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A Mathematical Programming Formulation for the Single-Picker Routing Problem in a Multi-Block Layout

Author

Listed:
  • Yann Ruberg

    (Faculty of Economics and Management, Otto-von-Guericke University Magdeburg)

  • André Scholz

    (Faculty of Economics and Management, Otto-von-Guericke University Magdeburg)

Abstract

The Single-Picker Routing Problem (SPRP) arises in warehouses when items have to be retrieved from their storage locations in order to satisfy a given demand. It deals with the determination of the sequence according to which the requested items have to be picked in the picking area of the warehouse and the identification of the corresponding paths to be travelled by human operators (order pickers). The picking area typically possesses a block layout, i.e. the items are located in parallel picking aisles, and the order pickers can only change over to another picking aisle at certain positions by means of so-called cross aisles. Using this special structure, Scholz et al. (2016) developed a model formulation whose size is independent of the number of locations to be visited. They presented the model for a single-block layout and briefly described how it can be extended to the case of multiple blocks. However, by extending this formulation, the number of variables and constraints is multiplied by the number of blocks and, therefore, the model is not suitable for solving the SPRP in warehouses composed of several blocks. In this paper, the extension to multiple blocks is considered and it is pointed out how to drastically reduce the size of the formulation. Depending on the storage locations of the requested items, the number of variables can be decreased by up to 96%.

Suggested Citation

  • Yann Ruberg & André Scholz, 2016. "A Mathematical Programming Formulation for the Single-Picker Routing Problem in a Multi-Block Layout," FEMM Working Papers 160002, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    • Handle: RePEc:mag:wpaper:160002
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    References listed on IDEAS

    as
    1. Scholz, André & Henn, Sebastian & Stuhlmann, Meike & Wäscher, Gerhard, 2016. "A new mathematical programming formulation for the Single-Picker Routing Problem," European Journal of Operational Research, Elsevier, vol. 253(1), pages 68-84.
    2. 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.
    3. Roodbergen, Kees Jan & de Koster, Rene, 2001. "Routing order pickers in a warehouse with a middle aisle," European Journal of Operational Research, Elsevier, vol. 133(1), pages 32-43, August.
    4. Letchford, Adam N. & Nasiri, Saeideh D. & Theis, Dirk Oliver, 2013. "Compact formulations of the Steiner Traveling Salesman Problem and related problems," European Journal of Operational Research, Elsevier, vol. 228(1), pages 83-92.
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    Cited by:

    1. Su, Yixuan & Zhu, Xi & Yuan, Jinlong & Teo, Kok Lay & Li, Meixia & Li, Chunfa, 2023. "An extensible multi-block layout warehouse routing optimization model," European Journal of Operational Research, Elsevier, vol. 305(1), pages 222-239.
    2. Saylam, Serhat & Çelik, Melih & Süral, Haldun, 2024. "Arc routing based compact formulations for picker routing in single and two block parallel aisle warehouses," European Journal of Operational Research, Elsevier, vol. 313(1), pages 225-240.
    3. Petra Kašparová & Jakub Dyntar, 2021. "Effective Designing of Order Picking Systems Using Dynamic Simulation," Acta Informatica Pragensia, Prague University of Economics and Business, vol. 2021(1), pages 108-120.
    4. Çelik, Melih & Archetti, Claudia & Süral, Haldun, 2022. "Inventory routing in a warehouse: The storage replenishment routing problem," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1117-1132.
    5. André Scholz, 2016. "An Exact Solution Approach to the Single-Picker Routing Problem in Warehouses with an Arbitrary Block Layout," FEMM Working Papers 160006, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    6. Silva, Allyson & Roodbergen, Kees Jan & Coelho, Leandro C. & Darvish, Maryam, 2022. "Estimating optimal ABC zone sizes in manual warehouses," International Journal of Production Economics, Elsevier, vol. 252(C).

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