A Convergence-Guaranteed Nonlinear Optimization Framework for the Modified Wilson EOQ Model under Time-Dependent Demand

This study develops an extended Economic Order Quantity (EOQ) model for inventory systems under linearly increasing demand.Unlike the classical Wilson model based on constant demand assumptions, the proposed approach incorporates dynamic demand behavior within a nonlinear programming framework.The solution methodology applies the Pshenichny linearization method, transforming the original problem into auxiliary quadratic programming subproblems with guaranteed convergence properties.A numerical application demonstrates the effectiveness of the proposed model in determining optimal order quantities under changing demand conditions.The obtained results show stable convergence of the algorithm and provide optimal replenishment policies that minimize total inventory costs under time-varying demand.The numerical experiments confirm the computational efficiency of the proposed approach and illustrate its applicability to inventory systems characterized by dynamic demand patterns.The study contributes to the inventory optimization literature by introducing a convergenceguaranteed nonlinear optimization approach for dynamic-demand inventory management problems.