Inventory Strategies for Warranty Replacements of Electric Vehicle Batteries Considering Symmetric Demand Statistics

Driven by growing environmental awareness and supportive regulatory frameworks, electric vehicles (EVs) are witnessing accelerating market penetration. However, a key consumer concern remains: the economic impact of battery degradation, manifesting as vehicle depreciation and diminished driving range. To alleviate this concern, EV manufacturers commonly offer performance-guaranteed free-replacement warranties, under which batteries are replaced at no cost if capacity falls below a specified threshold within the warranty period. This paper develops a symmetry-informed analytical framework to forecast time-varying aggregate warranty replacement demand (AWRD) and to design optimal battery inventory strategies. By coupling stochastic EV sales dynamics with battery performance degradation thresholds, we construct a demand forecasting model that presents structural symmetry over time. Based on this, two inventory optimization models are proposed: the Service-Level Symmetry Model (SLSM), which prioritizes reliability and customer satisfaction, and the Cost-Efficiency Symmetry Model (CESM), which focuses on economic balance and inventory cost minimization. Comparative analysis demonstrates that CESM achieves superior cost performance, reducing total cost by 20.3% while maintaining operational stability. Moreover, incorporating CESM-derived strategies into SLSM yields a hybrid solution that preserves service-level guarantees and achieves a 3.9% cost reduction. Finally, the applicability and robustness of the AWRD forecasting framework and both symmetry-based inventory models are validated using real-world numerical data and Monte Carlo simulations. This research offers a structured and symmetrical perspective on EV battery warranty management and inventory control, aligning with the core principles of symmetry in complex system optimization.