Optimization of multi-feeder (depot) printed circuit board manufacturing with error guarantees

This paper considers an integrated optimization problem enhancing productivity in printed circuit board (PCB) manufacturing. The problems of assigning component types to feeder locations and sequencing component placements on the PCB are simultaneously formulated in a mathematical model. Our model differs from earlier studies by allowing component types to be placed in multiple feeders. Although such flexibility adds complexity to the original problem, we develop an integrated solution that has promising results. We develop an integrated algorithm that finds the optimal solution when the optimal solutions for the multi-depot, vehicle routing problem (MDVRP) are given. Otherwise, given an ϵ-approximation algorithm for the MDVRP, our integrated solution has a theoretical ϵ-error guarantee for PCB problem. The effectiveness of the integrated approach is shown with extensive computational experiments.