Tool-feeder partitions for module assignment in PCB assembly

The assembly of electronic components on printed circuit boards is performed in a line of automated placement machines, each equipped with a feeder unit that contains the component reels required for a product type. Assembling multiple product types by a single machine requires the replacement of certain components in the feeder unit. Increasingly, assembly machines are equipped with modular feeder units, enabling the replacement of a larger group of component reels. To minimize the machine setup time, component reel modules can be preassigned with the necessary component types, thus requiring only the loading of a suitable module set for each product. This work introduces and analyzes the problem of constructing the minimum number of component reel modules, with the objective that a set of jobs can be manufactured without individual component reel changes. We show that the problem is NP-hard and provide an integer programming formulation for it. We also introduce two heuristics based on job grouping, and analyze the results.