Efficient tool loading heuristic for machines with modular feeders

Abstract

<p>Numerically controlled placement machines are often equipped with modular feeder units. These allow the group loading of a large number of component reels in one step. While the loading of individual component reels has been extensively studied in the past, there has not been any algorithmic solutions published for modular feeder loading. The problem in known to be NP-hard even for a fixed job sequence. A mathematical 0-1 formulation, a lower bound on the optimal result, and an efficient heuristics will be given in the present study. The heuristic is evaluated against the lower bound, and the ratio of the heuristic result and lower bound value is reported. We found that for randomly generated problems, this ratio is between 2 and 4, while for some of the large industrial problems we obtain a ratio between 6 and 12.</p>