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On the expectation of the largest gap in a warehouse

Author

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  • Rao, Subir S.
  • Adil, Gajendra K.
  • Venkitasubramony, Rakesh

Abstract

The expectation of the largest gap between two consecutive picks in an aisle is a basic building block in modelling the pick travel distance for the largest gap routing policy in a warehouse. Researchers have predominantly used either simulation or recursive algorithms for its estimation. This paper develops analytical expressions for this statistic in, both, continuous and discrete aisles using the statistical theory of ordered uniform spacings. We further demonstrate how these results can apply to the entire multi-aisle warehouse. Our results show that these expressions are accurate and extremely fast to evaluate as compared to the existing approaches.

Suggested Citation

  • Rao, Subir S. & Adil, Gajendra K. & Venkitasubramony, Rakesh, 2020. "On the expectation of the largest gap in a warehouse," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 143(C).
    • Handle: RePEc:eee:transe:v:143:y:2020:i:c:s1366554520307511
    DOI: 10.1016/j.tre.2020.102103
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    References listed on IDEAS

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    1. Dijkstra, Arjan S. & Roodbergen, Kees Jan, 2017. "Exact route-length formulas and a storage location assignment heuristic for picker-to-parts warehouses," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 102(C), pages 38-59.
    2. de Koster, Rene & Le-Duc, Tho & Roodbergen, Kees Jan, 2007. "Design and control of warehouse order picking: A literature review," European Journal of Operational Research, Elsevier, vol. 182(2), pages 481-501, October.
    3. Silva, Allyson & Coelho, Leandro C. & Darvish, Maryam & Renaud, Jacques, 2020. "Integrating storage location and order picking problems in warehouse planning," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 140(C).
    4. Donald D. Eisenstein, 2008. "Analysis and optimal design of discrete order picking technologies along a line," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(4), pages 350-362, June.
    5. Subir Rao & Gajendra Adil, 2013. "Optimal class boundaries, number of aisles, and pick list size for low-level order picking systems," IISE Transactions, Taylor & Francis Journals, vol. 45(12), pages 1309-1321.
    6. H. Donald Ratliff & Arnon S. Rosenthal, 1983. "Order-Picking in a Rectangular Warehouse: A Solvable Case of the Traveling Salesman Problem," Operations Research, INFORMS, vol. 31(3), pages 507-521, June.
    7. Gu, Jinxiang & Goetschalckx, Marc & McGinnis, Leon F., 2010. "Research on warehouse design and performance evaluation: A comprehensive review," European Journal of Operational Research, Elsevier, vol. 203(3), pages 539-549, June.
    8. Ismihan Bairamov & Alexandre Berred & Alexei Stepanov, 2010. "Limit results for ordered uniform spacings," Statistical Papers, Springer, vol. 51(1), pages 227-240, January.
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