Shade Band Grouping & Roll Allocation to Cut Lays

The formula

This is the expression the tool evaluates. Every term is named underneath, with the unit it must be supplied in.

How the result is derived

Step by step, from the values you type to the figure on screen.

1. The 7 inputs are read from the form on every keystroke: Rolls in the Consignment, Average Roll Length, Total Colour Spread, Shade Band Width, Marker Length, Plies per Lay and Garments per Marker.
2. Each value is checked against the accepted range in the input table below. A value outside its range stops the calculation rather than producing a misleading figure — the results blank out and a message appears.
3. The validated values are substituted into the expression above, which resolves Shade Bands Required together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Fabric Stranded as Remnants, Stranded Fabric, Full Lays per Band, Rolls per Band, Fabric per Band, Fabric Consumed per Lay, Rolls Consumed per Lay, Garments Cut from Full Lays and Consignment Total — come from the same pass, so they always describe the same case as the headline figure.
5. Results are rounded for display only. The full-precision value is used throughout the chain, so reading a rounded intermediate figure back into the tool by hand can shift the last digit.

What each input means

Where to read each value on the floor, the unit it must be in, and the range the tool accepts.

What the tool returns

The headline figure and every supporting value it is built from.

Worked example

Substituting

Note what happens if the band is tightened to 0.2 dE: six bands, 1,200 m each, three full lays and 30 m stranded per band - 180 m again, but now spread over six tails and six separate lay set-ups. The stranded quantity is roughly stable while the handling cost doubles, and that asymmetry is the argument for setting the band from the measured spread rather than from habit.

How to use it

1. Work through the input groups in order — The Consignment and The Cut Plan. The defaults are a realistic case, so you can change one value at a time and watch what moves.
2. There is no calculate button. Every figure recalculates as you type or drag, which is what makes this usable for a what-if sweep rather than a single answer.
3. Read Shade Bands Required in the dark results panel — that is the headline figure, expressed in the unit shown.
4. Check the supporting rows underneath (Fabric Stranded as Remnants, Stranded Fabric, Full Lays per Band, Rolls per Band, Fabric per Band, Fabric Consumed per Lay, Rolls Consumed per Lay, Garments Cut from Full Lays and Consignment Total) before acting on the headline — they are where an implausible input usually shows itself first.
5. Reset to defaults returns every field to the reference case, which is the quickest way to check whether a surprising result came from the tool or from an input you had changed earlier.

Where this is used

• Process planning — establishing Shade Bands Required before a trial is booked, so machine time and material in Apparel Manufacturing & Garmenting are committed against a calculated figure rather than an estimate.
• Costing and quotation — Shade Bands Required is an input to the cost sheet, and quoting from a worked number rather than a remembered one is what keeps a margin intact.
• Troubleshooting — when the floor result drifts from plan, entering the measured values (starting with Rolls in the Consignment) shows how much of the gap in Shade Bands Required each variable explains.
• Teaching and study — the accepted ranges bracket normal Apparel Manufacturing & Garmenting practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Reading the result

Typical bands and what each one is telling you.

Assumptions and limits

• This model assumes rolls are evenly distributed across the colour spread, which is what an unsorted consignment from several dye machines looks like. A bimodal lot - two machines, each internally tight - produces two dense bands and empty space between them, so the even-distribution figure for rolls per band will be wrong even though the band count is right; band from the actual histogram when one is available. Within-roll variation is not modelled and is not always small: side-to-centre-to-side shading on a stenter or a jet can approach the roll-to-roll spread, and no allocation scheme fixes it. Remnant fabric is treated as stranded rather than lost. The lay figure assumes every lay is cut at the stated ply depth; step lays and mixed markers change the arithmetic and generally reduce the remnant.
• Every input is bounded to the range normal practice occupies (Rolls in the Consignment 1 to 5000, Average Roll Length 5 to 500 m and Total Colour Spread 0.05 to 8 dE, and so on for the rest). Those bounds are guard rails against typing errors, not a claim that the formula fails one unit outside them.
• The calculation is deterministic: the same inputs always give the same result. It carries no allowance for machine condition, operator skill, ambient conditions or lot-to-lot material variation unless an input above explicitly represents one.
• Nothing is sent anywhere. The maths runs in your browser, so the numbers you type never leave the page.

Standards and further reading

• ISO 105-A05 - instrumental assessment of change in colour.
• AATCC Evaluation Procedure 6 - instrumental colour measurement.
• ASTM D2244 - calculation of colour tolerances and colour differences.
• AATCC Evaluation Procedure 7 - instrumental assessment of the degree of chemical or physical change.

Questions people ask