This paper proposes a new concept called virtual inertia scheduling (VIS) to efficiently handle the high penetration of inverter-based resources (IBRs). VIS is an inertia management framework that targets security-constrained and economy-oriented inertia scheduling and generation dispatch of power systems with a large scale of renewable generations. Specifically, it schedules the proper power setting points and reserved capacities of both synchronous generators and IBRs, as well as the control modes and control parameters of IBRs to provide secure and cost-effective inertia support. First, a uniform system model is employed to quantify the frequency dynamics of the IBRs-penetrated power system after disturbances. Based on the model, the s-domain and time-domain analytical responses of IBRs with inertia support capability are derived. Then, VIS-based real-time economic dispatch (VIS-RTED) is formulated to minimize generation and reserve costs, with a full consideration of dynamic frequency constraints and derived inertia support reserve constraints. The virtual inertia and damping of IBRs are formulated as decision variables. To address the non-linearity of dynamic constraints, deep learning-assisted linearization is employed to solve the optimization problem. Finally, the proposed VIS-RTED is demonstrated on a modified IEEE 39-bus system. A full-order time-domain simulation is performed to verify the scheduling results.