Integer programming approach to the printed circuit board grouping problem

A printed circuit board (PCB) grouping problem arising from the electronics industry is considered. Given a surface-mounting device with a number of component feeders and several types of PCBs to be produced, the problem is how to group the PCBs so that the total set-up time for component feeders is minimized. The problem is formulated as an integer-programming problem and a column generation approach is proposed to solve it. In this approach, the original problem is decomposed into a master problem and a column-generation subproblem. Starting with a few columns in the master problem, new columns are generated successively by solving the subproblem optimally. To solve the subproblem, a branch-and-cut approach is used. To solve the master problem, a branch-and-bound algorithm is used with the generated columns. However, a branching strategy is also proposed that maintains consistency in the column-generation procedure after branching. Computational experiments show that the solution approach gives high-quality solutions in reasonable computing time.