Imposing precedence constraints on NC punch press sequences

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Abstract
A few years ago D. Dornfeld, R. Gil and I addressed the problem of numerically controlled punch press sequencing, but did not formally treat the obstacle of how to impose precedence constraints on the sequences (Svestka et al. 1981). This has been accomplished by partitioning the problem into smaller problems and patching them together to satisfy the constraints, or by direct construction of such sequences, usually involving the closest unvisited city (CUC) heuristic. However, these approaches do have some difficulties. For example, the CUC heuristic can fail to generate a feasible solution for such problems even though solutions can be shown to exist. Here, we introduce a new method for imposing precedence constraints, which either finds a feasible solution or shows that there are none. The method can also be more efficient that CUC, for problems with more than 30 hits.