Modelling the operation optimization of multi-head surface mounting machines with over-head gantry in printed circuit board assembly

The operation optimization problem considered in this paper arises on a multi-head surface mounting machine with over-head gantry when it mounts electronic components on the surface of a printed circuit board (PCB) in PCB assembly. The aim of the problem is to minimize the time that a machine takes to mount all the required components. It is a complex optimization problem involving three inner-related sub-problems: (i) the assignment of nozzle types to heads, (ii) the assignment of feeders to slots, and (iii) the component placement optimization, specifying for each component on which head it is grasped and in which mount cycle it is processed, and in which orders the components are picked and mounted. A mathematical model with two stages is presented for it in this paper. In the first stage, nozzle assignment is formulated to a Mixed Integer Linear Programming (MILP). In the second stage, the latter two sub-problems are firstly integrated and formulated as a MILP model. The model could be solved to optimality only for very small size of problem instances.