Dimensionality Reduction-Based Integrated Optimization for Matrix System Layout Design

The manufacturing system layout optimization problem involves subproblems with interdependent relationships, necessitating an integrated optimization approach. The choice of integration approach significantly influences the complexity, search strategy, and applicable methodologies of the resulting optimization problem. Therefore, a systematic approach reflecting an understanding of the problem structure and its structural characteristics is required. This paper presents a dimensionality reduction-based integrated optimization framework for matrix system facility layout design. The layout problem is formulated from two structural perspectives: (1) a decomposition-based hierarchical formulation and (2) a dimensionality reduction-based monolithic formulation. The two problem structures are comparatively analyzed in terms of computational complexity, solution representation, and applicable optimization algorithms. A case study on automotive trim part assembly was conducted to validate the proposed framework. Optimization algorithms for the (1) decomposition, and (2) dimensionality reduction approach were implemented and compared. As a result, this paper confirmed that the proposed problem structure and optimization methodology can secure a higher expected net profit than other methodologies, and specifically, can achieve up to 96.76% improvement compared to decomposition approaches.,The originality of this paper lies in its presentation of the originality matrix system layout design as both a decomposition-based problem and a dimensionality reduction-based problem, and in its comparative analysis of the differences based on structural characteristics. The findings provide a structural perspective on optimization methodology design for matrix system-based scalable manufacturing.