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A new modeling approach for the unrestricted block relocation problem

Author

Listed:
  • Alf Kimms

    (University of Duisburg-Essen)

  • Fabian Wilschewski

    (University of Duisburg-Essen)

Abstract

We consider the block relocation problem (BRP), a combinatorial optimization problem that may arise in storage systems where items are organized in stacks. The objective is to retrieve all items in a predefined order with a minimal number of relocations. It can be distinguished between a restricted and an unrestricted version of the BRP. While in the restricted BRP (R-BRP) only relocations of items located above the item to be retrieved next are permitted, in the unrestricted BRP (U-BRP) all possible relocations are allowed. Existing exact methods concerning the BRP are frequently search-based methods which appear to be very effective. Nevertheless, recent literature concerning the R-BRP has shown that model-based methods can be competitive and therefore should also be taken into consideration. In this paper, we propose a new model-based approach for the U-BRP. It eliminates the fact that the number of variables is increasing with the number of necessary relocations; a disadvantage most mathematical models for the U-BRP have in common.

Suggested Citation

  • Alf Kimms & Fabian Wilschewski, 2023. "A new modeling approach for the unrestricted block relocation problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(4), pages 1071-1111, December.
    • Handle: RePEc:spr:orspec:v:45:y:2023:i:4:d:10.1007_s00291-023-00728-w
    DOI: 10.1007/s00291-023-00728-w
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