Textile color formulation using linear programming based on Kubelka-Munk and Duncan theories

In this article, a new approach based on linear programming optimization is proposed to solve the textile color formulation problem. The principle aims to find the appropriate dyes to mix and their exact concentrations, which, when applied correctly, produce the required color. Two ranges of reactive dyes were used for dyeing cotton fabrics. The objective function and all the constraints of the model are expressed linearly according to the decision variables. The objective function is to minimize the differences between the K/S spectra of the sample dyed with the proposed mixture and the target color. The constraints of the model are formulated based on Kubelka-Munk and Duncan theories in the same way as those of the single-constant model. The relevance of the method developed using linear programming optimization was evaluated and proven by calculating errors between the proposed and actual recipes, errors in K/S spectra, and Colour Measurement Committee CMC(2:1) differences between the reproduced and target colors. The proposed program showed very good results with very small values of errors and color differences.

Automated summary

This article introduces a new approach based on linear programming optimization to solve the textile color formulation problem, using two ranges of reactive dyes for dyeing cotton fabrics. The method aims to find the appropriate dye mixtures and concentrations, effectively minimizing errors and color differences between the reproduced and target colors. Evaluation of the proposed program shows very good results with very small values of errors and color differences.