Joule-heated electric glass melters are highly energy-intensive and operate under stringent throughput, quality, and refractory-protection constraints, yet existing optimization approaches either rely on offline high-fidelity CFD—which is too slow for day-to-day operating decisions—or on purely data-driven energy models that do not enforce physics-based glass-quality constraints. This work presents a simulation-informed supervisory optimization framework that closes this gap by integrating (i) a high-fidelity CFD design of experiments on a cold-top electric glass melter, (ii) interpretable linear reduced-order models (ROMs) for furnace temperatures and glass-process indices (residence time, sand dissolution, mixing, and melting indices), and (iii) a convex linear-program supervisory optimizer that minimizes electrical power subject to throughput, glass-quality, and refractory-protection constraints. Sixteen CFD operating points spanning power inputs of 900–1671 kW, pull rates of 0.12–0.36 kg/s, and cullet fractions of 0–30% are used to fit and cross-validate the ROMs. The novelty of this contribution is the unification of CFD-derived multi-KPI quality constraints with a fast, interpretable supervisory optimizer suitable for advisory deployment on industrial electric melters. For a representative 1350 kW baseline, the optimizer recommends a reduced operating power of 1256 kW (~7% reduction) while satisfying all quality, throughput, and refractory constraints—demonstrating a practical ROM-enabled digital-twin pathway for energy-efficient electric glass melting.