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Model of megalopolises in the tool path optimisation for CNC plate cutting machines

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  • Alexander G. Chentsov
  • Pavel A. Chentsov
  • Alexander A. Petunin
  • Alexander N. Sesekin

Abstract

We consider the issues of tool path optimisation under constraints and formulate a mathematical problem of visiting megalopolises. The megalopolises model is the result of the discretisation of the tool path problem for CNC plate cutting machines. The order of visits is subject to precedence constraints. In addition, the cost functions depend on the set of pending tasks. The quality criterion is a variety of the additive criterion. The problem is established within the dynamic programming framework, however, a heuristic is proposed and implemented to solve practical problems of large dimensionality.

Suggested Citation

  • Alexander G. Chentsov & Pavel A. Chentsov & Alexander A. Petunin & Alexander N. Sesekin, 2018. "Model of megalopolises in the tool path optimisation for CNC plate cutting machines," International Journal of Production Research, Taylor & Francis Journals, vol. 56(14), pages 4819-4830, July.
    • Handle: RePEc:taf:tprsxx:v:56:y:2018:i:14:p:4819-4830
    DOI: 10.1080/00207543.2017.1421784
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    Cited by:

    1. Khachai, Daniil & Sadykov, Ruslan & Battaia, Olga & Khachay, Michael, 2023. "Precedence constrained generalized traveling salesman problem: Polyhedral study, formulations, and branch-and-cut algorithm," European Journal of Operational Research, Elsevier, vol. 309(2), pages 488-505.

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