An optimal assembly mode of multi-type printed circuit boards

We deal with the problem of assembling several types of PCBs on a machine with multiple pick-insertion heads. We partition the PCB types into subsets, which constitute the modes of operation. The subsets are selected so that the components required for assembly on the PCBs in a subset fit within the limited capacity of the reel carrier. Each PCB type in the subset is assembled successively lot-by-lot without setup between the lots. Setup is needed only in the changeover between subsets. An optimal assembly mode minimizes the sum of assembly times and setup times of all PCB types demanded. Our approach is to divide the overall problem into three sub-problems: an insertion sequence problem (ISP), a reel positioning problem (RPP), and an optimal assembly mode problem (OAMP). The ISP for each type of PCB is formulated as a traveling salesperson problem for a fixed reel positioning. The RPP is formulated as an assignment problem for which the assignment cost is the sum of the weighted tour costs of the traveling salesperson problems for the subsets of PCB types. The ISPs and RPP are solved by a heuristic algorithm based on the two-optimal local search heuristic for the traveling salesperson problem, and an evolution strategy for the RPP. The OAMP is formulated as a set partitioning problem with added traveling salesperson type constraints. The proposed algorithm was implemented on a real life problem, and the optimal assembly mode was determined.