Against the risk of frequency instability arising from reduced system inertia due to the integration of high-proportion new energy into the power grid, this paper proposes a power system safety forewarning and auxiliary decision-making method considering minimum inertia constraints. Firstly, a dual-constraint critical inertia evaluation model is established, which calculates the critical inertia by integrating the rate of change of frequency constraint and the minimum frequency constraint, thereby improving the accuracy of the inertia safety boundary. Secondly, an equivalent inertia calculation framework for the source-grid-load-storage system is constructed to accurately calculate the total system inertia level and quantify the specific contributions of virtual inertia from conventional units and new energy sources, load inertia, and dynamic inertia from energy storage. Once the actual system inertia falls below the critical inertia threshold, a forewarning is activated and the inertia deficit is quantified; meanwhile, to minimize the system operating cost, a multi-resource optimal dispatch model incorporating inertia security constraints is developed. By coordinately adjusting the output of conventional units, the frequency regulation strategies of new energy sources, and the charging-discharging strategies of energy storage, the proposed method achieves inertia safety forewarning and auxiliary decision-making for power systems. Simulation results demonstrate that: the proposed dual-constraint inertia safety model effectively avoids the risk of missed judgment inherent in traditional single-constraint models; the proposed forewarning mechanism enables advance identification of inertia shortages and quantifies the deficit; the proposed auxiliary decision-making scheme significantly reduces system operating costs while ensuring frequency security.