A divide and combine method for machine configuration and workload balancing problem in multiple product PCB assembly

In recent electronic industry, the assembly of electronic components on Printed Circuit Boards (PCB) is one of the most crucial tasks. Here, gantry type placement machines are popular because of the flexibility of their configurations. The Machine Configuration and (Work) Load Balancing (MCLB) problem determines the proper configurations of the machine modules in the assembly line and the allocation of the component placements among the modules minimizing the total production time. This is a difficult optimization problem, especially when the assembly line produces several batches of multiple PCB types using a common machine setup for all PCB types. In the present study, a graph model and a mathematical formulation are given for the multi-model problem (MCLB-M). A heuristic method is also presented, called Divide and Combine (DaC), which divides the multi-model problem into single product problems and solves them independently. The solutions are then combined to form a common sub-configuration of the modules. Finally, the global problem is solved by reducing its size using the fixed sub-configuration. The presented method is independent of the optimization algorithms used for the sub-problems; an integer programming model and a heuristic algorithm are used for the single problems, and an integer programming for the reduced global problem. The tests showed that the DaC method is robust and works well for problems of different size.