An integrated mathematical model for optimizing the component placement process with a multi-heads placement machine

The placement machine with multi-heads is broadly applied in practice and is generally much more efficient than the machine with a single head on placing components on Printed Circuit Boards (PCBs). However, the formation of a placement process using a machine with multi-heads becomes very complicated. The component placement problem with multi-heads machine is known to be NP-hard and is usually solved by solving two sub-problems: feeders arrangement problem and components sequencing problems in sequence. Hence, the optimization is compromised. To solve the problem more effectively, an integrated mathematical model is proposed in this paper, which can represent the problem precisely. In the model, both the assignments of all feeder slots and orders of all components to be placed are treated as variables while the whole process is regarded as a series of picking-up and placing loops. Experiments show that the proposed model is efficient and applicable to solving the placement problem with multi-heads.