<p>Inventory management in modern supply chains increasingly requires the integration of economic efficiency, environmental sustainability, and operational stability under uncertain demand conditions. This paper develops a sustainable inventory framework that integrates hybrid rational stochastic demand, energy-stabilized production, carbon emission penalties, and production learning effects. The proposed demand structure combines nonlinear time effects, bounded price responsiveness, and product quality sensitivity while accounting for stochastic market disturbances, thereby ensuring economically consistent demand behavior. A risk-aware optimization model is formulated using a mean–variance objective function that captures both expected profit and profit variability arising from demand uncertainty. The production system incorporates stabilization costs associated with production–demand mismatches, environmental costs arising from carbon emissions, and learning-by-doing effects that improve production efficiency over time. Analytical results establish the existence of an optimal solution and characterize the structural properties of optimal pricing and production policies. Numerical experiments under deterministic, normal, exponential, and Erlang distributions further illustrate how different demand uncertainty structures influence optimal pricing, production decisions, and risk-adjusted profitability. The resulting model remains computationally tractable and can be solved using nonlinear optimization techniques. The proposed framework provides managerial insights into the joint effects of pricing decisions, sustainability considerations, and production learning in risk-sensitive inventory systems.</p>