Component grouping for automatic printed circuit board assembly

This paper addresses a component grouping problem in an automatic printed circuit board (PCB) assembly line with several non-identical placement machines. After the problem is defined, an integer linear programming model is formulated with the objective of minimising the cycle time of the assembly line. The integer linear programming model can be solved by the general branch-and-bound (B&B) algorithm; however, it is not efficient. So, the integer linear programming model is relaxed as a linear programming formulation because a near-optimal solution is acceptable in the real situation. A new algorithm is developed for the dual of the linear programming model. To demonstrate the efficiency of this algorithm, an example is presented and compared with its integer solution from a commercial package, CPLEX.