Modeling the machine configuration and line-balancing problem of a PCB assembly line with modular placement machines

This paper studies the combined task of determining a favorable machine configuration and line balancing (MCLB) for an assembly line where a single type of printed circuit board is assembled by a set of interconnected, reconfigurable machine modules. The MCLB problem has been solved previously by heuristic methods. In the present work, we give a mathematical formulation for it and transform the model into a linear integer programming model that can be solved using a standard solver for problems of moderate size. The model determines the best machine configuration and allocation of components to the machine modules with the objective of minimizing the cycle time. Because the solutions found in this way are globally optimal, they can be used to evaluate the efficiency of previous heuristics designed for the MCLB problem. In our experiments, an evolutionary algorithm gave near optimal results.