Using Regression to Predict Dyeing Recipe Cost Before the Batch Runs

Dyeing cost is usually estimated from a recipe book that is updated when someone remembers. A regression built on two years of actual batch data does better, and it exposes which factors genuinely drive cost rather than which ones the recipe book assumes.

The data

The model used 1,840 completed batches with the following recorded per batch: fabric type, fabric weight, shade depth as total dye percentage on weight of fabric, machine liquor ratio, number of shading additions, and actual chemical and dye cost per kilogram.

Model specification

cost_per_kg = b0
            + b1 x shade_depth
            + b2 x liquor_ratio
            + b3 x additions
            + b4 x is_polyester
            + b5 x is_blend
            + error

Shade depth entered as a continuous variable in per cent on weight of fabric. Fabric type entered as dummy variables with cotton as the reference level.

Results

Adjusted R-squared 0.83, residual standard error 0.09 per kg, mean absolute percentage error on a 20 per cent holdout sample 6.1 per cent.

What the coefficients say

Each additional shading addition costs about 0.126 per kilogram — which across roughly 4,000 tonnes a year and a 14 per cent addition rate is a meaningful annual number attributable entirely to right-first-time performance. That single coefficient made a stronger case for RFT investment than three years of quality presentations had.

The liquor ratio coefficient of 0.041 per unit quantified what the engineering team had argued qualitatively: moving the average liquor ratio from 1:8 to 1:6 is worth about 0.08 per kilogram in chemicals alone, before water and steam.

Limitations I would want reviewed

• The model is fitted on one mill's data and its coefficients are not transferable without refitting.
• Dye price changes over the two-year window are not deflated, so part of the intercept absorbs price drift.
• Turquoise and certain navy shades are systematically under-predicted; they likely need their own dummy variable.