Optimization of Integrated Inventory Vendor - Buyer Model using Hexagonal Fuzzy Numbers Under Genetic Algorithm

Healthcare inventory systems demand high reliability, as shortages or delays in critical supplies can directly affect patient survival. Traditional Economic Order Quantity (EOQ) models are inadequate for such contexts because they rely on precise demand and cost data, which are rarely available in practice. It is an integrated inventory model for injection procurement in infection treatment, paper proposing the uncertainty of holding, ordering and demanding cost Where demand, ordering cost, and holding cost are uncertain. This model incorporates the buyer’s ordering cost, the vendor’s ordering cost, screening cost, also penalty for lost sales, reflecting the realities of medical supply chains. To capture uncertainty more effectively, parameters are expressed as Hexagonal Fuzzy Numbers (HFNs), which generalize traditional fuzzy sets offer a richer description of vagueness. The defuzzified model is solved analytically to obtain a closed-form optimal order quantity. To ensure robustness under uncertainty, Genetic Algorithm (GA) is employed to optimize the same cost function. Numerical experiments show that the fuzzy–GA approach produces consistent and resilient solutions, outperforming crisp models in terms of adaptability to fluctuating healthcare demand. The results highlight the practical applicability of combining HFNs and GA in healthcare inventory planning, ensuring cost efficiency without compromising patient safety.