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Robotic-Cell Scheduling: Special Polynomially Solvable Cases of the Traveling Salesman Problem on Permuted Monge Matrices

Author

Listed:
  • Vladimir G. Deineko

    (The University of Warwick)

  • George Steiner

    (McMaster University)

  • Zhihui Xue

    (McMaster University)

Abstract

In this paper, we introduce the 1 − K robotic-cell scheduling problem, whose solution can be reduced to solving a TSP on specially structured permuted Monge matrices, we call b-decomposable matrices. We also review a number of other scheduling problems which all reduce to solving TSP-s on permuted Monge matrices. We present the important insight that the TSP on b-decomposable matrices can be solved in polynomial time by a special adaptation of the well-known subtour-patching technique. We discuss efficient implementations of this algorithm on newly defined subclasses of permuted Monge matrices.

Suggested Citation

  • Vladimir G. Deineko & George Steiner & Zhihui Xue, 2005. "Robotic-Cell Scheduling: Special Polynomially Solvable Cases of the Traveling Salesman Problem on Permuted Monge Matrices," Journal of Combinatorial Optimization, Springer, vol. 9(4), pages 381-399, June.
    • Handle: RePEc:spr:jcomop:v:9:y:2005:i:4:d:10.1007_s10878-005-1778-8
    DOI: 10.1007/s10878-005-1778-8
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    References listed on IDEAS

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    1. Y. Crama & V. Kats & J. van de Klundert & E. Levner, 2000. "Cyclic scheduling in robotic flowshops," Annals of Operations Research, Springer, vol. 96(1), pages 97-124, November.
    2. Nicholas G. Hall & Hichem Kamoun & Chelliah Sriskandarajah, 1997. "Scheduling in Robotic Cells: Classification, Two and Three Machine Cells," Operations Research, INFORMS, vol. 45(3), pages 421-439, June.
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