Global solution of optimization problems with signomial parts
Discrete Optimization
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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 pseudoconvex 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.