Considering Assembly Relationship Complexity in U-Shaped Assembly Line Balancing

U-shaped assembly lines (U-lines), increasingly adopted in Lean Manufacturing to facilitate one-piece flow and reduce lead times, relax precedence constraints relative to straight lines. This flexibility and the expectation that operators be multi skilled increase the need to balance not only task times but also the intrinsic difficulty and interdependency of tasks. Assembly relationship complexity (ARC) — the complexity induced by interdependencies among components and tasks — has a direct effect on error rates, operator cognitive load, and product quality. U-shaped assembly line balancing (UALBP) is a critical methodology used to optimize task allocation across workstations in U-lines. Conventional UALBP methodologies predominantly emphasize cost reduction and efficiency improvements, often neglecting the critical role of ARC in determining task difficulty and, consequently, worker workload distribution. This paper addresses the U-shaped assembly line balancing problem (UALBP) by integrating an entropy-based measure of ARC. An ALBP mathematical model incorporating the proposed ARC measure alongside traditional time-based constraints and objectives is formulated in this paper. An improved NSGA-2 is developed to solve the problem. The real-world industrial case studies demonstrate that including the ARC metric leads to more equitable distributions of task difficulty. The results indicate that consideration of ARC is essential for effective U-shaped assembly line design.