IDEAS home Printed from https://ideas.repec.org/p/jgu/wpaper/2508.html

Exact Solution of Picker Routing Problems in Zoned Warehouses with Scattered Storage

Author

Listed:
  • Laura Lüke

    (Johannes-Gutenberg University, Germany)

Abstract

We present two picker routing problems in a warehouse split into multiple disjoint zones with a picker assigned to each zone. Scattered storage is applied, meaning an article can be stored at several pick positions in one or more zones, and capacity restrictions limit the number of collected articles for each picker. Both problems seek picker tours that collect all requested articles, with each tour operating within one zone. While the multi-zone picker routing problem (MZPRP) minimizes the total length of all picker tours, the balanced multi-zone picker routing problem (BMZPRP) balances the tour lengths by minimizing the length of the longest picker tour. Both problems constitute a three-level optimization problem. While on the higher levels, zone assignment decisions and the selection of pick positions must be made, on the lower level, picker tours for each zone are determined. To solve both problems, we use a network-flow model with covering constraints and varying objectives. This type of model was recently presented for the single picker routing problem with scattered storage, building on an extended state space of the dynamic-programming approach by Ratliff and Rosenthal. Our model contains a network for each zone, and demand-covering constraints across all zones ensure that the requested articles are collected. Computational experiments, including large instances with up to 200 articles, show that our solution approach efficiently solves the two problems within (milli-)seconds. An analysis of the number of zones demonstrates that in larger warehouse layouts, zoning reduces costs compared to single-Zone picker routing.

Suggested Citation

  • Laura Lüke, 2025. "Exact Solution of Picker Routing Problems in Zoned Warehouses with Scattered Storage," Working Papers 2508, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    • Handle: RePEc:jgu:wpaper:2508
    as

