International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/2575 2020 2020 PG and Research Department of Mathematics, Cauvery College for Women (Autonomous), Affiliated to Bharathidasan University, Tiruchirappalli-620018, Tamil Nadu, India; D. Sc (Mathematics) Researcher Fellow, Srinivas University, Surathkal, Mangaluru, Karnataka-574146. K. K. Department of Mathematics, Periyar University Centre for Postgraduate and Research Studies, Dharmapuri - 635205, Tamil Nadu, India N. Anitha Ph.D Research Scholar, PG and Research Department of Mathematics, Cauvery College for Women (Autonomous), Affiliated to Bharathidasan University, Tiruchirappalli-620018, Tamil Nadu, India. S. Swathi Department of Mathematics, Mohan Babu University, Tirupati-517501, Andra Pradesh, India B. Ranjitha This research introduces the Neutrosophic Vendor-Buyer Economic Order Quantity (EOQ) model, integrating Neutrosophic Set Theory and Particle Swarm Optimization (PSO) for advanced inventory management. Addressing uncertainties in demand and costs, Neutrosophic Sets quantify truth, indeterminacy, and falsity degrees for key parameters. The model, employing PSO inspired by collective behaviour in nature, aims to minimize the combined total cost (C) encompassing vendor and buyer expenses. A grocery store scenario illustrates the approach, demonstrating substantial total cost reduction through the optimization of decision variables. MATLAB R2015a visualizations include a mesh plot depicting cost changes across varying EOQ and demand variability values, emphasizing optimal solutions. A bar chart compares initial and optimized total costs, showcasing efficiency gains. Cost breakdowns and pie charts detail the impact on vendor and buyer expenses. Sensitivity analysis systematically explores variable influences, aiding decision-makers in understanding trade-offs and optimal ranges by using Python. This comprehensive framework contributes empirical insights for practical implementation, enabling businesses to make informed decisions and enhance adaptive inventory strategies efficiently. 2024 2024 181 193 10.54216/IJNS.230414 https://www.americaspg.com/articleinfo/21/show/2575