Solving Linear Programming Problems Using Sensitivity Analysis and Heptagonal Ranking Function

Abstract

This research presents an integrated approach that combines sensitivity analysis with fuzzy logic to address uncertainty in operations research models. The study focuses on the right-hand side (RHS) of constraints as a key parameter subject to variation. To capture this uncertainty, a symmetric heptagonal fuzzy membership function is proposed, where the seven representative values are governed by a single weight parameter (r). A corresponding fuzzy ranking function is developed to transform the fuzzy outcomes into comparable crisp values. The methodology is applied to two illustrative linear programming examples drawn from textbooks, covering both maximization and minimization problems. The results demonstrate that the fuzzy ranking approach, particularly under specific weight configurations, provides more robust and realistic solutions than traditional sensitivity analysis. These findings confirm the effectiveness of integrating fuzzy logic into sensitivity analysis for enhancing decision-making in linear programming under uncertainty.