Selecting the nozzle assortment for a Gantry-type placement machine

Electronics manufacturing systems employ increasingly multi-head gantry machines, where several vacuum nozzles are used simultaneously in pick-and-place operations to insert components on bare PCBs. Their use includes several options that have an impact on the overall manufacturing speed of the machine. In the present paper we address the problem of selecting the nozzles for this kind of a gantry machine, which is an important subproblem of the larger scheduling problem of multi-head gantry machines. Nozzles come in different types, and different types of components may require different types of nozzles in their placing. We address first a case where a single PCB type is manufactured and the only limitation on the number of nozzles is given by the capacity of the placement head. Then we discuss the case where there is a budget limitation on the total cost of the nozzles we can buy. We show that both of these problems can be solved optimally by the means of efficient greedy algorithms. We also discuss the case of selecting nozzles when manufacturing multiple different PCB types.