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Routing two stacking cranes with predetermined container sequences

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  • Dirk Briskorn

    (Bergische Universität Wuppertal)

Abstract

The scheduling of gantry cranes with respect to mutual interference has received considerable attention in recent years. We consider a subproblem which arises when each crane has a sequence of tasks to be assigned. The problem is concerned with resolving the interference between two cranes by determining which crane avoids the other in order to let it complete its next task first. We provide a fairly general problem framework accounting for different crane systems and various side constraints. We assume a cost function for each task that determines the cost of completing the task at a specific point in time. We then distinguish between the objectives to minimize both the total cost and the maximum cost among tasks. A general dynamic programming framework is provided which allows us to solve all problem versions in pseudo-polynomial time. Furthermore, we show that while the general problem aiming for minimum total cost is binary NP-hard, the general problem aiming for minimum maximum cost can be solved in polynomial time. Finally, we address two important special cases of the former, and we show that they can be solved in polynomial time as well.

Suggested Citation

  • Dirk Briskorn, 2021. "Routing two stacking cranes with predetermined container sequences," Journal of Scheduling, Springer, vol. 24(4), pages 367-380, August.
    • Handle: RePEc:spr:jsched:v:24:y:2021:i:4:d:10.1007_s10951-021-00689-4
    DOI: 10.1007/s10951-021-00689-4
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    References listed on IDEAS

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    1. Gharehgozli, Amir Hossein & Yu, Yugang & de Koster, René & Udding, Jan Tijmen, 2014. "An exact method for scheduling a yard crane," European Journal of Operational Research, Elsevier, vol. 235(2), pages 431-447.
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    8. Nils Boysen & Dirk Briskorn & Simon Emde, 2015. "A decomposition heuristic for the twin robots scheduling problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(1), pages 16-22, February.
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    14. Dirk Briskorn & Lennart Zey, 2020. "Interference aware scheduling of triple-crossover-cranes," Journal of Scheduling, Springer, vol. 23(4), pages 465-485, August.
    15. Dirk Briskorn & Lennart Zey, 2018. "Resolving interferences of triple‐crossover‐cranes by determining paths in networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(6-7), pages 477-498, September.
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    17. Boysen, Nils & Briskorn, Dirk & Meisel, Frank, 2017. "A generalized classification scheme for crane scheduling with interference," European Journal of Operational Research, Elsevier, vol. 258(1), pages 343-357.
    18. Amir Hossein Gharehgozli & Gilbert Laporte & Yugang Yu & René de Koster, 2015. "Scheduling Twin Yard Cranes in a Container Block," Transportation Science, INFORMS, vol. 49(3), pages 686-705, August.
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    Cited by:

    1. Lennart Zey & Dirk Briskorn & Nils Boysen, 2022. "Twin-crane scheduling during seaside workload peaks with a dedicated handshake area," Journal of Scheduling, Springer, vol. 25(1), pages 3-34, February.

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