(untitled) (Contemporary Mathematics, 2025)
Amelioration and deterioration rates play a vital role in inventory management. Some animals lose value due to illness, death, or other incidents as they gain weight when kept on farms in good health. Organizations and entrepreneurs can maximize the operational efficiency and health of their animals through a well-organized and efficient inventory system. The proposed inventory model provides a more realistic assumption of livestock with a Weibull amelioration rate and constant deterioration rate. In the inventory domain, trade credit plays a vital role in minimizing costs, in maintaining an adequate livestock supply, and in maximizing the credit period. The main objective of this article is not only to improve financial performance but also to enable livestock operations to satisfy market demands, to manage resources, and to successfully navigate the complex world of credit-based transactions. This inventory system is mathematically modelled by differential equations, and the total cost is determined. The optimality of the solved nonlinear minimization problem is verified by using pseudo concavity. Partial Swam Optimization (PSO) and Genetic Algorithm (GA) are designed to determine the optimal cycle length, the optimal credit period and the order quantity. Numerical examples are presented to illustrate the solution procedure for various cases of the proposed inventory model. Sensitivity analysis serves as a validation tool, providing a discerning assessment of the strength and flexibility of the model in response to variations in key parameters.