The expenses of an organization shift if the costs of its commodity change. Since the actual manufacturing costs might fluctuate or be uncertain owing to a little rise and fall in the availability of different constraints, this study provides two different cases of uncertainty and generates authentic models to mitigate the influence on expense management. In this study, a rigorous comparative analysis elucidating the intricacies of both modeling and optimization procedures for manufacturing expenses of Rail Coach Factory Kapurthala through Poly-fuzzy and \(\left( {S, l, r} \right) \) —bidirectional triangular fuzzy graded model has been examined. The veracity of optimized cost with the assistance of the newly proposed Poly-fuzzy programming model has been identified and compared with existing \(\left( {S, l, r} \right)\) —triangular fuzzy linear optimization problem model. The production expenses associated with various coach variants are regarded as input parameters, with the overarching target of minimizing the total expenditure being pursued as the primary objective. The Least-lower, Lower, Intermediate, Upper and Greatest-Upper bounds for both proposed cases of the Poly-fuzzy linear programming problem are calculated. Subsequently, systems of optimized fuzzy linear programming problems are being structured. Also, the reliability of each model of Poly-fuzzy has been obtained, and then the minimum and greatest minimum cost using this fuzzy degree function is illustrated through the graphs. In accordance with the suggested degree of satisfaction, an evaluation is conducted to compare the performance of each Poly-fuzzy model across various scenarios with the \(\left( {S, l, r} \right)\) —triangular fuzzy linear programming model. This analysis aims to investigate the influence of Poly-fuzzy parameters on optimized cost. It is observed that the Poly-fuzzy model provides a better edge on constraints availability management over the \(\left( {S, l, r} \right) \) —triangular fuzzy model. The results from the study provide new competence conducive to a successful shift to circular business models for the Rail Coach Factory.
