IDEAS home Printed from https://ideas.repec.org/a/inm/orijoc/v36y2024i6p1417-1435.html
   My bibliography  Save this article

Exact Solution of the Single-Picker Routing Problem with Scattered Storage

Author

Listed:
  • Katrin Heßler

    (Global Data & AI, Schenker AG, D-45128 Essen, Germany)

  • Stefan Irnich

    (Chair of Logistics Management, Gutenberg School of Management and Economics, Johannes Gutenberg University Mainz, D-55128 Mainz, Germany)

Abstract

We present a new modeling approach for the single-picker routing problem with scattered storage (SPRP-SS) for order picking in warehouses. The SPRP-SS assumes that an article is, in general, stored at more than one pick position. The task is then the simultaneous selection of pick positions for requested articles and the determination of a minimum-length picker tour collecting the articles. It is a classical result of Ratliff and Rosenthal that, for given pick positions, an optimal picker tour is a shortest path in the state space of a dynamic program with a linear number of states and transitions. We extend the state space of Ratliff and Rosenthal to include scattered storage so that every feasible picker tour is still a path. The additional requirement to make consistent decisions regarding articles to collect is not modeled in the state space so that dynamic programming can no longer be used for the solution. Instead, demand covering can be modeled as additional constraints in shortest-path problems. Therefore, we solve the resulting model with a mixed-integer (linear) programming (MIP) solver. The paper shows that this approach is not only convenient and elegant for single-block parallel-aisle warehouse SPRP-SSs but also generalizable: the solution principle can be applied to different warehouse layouts (we present additional results for a two-block parallel-aisle warehouse) and can incorporate further extensions. Computational experiments with other approaches for the SPRP-SS show that the new modeling approach outperforms the available exact algorithms regarding computational speed.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:orijoc:v:36:y:2024:i:6:p:1417-1435
    DOI: 10.1287/ijoc.2023.0075
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/ijoc.2023.0075
    Download Restriction: no
    File URL: https://libkey.io/10.1287/ijoc.2023.0075?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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. Ömer Öztürkoğlu & Kevin Gue & Russell Meller, 2012. "Optimal unit-load warehouse designs for single-command operations," IISE Transactions, Taylor & Francis Journals, vol. 44(6), pages 459-475.
    3. 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).
    4. 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.
    5. 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.
    6. 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.
    7. Kevin Gue & Russell Meller, 2009. "Aisle configurations for unit-load warehouses," IISE Transactions, Taylor & Francis Journals, vol. 41(3), pages 171-182.
    8. 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.
    9. Masae, Makusee & Glock, C. H. & Vichitkunakorn, Panupong, 2019. "Optimal Order Picker Routing in the Chevron Warehouse," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 117712, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    10. Masae, Makusee & Glock, C. H. & Vichitkunakorn, Panupong, 2019. "Optimal order picker routing in the chevron warehouse," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 119772, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Öztürkoğlu, Ömer & Hoser, Deniz, 2019. "A discrete cross aisle design model for order-picking warehouses," European Journal of Operational Research, Elsevier, vol. 275(2), pages 411-430.
    16. A. Scholz & G. Wäscher, 2017. "Order Batching and Picker Routing in manual order picking systems: the benefits of integrated routing," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(2), pages 491-520, June.
    17. 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).
    18. Masae, M. & Glock, C. H. & Vichitkunakorn, P., 2021. "A method for efficiently routing order pickers in the leaf warehouse," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 125847, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    19. 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).
    20. 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.
    21. 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.
    22. Masae, Makusee & Glock, C. H., 2019. "Optimal Order Picker Routing in the Chevron Warehouse," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 116148, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    23. Masae, Makusee & Panupong, Vichitkunakorn & Glock, C. H., 2019. "Optimal routing of order pickers in the leaf warehouse," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 115506, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    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. 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.
    2. 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.
    3. 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.
    4. Mustapha Haouassi & Yannick Kergosien & Jorge E. Mendoza & Louis-Martin Rousseau, 2022. "The integrated orderline batching, batch scheduling, and picker routing problem with multiple pickers: the benefits of splitting customer orders," Flexible Services and Manufacturing Journal, Springer, vol. 34(3), pages 614-645, September.
    5. Xie, Lin & Li, Hanyi & Luttmann, Laurin, 2023. "Formulating and solving integrated order batching and routing in multi-depot AGV-assisted mixed-shelves warehouses," European Journal of Operational Research, Elsevier, vol. 307(2), pages 713-730.
    6. 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.
    7. 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.
    8. Michele Barbato & Alberto Ceselli & Giovanni Righini, 2024. "A polynomial-time dynamic programming algorithm for an optimal picking problem in automated warehouses," Journal of Scheduling, Springer, vol. 27(4), pages 393-407, August.
    9. David Füßler & Nils Boysen & Konrad Stephan, 2019. "Trolley line picking: storage assignment and order sequencing to increase picking performance," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(4), pages 1087-1121, December.
    10. Lam, H.Y. & Ho, G.T.S. & Mo, Daniel Y. & Tang, Valerie, 2023. "Responsive pick face replenishment strategy for stock allocation to fulfil e-commerce order," International Journal of Production Economics, Elsevier, vol. 264(C).
    11. 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.
    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. 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).
    14. 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.
    15. 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).
    16. 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.
    17. Yang, Peng & Zhao, Zhijie & Guo, Huijie, 2020. "Order batch picking optimization under different storage scenarios for e-commerce warehouses," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 136(C).
    18. Tutam, Mahmut & De Koster, René, 2024. "To walk or not to walk? Designing intelligent order picking warehouses with collaborative robots," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 190(C).
    19. 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.
    20. Gharehgozli, Amir & Zaerpour, Nima, 2020. "Robot scheduling for pod retrieval in a robotic mobile fulfillment system," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 142(C).

    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:inm:orijoc:v:36:y:2024:i:6:p:1417-1435. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.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.