A DYNAMIC INVENTORY OPTIMIZATION MODEL UNDER DUAL-INNOVATION DIFFUSION IN COMPETITIVE MARKETS

Abstract

This paper develops a dynamic inventory optimization model that integrates dual-innovation diffusion with competitive market interactions. Unlike traditional EOQ models that assume constant or exogenous demand, the proposed framework embeds the Bass-type innovation diffusion mechanism into a dynamic inventory environment where two interrelated innovations evolve concurrently. The demand for each innovation follows time-dependent diffusion dynamics influenced by innovation, imitation, and cross-adoption effects. A continuous optimal control approach is employed to derive the optimal replenishment and inventory policies that minimize the total expected cost over a finite planning horizon. Analytical derivations establish the necessary conditions for optimality, and stability of the solution is verified through differential analysis. The proposed model demonstrates that accounting for cross-innovation diffusion and market interaction significantly reduces inventory cost and enhances demand forecasting accuracy. The study contributes to both diffusion theory and inventory management by providing a unified analytical framework suitable for dynamic, innovation-driven markets.