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On solving the order processing in picking workstations

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Abstract

The Order Processing in Picking Workstations is a real problem derived from the industry in the context of supply chain management. It looks for an efficient way to process orders arriving to a warehouse by minimizing the number of movements of goods, stored in containers in the warehouse, from their storage location to the processing zone. In this paper, we tackle this real optimization problem by providing a new Integer Linear Programming (ILP) formulation for the problem. Due to the \(\mathcal {NP}\)-Hardness of the problem we have also designed several heuristic procedures, to find high-quality solutions in a reasonable amount of time, which is mandatory for handling real instances. Particularly, the heuristics proposed were combined into a General Variable Neighborhood Search algorithm. Finally, we have performed an extensive experimentation indicating an increased performance of our proposals (ILP and heuristic) over previous approaches in the state of the art, using both synthetic and real datasets of instances.

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Acknowledgements

This research has been partially supported by Association Nationale de la Recherche et de la Technologie (France) with PhD Grant Ref. 2017/1525; by Ministerio de Economía y Competitividad (Spain) with grant ref. TIN2015-65460-C2-2-P; by Ministerio de Ciencia, Innovación y Universidades (Spain), grant ref. PGC2018-095322-B-C22; and by Comunidad de Madrid and European Regional Development Fund, grant ref. P2018/TCS-4566. Finally, we would like to thank the authors from [5] who kindly provided us with their implementation of the proposed algorithms.

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Authors and Affiliations

  1. Université Bretagne Sud, Lab-STICC, UMR 6285, CNRS, Lorient, France

    Abdessamad Ouzidan, Marc Sevaux & Alexandru-Liviu Olteanu

  2. Department of Computer Science, Universidad Rey Juan Carlos, Madrid, Spain

    Eduardo G. Pardo & Abraham Duarte

Authors
  1. Abdessamad Ouzidan
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  2. Marc Sevaux
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  3. Alexandru-Liviu Olteanu
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  4. Eduardo G. Pardo
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  5. Abraham Duarte
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Correspondence to Eduardo G. Pardo.

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Appendices

Appendix A: Mathematical models results over the synthetic dataset

In this appendix, we report the detailed results of the state-of-the-art mathematical model and the model proposed in this paper over the small (see Table 8), medium (see Table 9), and large-sized (see Table 10) synthetic instances.

Table 8 Exact results over the synthetic small-sized instances
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Table 9 Exact results over the synthetic medium-sized instances
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Table 10 Exact results over the synthetic large-sized instances
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Appendix B: Heuristics results over the synthetic dataset

In this appendix, we report the detailed results of the state-of-the-art heuristics (SA-OS and H123) and the GVNS procedure proposed in this paper over the small (see Table 11), medium (see Table 12), and large-sized (see Table 13) synthetic instances.

Table 11 Heuristics results over the small-sized instances of the synthetic dataset
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Table 12 Heuristics results comparison over the medium-size instances of the synthetic dataset
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Table 13 Heuristics results comparison over the large-size instances of the synthetic dataset
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Appendix C: Best results found for real instances

In this appendix, we report the results found by the GVNS approach over the instances of warehouse #2 (W2) with a time limit of one hour.

Table 14 GVNS results for the real instances of Warehouse #2 (W2)
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Ouzidan, A., Sevaux, M., Olteanu, AL. et al. On solving the order processing in picking workstations. Optim Lett 16, 5–35 (2022). https://doi.org/10.1007/s11590-020-01640-w

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