Component allocation for printed circuit board assembly using modular placement machines

In automated printed circuit board (PCB) assembly, modular placement machines represent the most recent type of machinery. Similar to assembly lines they require the workload between their modules to be balanced in order to achieve the desired output rate. To optimize the operations of this type of machinery, we present an integer programming (IP) model and two different heuristic solution procedures. In the first stage of both heuristics, a feasible solution with respect to the limited component magazine capacity at each module of the placement machine is determined. Priority rules are used for generating an initial assignment of components to the various modules of the machine. In the second stage, the workload of the modules is balanced in order to minimize the resulting cycle time. Two alternative approaches are offered. The first one uses priority rules in order to de-bottleneck the workload by reassigning assembly operations to other modules of the machine, whereas the second one determines an exact solution to this sub-problem by solving an IP. The approaches presented are especially designed to consider the technological constraints arising from the design of modular placement machines. Numerical investigations reveal that optimal solutions can be obtained for all but a few extreme and hypothetical cases within short CPU times. In a case study investigation, it could be shown that the output rate of a modular placement machine is considerably increased compared with solutions applied in industry.