The main stages of printed circuit board (PCB) manufacturing are the design, fabrication, assembly, and testing. This paper focuses on the scheduling of the pressing process, which is a part of the fabrication process of a multi-layer PCB and is a new application since it has never been investigated in the literature. A novel mixed-integer linear programming (MILP) formulation for short-term scheduling of the pressing process is presented. The objective function is to minimize the makespan of the overall process. Moreover, a three-phase-PCB-pressing heuristic (3P-PCB-PH) for short-term scheduling of the pressing process is also presented. To illustrate the proposed MILP model and 3P-PCB-PH, the test problems generated from the real data acquired from a PCB company are solved. The results show that the proposed MILP model can find an optimal schedule for all small- and medium-sized problems but can do so only for some large-sized problems using the CPLEX solver within a time limit of 2 h. However, the proposed 3P-PCB-PH could find an optimal schedule for all problems that the MILP could find using much less computational time. Furthermore, it can also quickly find a near-optimal schedule for other large-sized problems that the MILP could not solved optimally.
The pressing process is a part of the fabrication process of multi-layer printed circuit board (PCB) manufacturing. This paper presents the application of a new mixed-integer linear programming model to the short-term scheduling of the pressing process. The objective was to minimize the makespan. The proposed model is an improvement from our previous model in the literature. The size complexity of the proposed model is better than that of the previous model, whereby the number of variables, constraints, and the dimensionality of variables in the previous model are reduced. To compare their performance, problems from literature and additional generated test problems were solved. The proposed model was shown to outperform the previous model in terms of computational complexity. It can verify a new optimal solution for some problems. For the problems that could not be solved optimally, the proposed model could find the incumbent solution using much less computational time than the previous model, and the makespan of the incumbent solution from the proposed model was better than or equal to that of the previous model. The proposed model can be a good option to provide an optimal schedule for the pressing process in any PCB industry.
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