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Optimal tool partitioning rules for numerically controlled punch press operations. (English) Zbl 0830.90064
Summary: The purpose of this paper is to formulate and solve an optimization problem arising in the operations of a numerical control machine such as a punch press. Holes of $$n$$ different types must be punched by a press on a linear object such as a metallic bar. Each type of hole requires a different tool and tools are mounted on a fixed rotating carousel. Holes are punched in several passes on the bar, using each time a contiguous subset of tools. The problem is to determine a partition of the tools into subsets that will minimize expected completion time. The problem is first formulated as a shortest path problem on an acyclic graph. It is shown how this problem can be solved in $$O(n^2)$$ or in $$O(n^3)$$ time and that a closed form solution can sometimes be obtained in constant time.

##### MSC:
 90B30 Production models 90C90 Applications of mathematical programming 90C35 Programming involving graphs or networks 90C60 Abstract computational complexity for mathematical programming problems
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