Abstract
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.
Highlights
This paper shows an application of mixed integer linear programming (MILP) for solving pressing process scheduling, which is a problem from real-world industry
This paper proposes an improved MILP model for solving the pressing process scheduling that outperforms the previous model in the literature [10]
The BestInteger is the current best feasible solution that could be found by the model within the time limit, and the BestBound is the current lower bound that the model could obtain within the time limit
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Scheduling an efficient pressing process requires backgrounds in assignment and sequencing to reduce the production time and to increase machine utilization. The test problems generated from the data of an actual PCB company were solved using both methods to show the performance. Approximate methods, such as a heuristic algorithm, can solve an optimization problem within a relatively short time, it can be difficult to guarantee the quality of the solution to the problem. The MILP is a type of mathematical programming model that allows an exact method to solve a scheduling problem and gives an optimal solution if one exists.
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