Setting up a calculation: the task where the arithmetic says no

The task, and its number

Working out what a style consumes — how much cloth each garment needs — and what that costs is the most numerical thing a merchandiser does. So it is the most obvious thing to hand over. Marasem logged 14 uses.

Four minutes a use in the wrong direction. That is −56.0 minutes over six weeks, or USD 8.96. Small enough that nobody noticed, which is the point. On the log it sat between two tasks that were saving time, and nothing about using it felt like losing.

The reason is lesson 3's ratio. A check ratio of 90.9% against a threshold of 54.5%. The output can only be disbelieved by producing the answer independently, and producing the answer independently is the task. This is class 2, and class 2 does not pay.

Nine errors, and the two kinds are not equally visible

Across the 14 uses, checking eventually found 9 errors. Sorted by kind:

Six were visible. A total that did not add up. A quantity carried into the wrong row. A metre and a yard in the same column. Each of them is a mistake inside the working, and each is caught by the cheap check: reading down the output and seeing whether it hangs together. The read-check caught 6 of 6.

Three were premise errors. A premise is a number the calculation is built on. One of those was wrong, and everything below it was then computed correctly from a wrong start. The read-check caught 0 of 3.

Here is why, and it is the finding of this lesson.

A premise error is not hidden. It is stated. The output said, in a line of its own, wastage allowance 4%. Nothing about that line is concealed, mistyped or inconsistent. It is printed exactly where a wastage allowance belongs, in the format a wastage allowance takes.

Checking is comparison, and a stated premise has nothing beside it to compare against. Every other figure on the page can be checked against another figure on the page. The premise can only be checked against something you know that is not on the page. And if you knew it, you would have put it in the input.

What it cost

Marasem's own measured wastage on this cloth is 6.6%. Nobody had told the assistant that, so it supplied 4%. That is the mechanism lesson 2 measured: a gap in the input becoming a figure in the output.

The marker — the cutting plan that shows how the pattern pieces are laid on the cloth — gives a net consumption of 2.20 metres for style RV-4180. At 6.6% wastage the garment consumes 2.35 metres. At 4% it consumes 2.29. The 0.06-metre difference went into a quotation.

On 24,000 pieces at USD 3.85 a metre, that is 1,440 metres and USD 5,544.00. It is USD 0.231 a garment, and 1.08% of the FOB price of USD 21.40, on an order whose margin the desk had spent all of February defending.

Two more premise errors were caught before they left the building. A trim price list from last season, worth USD 1,284.00, found when the buyer asked for a breakdown. And a fabric width taken from a different quality, worth USD 640.00, found by the mill's invoice.

The comparison that decides it

The six visible errors would have cost, at worst, a re-issued sheet. Fifteen minutes each, USD 14.40 in total. That is 0.19% of the money that was actually at risk.

The cheap check caught everything that did not matter, and nothing that did. Not because it was done badly. It was done properly, by an experienced merchandiser, and it worked exactly as designed. It is a check on internal consistency, and these three errors were internally consistent.

The verdict, and the course means it

There is a version of this task that is not negative. Supply every premise yourself — the marker consumption, your own wastage, your own prices, your own fabric widths — and ask only for the arrangement and the multiplication. The output becomes class 1. The premises are checked by comparing them with what you typed, and the arithmetic is checked by footing.

Marasem measured that version too: input 5.5 minutes, wait 1.0, check 2.0, repair 0.5, against a manual 11.0. A saving of 2.0 minutes a use. Over the same 14 uses that is 28.0 minutes and USD 4.48.

So the honest arithmetic reads: USD 4.48 over six weeks, against a class of error that has already cost USD 5,544.00 once, and that the review cannot see. The gain is capped by the setup time you cannot avoid. The loss is capped by the value of the order.

Marasem retired the task. Not restricted, not flagged, not run with more care. Removed from the list of things this desk hands over. When the check that makes an output safe costs as much as producing it, you are not using a tool. You are paying for a second opinion you cannot read.