Enhancing Strategic Management Through Linear Programming: A Comparative Study Involving Doolittle’s and Simplex Methods

This research paper explores the application of Linear Programming (LP) as a strategic decision-making tool across diverse domains such as agriculture, management, site selection, services, investment, and transportation, with the overarching aim of maximizing profitability.The study introduces Octagonal Fuzzy Numbers (OFNs) and proposes a novel approach for defuzzification using a ranking function derived from Pascal's triangle to handle the left and right spreads of OFNs effectively.To obtain optimal solutions, the formulated LP problems are solved using Doolittle's method, the Simplex method, and the Graphical method.A comparative analysis of the results obtained from these techniques is carried out to determine the most optimal solution.The findings demonstrate the practical applicability and efficiency of LP in real-world scenarios and underscore the advantages of incorporating octagonal fuzzy numbers in uncertain decision-making environments.