Against the risk of frequency instability arising from reduced system inertia due to the integration of highproportion new nergy into the power grid, this paper proposes a power system safety forewarning and auxiliary decisionmaking  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 multiresource 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.