The Component retrieval problem in printed circuit board assembly

The minimization of the makespan of a printed circuit board assembly process is a complex problem. Decisions involved in this problem concern the specification of the order in which components are to be placed on the board, and the assignment of component types to the feeder slots of the placement machine. If some component types are assigned to multiple feeder slots, then the additional problem emerges of selecting, for each placement on the board, the feeder slot from which the related component type is to be retrieved. In this paper, we consider this Component Retrieval Problem for placement machines that operate in a similar way as the Fuji CP II. We explain why a simple forward dynamic programming scheme cannot provide an efficient solution to this problem, thereby invalidating the correctness of an earlier published approach. We then present a polynomial algorithm that solves the problem to optimality. The analysis of the Component Retrieval Problem is greatly facilitated by its reformulation as a longest path problem in a PERT/CPM network with design aspects; Finding the minimal makespan of the assembly process thus amounts to identifying a design for which the longest path in the induced network is shortest. As an alternative interpretation, the Component Retrieval Problem can be viewed as a shortest path problem with side-constraints. The complexity of these network problems is analysed, and it is proven that the polynomial solvability of the Component Retrieval Problem is caused by the speci c structure it in icts on the arc lengths in the network. In the absence of this structure, the network problems are shown to be NP-hard in general.