Economic order quantity
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The cost of holding a unit is the one people leave out. It is not just the warehouse: it is the money tied up in the stock, which would have been earning something else.
Results
The lot that costs the least over a year
—
| What that costs you in a year | — |
| Of that, the part spent on placing orders | — |
| And the part spent on holding stock | — |
| Orders you would place in a year | — |
| Days between one order and the next | — |
| What your own lot would cost instead | — |
What it costs to get the lot wrong
| Share of the best lot | Units | Extra cost over the year |
|---|
Read that table before trusting the big number too much. Ordering a tenth away from the best lot costs about half of one percent more over the whole year. Being thirty percent off costs three and a half percent. You have to order double, or half, before the bill goes up by a quarter, and those two mistakes cost exactly the same.
That penalty depends on nothing but the ratio between your lot and the best one. It does not care how much you use, what an order costs you or what holding a unit costs: two businesses with nothing in common, both ordering thirty percent above their own best lot, are both paying the same three and a half percent. Checked against twenty thousand made up sets of figures.
One thing the method does assume, and it is worth saying out loud: that demand is steady and known, that the price per unit does not fall when you buy more, and that stock arrives when it is supposed to. Where a supplier gives a discount for a bigger lot, the answer here is only the starting point.
How much does it cost to get the lot size wrong?
Far less than the precision of the formula suggests, and this is the useful part. Ordering ten percent away from the best lot costs about half of one percent more across the whole year. Thirty percent away costs three and a half percent.
You have to order double the best lot, or half of it, before the bill rises by a quarter. And those two mistakes cost exactly the same amount, because the penalty depends on the ratio and not on the direction.
So is the exact number worth chasing?
Usually not. Since the curve is nearly flat at the bottom, rounding to whatever the supplier sells, what fits a pallet or what fills a lorry costs you almost nothing against the exact answer, and it saves a real amount of trouble.
The number is best read as the middle of a comfortable region rather than as a target. Knowing the region is what changes decisions; knowing the decimal place does not.
Does the penalty depend on my own figures?
No, and that is the surprising part. The extra cost depends on nothing but the ratio between the lot you order and the best one. Two businesses with nothing in common, each ordering thirty percent above their own best lot, both pay the same three and a half percent.
The formula for it is half of the ratio plus its reciprocal, which was checked here against twenty thousand made up sets of demand, order cost and holding cost. The largest disagreement was in the fifteenth decimal place, which is floating point noise and not arithmetic.
What does the method quietly assume?
That demand is steady and known in advance, that the price per unit is the same however much you buy, and that deliveries arrive when they should. Real life bends all three.
The one that bends hardest is the price. Where a supplier discounts a bigger lot, the answer here is the starting point of the comparison and not the end of it: you would work out the total at the best lot, then at each price break, and pick the cheaper.
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