<p>Mathematical techniques have become indispensable for improving manufacturing processes, enhancing efficiency, reducing costs, and achieving sustainability goals. This study explores mathematical optimization models based on deterministic and probabilistic methods in steelmaking and aluminum production industries, with an emphasis on alloy addition and scrap utilization. The processes involve blending primary alloys, scraps, and additives to meet strict target chemistry requirements while addressing unique constraints such as melt efficiency, impurity control, and energy demands. Steelmaking operations prioritize tighter tolerances and oxygen management, whereas aluminum production focuses on broader grade flexibility and mitigating melt losses. The study compares traditional mass balance methods to advanced optimization models such as linear programming, mixed integer programming, and multi-objective programming, highlighting their respective applications, advantages, and limitations. Experimental validation using stainless steel blending model based on non-linear programming approach demonstrated effectiveness in optimizing cost and alloy quality. As manufacturing industries increasingly integrate Industry 4.0 and digital technologies, optimization models offer a key pathway for system integration for automation, real-time process integration, and sustainability.</p> Graphical Abstract <p></p>