A new modeling approach for the unrestricted block relocation problem

Alf Kimms () and Fabian Wilschewski ()
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Alf Kimms: University of Duisburg-Essen
Fabian Wilschewski: University of Duisburg-Essen

OR Spectrum: Quantitative Approaches in Management, 2023, vol. 45, issue 4, No 1, 1111 pages

Abstract: 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.

Keywords: Combinatorial optimization; Block relocation problem; Mixed integer linear model; Row generation (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00291-023-00728-w

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