Abstract: This paper develops a dynamic inventory model that integrates the diffusion of innovation with product deterioration under constant demand. Replenishment is modeled as a function of innovation adoption, governed by the Bass diffusion model, while inventory depletion is influenced by both demand and deterioration. The study formulates a coupled system of differential equations to represent these dynamics and solves the system analytically using integrating factors, followed by numerical evaluation where closed-form solutions are not feasible. A comprehensive sensitivity analysis is performed on key parameters—deterioration rate, innovation coefficient, and replenishment capacity—to understand their effects on final inventory levels. Scenario simulations demonstrate that faster innovation adoption significantly improves inventory stability, especially in high-loss environments, whereas delayed adoption results in accelerated inventory depletion. The model provides theoretical insight and practical decision-making support for managing inventory in environments where technology adoption evolves gradually. The findings emphasize that the timing and speed of innovation adoption are as critical as replenishment capacity, especially in industries dealing with perishable or fast-moving goods.

Keywords: Innovation Diffusion, Inventory Modelling, Bass Diffusion Model, Replenishment Strategy, Deterioration Rate.