Grouping printed circuit board assembly jobs with feeders of several types

A variant of the classical job grouping problem (JGP) in printed circuit board (PCB) assembly is considered. Studies on JGPs have assumed a single feeder from which the components are retrieved and then placed on the PCB. Recent advances in technology have made it possible to use several different kinds (types) of feeders at the same time. In a JGP, the aim is to group the PCBs so that the cardinality of the grouping is minimal and each group can be processed without rearranging the contents of the feeder. In the job grouping problem with several feeder types (JGP-T) the goal is the same but instead of one linear feeder we have several feeders and each component is associated with a given feeder type which restricts its placement. We give a mathematical formulation for the JGP-T and show that it is hard to solve to optimality for problems of practical size. The connections of JGP-T to known problems are discussed. We also propose several efficient heuristics and compare their results against optimal solutions.