Solving a printed circuit board assembly problem: methodology and practice

With manufacturers grappling with the complexities of managing diverse components and frequent product changes, this article addresses the need for efficient scheduling solutions in printed circuit board assembly lines, focusing on optimizing machine utilization, component placement, storage box assignment and production line balancing. The goal is to minimize total processing time while using the fewest machines. The base model presents challenges owing to decision variables in the denominator of the fractional objective function, which standard optimization tools cannot solve directly. To overcome this, an iterative algorithm is proposed that separates component assignment and storage box allocation, introduces new variables and bilinear constraints, and applies the Piecewise McCormick method for linearization. The model is then reformulated into a 0–1 Integer Programming problem, accelerating the solution process. This framework offers valuable insights for tackling component assignment challenges in electronics manufacturing.