Mathematical optimization plays a pivotal role in industrial engineering by providing systematic and quantitative methods for improving complex systems. This article reviews the fundamental optimization techniques utilized in industrial engineering, focusing on linear programming, integer programming, nonlinear optimization, and metaheuristic methods. Applications range from production scheduling and supply chain management to resource allocation and quality control. Emphasis is placed on the integration of these techniques to solve real-world industrial problems efficiently. The paper also discusses recent advances in computational optimization and their impact on industry practices.