Workload balancing in printed circuit board assembly

Line balancing of a printed circuit board (PCB) assembly line is considered in the present paper. The production line consists of a number of machines for inserting electronic components on bare PCBs. The aim is to distribute the assembly operations of a single PCB type to the different machines in such a way that the throughput (i.e., the number of finished PCBs per time unit) of the line is maximized. We suppose that the total time for placements is a linear function of the number of component insertions performed by a machine. Effective mathematical formulations of the balancing problem are then available but previous models omit several aspects having an effect on the actual placement times. In particular, we extend an existing MILP formulation of the problem to consider the usage of feeder modules, precedence constraints among the placement operations, and duplication of frequently used components in several machines. We consider production lines consisting of several gantry-type placement machines. Unlike previous research, we applied standard optimization tools for solving the balancing problems. We then observed that the CPLEX-software was able to solve MILP formulations of 2- and 3-machine problems with up to 150 different component types and relatively large number of component placements (from 400 to 6,000). On the other hand, the running time was rather unstable so that heuristics are still needed for cases where exact methods fail.