Application of a Fuzzy Programming Technique to Production Planning in the Textile Industry

Many engineering optimization problems can be considered as linear programming problems where all or some of the parameters involved are linguistic in nature. These can only be quantified using fuzzy sets. The aim of this paper is to solve a fuzzy linear programming problem in which the parameters involved are fuzzy quantities with logistic membership functions. To explore the applicability of the method a numerical example is considered to determine the monthly production planning quotas and profit of a home textile group.

💡 Research Summary

The paper tackles the pervasive issue of uncertainty in production planning for the textile industry by integrating fuzzy set theory with linear programming. Traditional linear programming (LP) assumes that all coefficients and constraints are known precisely, an assumption that rarely holds in real‑world manufacturing where raw‑material costs, labor productivity, and market demand are often described in linguistic terms such as “high,” “moderate,” or “volatile.” To bridge this gap, the authors model these ambiguous parameters as fuzzy quantities using logistic membership functions, which provide a smooth S‑shaped transition between a lower bound (L) and an upper bound (U) while allowing the decision‑maker to control the central tendency (C) and the steepness (k) of the curve.

The methodological core consists of three steps. First, each fuzzy parameter is expressed by a logistic membership function derived from expert judgments and historical data. Second, the fuzzy model is transformed into a family of crisp LP problems through the α‑cut technique. For a given α‑level (0 ≤ α ≤ 1), the fuzzy coefficient is replaced by an interval