IDEAS home Printed from https://ideas.repec.org/a/spr/orspec/v44y2022i2d10.1007_s00291-021-00662-9.html
   My bibliography  Save this article

Analysis of semi-open queueing networks using lost customers approximation with an application to robotic mobile fulfilment systems

Author

Listed:
  • Sonja Otten

    (Leuphana University of Lüneburg
    Hamburg University of Technology)

  • