This paper studies a production planning problem in printed circuit board (PCB) assembly. A PCB assembly line has several non‐identical placement machines, so the placement times by different machines are various to the same type of components. Several mathematical models are formulated in order to obtain a best assignment of components to machines with the objective of minimizing the cycle time to have the best line throughput. Moreover, the data structures of the models are analyzed and compared with other similar models to search a good available algorithm. Finally, a numerical example is provided to illustrate these models and is solved by a computer package.
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 nearoptimal 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.
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