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Modeling Single-Picker Routing Problems in Classical and Modern Warehouses

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  • Dominik Goeke

    (Deutsche Post Chair – Optimization of Distribution Networks, School of Business and Economics, RWTH Aachen University, 52062 Aachen, Germany)

  • Michael Schneider

    (Deutsche Post Chair – Optimization of Distribution Networks, School of Business and Economics, RWTH Aachen University, 52062 Aachen, Germany)

Abstract

The standard single-picker routing problem (SPRP) seeks the cost-minimal tour to collect a set of given articles in a rectangular single-block warehouse with parallel picking aisles and a dedicated storage policy, that is, each stock-keeping unit is only available from one storage location in the warehouse. We present a compact formulation that forgoes classical subtour elimination constraints by directly exploiting two of the properties of an optimal picking tour used in the dynamic programming algorithm published in the seminal paper of Ratliff and Rosenthal. We extend the formulation to three important settings prevalent in modern e-commerce warehouses: scattered storage, decoupling of picker and cart, and multiple end depots. In numerical studies, our formulation outperforms existing standard SPRP formulations from the literature and proves able to solve large instances within short runtimes. Realistically sized instances of the three problem extensions can also be solved with low computational effort. For scattered storage, we note a rough tendency that runtimes increase with longer pick lists or a higher degree of duplication. In addition, we find that decoupling of picker and cart can lead to substantial cost savings depending on the speed and capacity of the picker when traveling alone, whereas additional end depots have rather limited benefits in a single-block warehouse. Summary of Contribution: Efficiently routing order pickers is of great practical interest because picking costs make up a substantial part of operational warehouse costs. For the prevalent case of a rectangular warehouse with parallel picking aisles, we present a highly effective modeling approach that covers—in addition to the standard setting—several important storage and order-picking strategies employed in modern e-commerce warehouses: scattered storage, decoupling of picker and cart, and multiple end depots. In this way, we provide practitioners as well as scientists with an easy and quick way of implementing a high-quality solution approach for routing pickers in the described settings. In addition, we shed some light on the cost benefits of the different storage and picking strategies in numerical experiments.

Suggested Citation

  • Dominik Goeke & Michael Schneider, 2021. "Modeling Single-Picker Routing Problems in Classical and Modern Warehouses," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 436-451, May.
  • Handle: RePEc:inm:orijoc:v:33:y:2021:i:2:p:436-451
    DOI: 10.1287/ijoc.2020.1040
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    References listed on IDEAS

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    1. Felix Weidinger & Nils Boysen, 2018. "Scattered Storage: How to Distribute Stock Keeping Units All Around a Mixed-Shelves Warehouse," Service Science, INFORMS, vol. 52(6), pages 1412-1427, December.
    2. S. Lin & B. W. Kernighan, 1973. "An Effective Heuristic Algorithm for the Traveling-Salesman Problem," Operations Research, INFORMS, vol. 21(2), pages 498-516, April.
    3. Weidinger, Felix & Boysen, Nils, 2018. "Scattered Storage: How to Distribute Stock Keeping Units All Around a Mixed-Shelves Warehouse," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 126188, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    4. 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.
    5. 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.
    6. 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.
    7. Valle, Cristiano Arbex & Beasley, John E. & da Cunha, Alexandre Salles, 2017. "Optimally solving the joint order batching and picker routing problem," European Journal of Operational Research, Elsevier, vol. 262(3), pages 817-834.
    8. Weidinger, Felix, 2018. "Picker routing in rectangular mixed shelves warehouses," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 126186, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    9. Zulj, I. & Glock, C. H. & Grosse, E. H. & Schneider, Michael, 2018. "Picker routing and storage-assignment strategies for precedence-constrained order picking," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 105391, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    10. Daniels, Richard L. & Rummel, Jeffrey L. & Schantz, Robert, 1998. "A model for warehouse order picking," European Journal of Operational Research, Elsevier, vol. 105(1), pages 1-17, February.
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    Cited by:

    1. 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.
    2. Maximilian Löffler & Nils Boysen & Michael Schneider, 2022. "Picker Routing in AGV-Assisted Order Picking Systems," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 440-462, January.
    3. Vichitkunakorn, Panupong & Emde, Simon & Masae, Makusee & Glock, Christoph H. & Grosse, Eric H., 2024. "Locating charging stations and routing drones for efficient automated stocktaking," European Journal of Operational Research, Elsevier, vol. 316(3), pages 1129-1145.

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