The relevance of conventional Economic Order Quantity (EOQ) models to today’s manufacturing systems with varying and unpredictable parts demand is small, as they often use closed-form analytical approaches with constant demand. In this paper, we propose a numerical scheme that integrates Newton-Raphson iterative techniques with finite difference methods to address complex EOQ models with variable demand. To achieve this, the EOQ problem is reformulated into a nonlinear minimization problem of a total cost model where a non-linear first-order condition needs to be solved to find the order quantity. Due to the variability of demand, it is often impossible to analytically derive the cost function’s gradient, thus the finite difference method is employed within the Newton-Raphson iteration process to approximate the gradient.To assess the method’s effectiveness, several manufacturing case scenarios with different demand profiles are used. The results show that the proposed hybrid procedure finds accurate solutions even for non-linear and non-stationary demand. The paper fills the gap between the theory of optimization and actual inventory management in the dynamic production environment by providing a flexible and widely applicable solution procedure for EOQ models with advanced elements.