MATHEMATICAL MODELING AND OPTIMIZATION OF MULTICOMPONENT MIXTURES FROM VARIOUS TYPES OF FIBERS

Abstract

The article addresses the mathematical modeling and optimization of multicomponent textile fiber blends. The study's relevance stems from the need to obtain materials with specified quality characteristics while minimizing raw material costs. To achieve this, an improved mathematical model and software for optimizing multicomponent fiber blend compositions are proposed.

The problem is formulated as a linear programming model, where decision variables represent the proportions of individual fiber components. The objective function minimizes total raw material costs while satisfying technological, economic, and quality requirements.

To solve the problem, an enhanced computational approach based on the two-phase simplex method is proposed. The first phase determines a feasible blend composition, while the second phase provides economic optimization using a preserved feasible basis. A preliminary analysis of the constraint system allows linearly dependent conditions to be identified and removed.

A key feature of the model is the analysis of dual estimates, which assesses the impact of individual quality requirements on the optimal blend's cost, alongside a diagnostic procedure for identifying mutually incompatible constraints. This enables timely adjustment of quality limits or available fiber ranges.

The proposed approach was implemented in the Composite 4.2.0 web-based software complex. The application allows users to define fiber components, specify costs and constraints, calculate optimal compositions and minimum costs, analyze dual estimates, and diagnose conflicting requirements. The developed complex expands the capabilities of mathematical optimization for the technological and economic substantiation of textile blends.