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Using Nonlinear Mixed Integer Optimization in Printed Circuit Board Assembly

Stefan Emet, Olli S. Nevalainen, Timo Knuutila, Using Nonlinear Mixed Integer Optimization in Printed Circuit Board Assembly. In: Alexander Zemliak, Nikos Mastorakis (Eds.), Applications of Mathematics & Computer Engineering, 213-216, World Scientific and Engineering Academy and Society (WSEAS), 2011.

Abstract:

The Printed Circuit Board (PCB) assembly business is a fast paced field of industry where the manufacturers must quickly adapt their production to meet the customer requirements. The goal of the production scheduling is to prioritize jobs and optimize the usage of the production lines by allocating the jobs optimally to different lines. For the efficient usage of the production lines the workload balancing between the machines must be done properly. Balancing is usually a challenging operation and doing it consists of multiple calculations that solve the optimal placement time for each machine for different groups of components. In the present paper, the problem is modeled and solved using Mixed Integer Nonlinear Programming (MINLP) techniques. A pseudo-convex objective function for optimizing the production planning is presented. Different convexification techniques of non-linear functions are presented. The convexified model guarantees, in theory, that the global optimal solution will be found. A set of test problems are solved using the CPLEX-software. The presented techniques can easily be applied in the design of new industrial systems, and, to improve the performance of already existing ones.

BibTeX entry:

@INPROCEEDINGS{iEmNeKn11a,
  title = {Using Nonlinear Mixed Integer Optimization in Printed Circuit Board Assembly},
  booktitle = {Applications of Mathematics & Computer Engineering},
  author = {Emet, Stefan and Nevalainen, Olli S. and Knuutila, Timo},
  editor = {Zemliak, Alexander and Mastorakis, Nikos},
  publisher = {World Scientific and Engineering Academy and Society (WSEAS)},
  pages = {213-216},
  year = {2011},
  keywords = {Mixed Integer Non-Linear Programming (MINLP), Printed Circuit Board (PCB), Assembly optimization},
}

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