    Download full text from publisher

    File URL: https://download.uni-mainz.de/RePEc/pdf/Discussion_Paper_2508.pdf
    File Function: first version, 2025
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Weidinger, Felix & Boysen, Nils & Schneider, Michael, 2019. "Picker routing in the mixed-shelves warehouses of e-commerce retailers," European Journal of Operational Research, Elsevier, vol. 274(2), pages 501-515.
    2. Grosse, E. H. & Glock, C. H. & Jaber, M. Y. & Neumann, W. P., 2015. "Incorporating human factors in order picking planning models: framework and research opportunities," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 65237, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    3. Maximilian Schiffer & Nils Boysen & Patrick S. Klein & Gilbert Laporte & Marco Pavone, 2022. "Optimal Picking Policies in E-Commerce Warehouses," Management Science, INFORMS, vol. 68(10), pages 7497-7517, October.
    4. Constantin Wildt & Felix Weidinger & Nils Boysen, 2025. "Picker routing in scattered storage warehouses: an evaluation of solution methods based on TSP transformations," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 47(1), pages 35-66, March.
    5. Pratik Parikh & Russell Meller, 2009. "Estimating picker blocking in wide-aisle order picking systems," IISE Transactions, Taylor & Francis Journals, vol. 41(3), pages 232-246.
    6. Eric H. Grosse & Christoph H. Glock & Mohamad Y. Jaber & W. Patrick Neumann, 2015. "Incorporating human factors in order picking planning models: framework and research opportunities," International Journal of Production Research, Taylor & Francis Journals, vol. 53(3), pages 695-717, February.
    7. 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.
    8. Singh, Kashi N. & van Oudheusden, Dirk L., 1997. "A branch and bound algorithm for the traveling purchaser problem," European Journal of Operational Research, Elsevier, vol. 97(3), pages 571-579, March.
    9. Jane, Chin-Chia & Laih, Yih-Wenn, 2005. "A clustering algorithm for item assignment in a synchronized zone order picking system," European Journal of Operational Research, Elsevier, vol. 166(2), pages 489-496, October.
    10. Julia Wahlen & Timo Gschwind, 2023. "Branch-Price-and-Cut-Based Solution of Order Batching Problems," Transportation Science, INFORMS, vol. 57(3), pages 756-777, May.
    11. 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.
    12. Masae, Makusee & Glock, Christoph H. & Grosse, Eric H., 2020. "Order picker routing in warehouses: A systematic literature review," International Journal of Production Economics, Elsevier, vol. 224(C).
    13. Katrin Heßler & Stefan Irnich, 2024. "Exact Solution of the Single-Picker Routing Problem with Scattered Storage," INFORMS Journal on Computing, INFORMS, vol. 36(6), pages 1417-1435, December.
    14. Makusee Masae & Christoph H. Glock & Panupong Vichitkunakorn, 2020. "Optimal order picker routing in the chevron warehouse," IISE Transactions, Taylor & Francis Journals, vol. 52(6), pages 665-687, June.
    15. Yu, Mengfei & de Koster, René B.M., 2009. "The impact of order batching and picking area zoning on order picking system performance," European Journal of Operational Research, Elsevier, vol. 198(2), pages 480-490, October.
    16. Wildt, Constantin & Weidinger, Felix & Boysen, Nils, 2025. "Picker routing in scattered storage warehouses: an evaluation of solution methods based on TSP transformations," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 156080, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    17. 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.
    18. 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.
    19. Weidinger, Felix & Boysen, Nils & Schneider, Michael, 2019. "Picker routing in the mixed-shelves warehouses of e-commerce retailers," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 126182, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    20. Serhat Saylam & Melih Çelik & Haldun Süral, 2023. "The min–max order picking problem in synchronised dynamic zone-picking systems," International Journal of Production Research, Taylor & Francis Journals, vol. 61(7), pages 2086-2104, April.
    21. 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.
    22. van Gils, Teun & Ramaekers, Katrien & Caris, An & de Koster, René B.M., 2018. "Designing efficient order picking systems by combining planning problems: State-of-the-art classification and review," European Journal of Operational Research, Elsevier, vol. 267(1), pages 1-15.
    23. Boysen, Nils & de Koster, René & Weidinger, Felix, 2019. "Warehousing in the e-commerce era: A survey," European Journal of Operational Research, Elsevier, vol. 277(2), pages 396-411.
    24. 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).
    25. Parikh, Pratik J. & Meller, Russell D., 2008. "Selecting between batch and zone order picking strategies in a distribution center," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 44(5), pages 696-719, September.
    26. Boysen, Nils & de Koster, René & Weidinger, Felix, 2019. "Warehousing in the e-commerce era: A survey," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 126185, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    27. Gu, Jinxiang & Goetschalckx, Marc & McGinnis, Leon F., 2007. "Research on warehouse operation: A comprehensive review," European Journal of Operational Research, Elsevier, vol. 177(1), pages 1-21, February.
    28. 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.
    29. Laura Lüke & Katrin Heßler & Stefan Irnich, 2024. "The single picker routing problem with scattered storage: modeling and evaluation of routing and storage policies," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 46(3), pages 909-951, September.
    30. Gray, Ann E. & Karmarkar, Uday S. & Seidmann, Abraham, 1992. "Design and operation of an order-consolidation warehouse: Models and application," European Journal of Operational Research, Elsevier, vol. 58(1), pages 14-36, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Boysen, Nils & de Koster, René, 2025. "50 years of warehousing research—An operations research perspective," European Journal of Operational Research, Elsevier, vol. 320(3), pages 449-464.
    2. Chen, Ran & Yang, Jingjing & Yu, Yugang, 2026. "Integrated scattered storage and picker routing in picker-to-parts warehouses," European Journal of Operational Research, Elsevier, vol. 329(3), pages 808-824.
    3. Constantin Wildt & Felix Weidinger & Nils Boysen, 2025. "Picker routing in scattered storage warehouses: an evaluation of solution methods based on TSP transformations," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 47(1), pages 35-66, March.
    4. Katrin Heßler & Stefan Irnich, 2024. "Exact Solution of the Single-Picker Routing Problem with Scattered Storage," INFORMS Journal on Computing, INFORMS, vol. 36(6), pages 1417-1435, December.
    5. Bock, Stefan & Bomsdorf, Stefan & Boysen, Nils & Schneider, Michael, 2025. "A survey on the Traveling Salesman Problem and its variants in a warehousing context," European Journal of Operational Research, Elsevier, vol. 322(1), pages 1-14.
    6. Katrin Heßler & Stefan Irnich, 2023. "Exact Solution of the Single Picker Routing Problem with Scattered Storage," Working Papers 2303, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    7. Anastasios Gialos & Vasileios Zeimpekis, 2024. "A state-of-the-art classification and review of parameters that affect the design, control, and operating strategies of order-picking systems," Operational Research, Springer, vol. 24(1), pages 1-52, March.
    8. Laura Korbacher & Katrin Heßler & Stefan Irnich, 2023. "The Single Picker Routing Problem with Scattered Storage: Modeling and Evaluation of Routing and Storage Policies," Working Papers 2302, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    9. Laura Lüke & Katrin Heßler & Stefan Irnich, 2024. "The single picker routing problem with scattered storage: modeling and evaluation of routing and storage policies," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 46(3), pages 909-951, September.
    10. Bock, Stefan & Boysen, Nils, 2025. "Stow & pick: Optimizing combined stowing and picking tours in scattered storage warehouses," European Journal of Operational Research, Elsevier, vol. 324(3), pages 1002-1016.
    11. Boysen, Nils & de Koster, René & Weidinger, Felix, 2019. "Warehousing in the e-commerce era: A survey," European Journal of Operational Research, Elsevier, vol. 277(2), pages 396-411.
    12. 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.
    13. van der Gaast, Jelmer Pier & Weidinger, Felix, 2022. "A deep learning approach for the selection of an order picking system," European Journal of Operational Research, Elsevier, vol. 302(2), pages 530-543.
    14. Onal, Sevilay & Zhu, Wen & Das, Sanchoy, 2023. "Order picking heuristics for online order fulfillment warehouses with explosive storage," International Journal of Production Economics, Elsevier, vol. 256(C).
    15. Bock, Stefan & Boysen, Nils, 2025. "Due date-oriented picker routing, an efficient exact solution algorithm, and its application to pick-from-store omnichannel retailing," European Journal of Operational Research, Elsevier, vol. 321(3), pages 775-788.
    16. Boysen, Nils & de Koster, René & Füßler, David, 2021. "The forgotten sons: Warehousing systems for brick-and-mortar retail chains," European Journal of Operational Research, Elsevier, vol. 288(2), pages 361-381.
    17. Giacomo Lanza & Mauro Passacantando & Maria Grazia Scutellà, 2023. "Sequencing and routing in a large warehouse with high degree of product rotation," Flexible Services and Manufacturing Journal, Springer, vol. 35(4), pages 1206-1255, December.
    18. 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.
    19. Prunet, Thibault & Absi, Nabil & Cattaruzza, Diego, 2025. "The storage location assignment and picker routing problem: A generic branch-cut-and-price algorithm," European Journal of Operational Research, Elsevier, vol. 327(3), pages 857-874.
    20. Gámez Albán, Harol Mauricio & Cornelissens, Trijntje & Sörensen, Kenneth, 2024. "A new policy for scattered storage assignment to minimize picking travel distances," European Journal of Operational Research, Elsevier, vol. 315(3), pages 1006-1020.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:jgu:wpaper:2508. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Research Unit IPP (email available below). General contact details of provider: https://edirc.repec.org/data/vlmaide.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.