder, and in a steady world you would coast to empty exactly as the new shipment lands.
The world is not steady, which is the second piece. Some weeks you sell more than 350, and if one of those weeks falls during the wait, 700 leaves you short. So you carry a buffer on top, sized to how much demand swings and to how sure you want to be. A number here surprises almost everyone the first time they meet it. The buffer tracks the square root of the wait rather than its full length. Double your lead time and the buffer you need grows by roughly 1.4 times, well short of double. Variability accumulates across weeks the way variance does, and standard deviation is its square root. You never have to follow that math to use the result. Longer waits need bigger buffers, just not proportionally bigger ones.
The dial worth turning slowly
The buffer also depends on how often you are willing to run out, and this is the one setting worth thinking hard about. Going from covering yourself 95% of the time to 99% of the time sounds like a modest upgrade. It costs roughly 40% more safety stock. Whether that is money well spent depends entirely on what a stockout does to you. A restaurant that runs out of a garnish improvises. A pharmacy that runs out of a prescription loses a patient and maybe worse. The formula will hand you a buffer for any service level you name; which one to name is a judgment about your customers, and it is the part of this that stays yours.
Where the arithmetic stops helping
Honesty about a model matters more than the model. This one assumes your demand wobbles around a steady average. That is a decent description of a dental office buying gloves and a terrible one for a ski shop in January or a rental outfit in July. If your demand has a season rather than a spread, do not average across the whole year. Run the numbers separately for each stretch that behaves differently, and treat them as different problems, because they are.
It also assumes your supplier's lead time holds. If the real chaos in your business is a vendor who says Tuesday and means sometime, the buffer you carry is a bandage over a wound you should be treating directly. No order quantity fixes an unreliable supplier. Fix the supplier.
The cost that never shows up
There is one more cost the arithmetic cannot see, and it is often the biggest. Plenty of owners do their own ordering because it feels like being careful with the money. It usually is not. If you are the highest-billing person in the building, the hour you spend counting boxes and calling suppliers is the most expensive hour on the schedule, and it never appears as a cost anywhere because nobody sends you a bill for your own time. That is the same trap that turns a business into a job you can't quit, and it is worth pricing out honestly before you decide the ordering is yours to keep.
The math for the first two questions, though, you can run in about a minute. We built a calculator that does it: put in your demand, your costs, and your lead time, and it tells you how much to order, when to reorder, and what your current habit is costing you against the answer. Nothing you type leaves your browser. If the number it gives you back is uncomfortable, that discomfort was already in your books. Now it just has a figure attached.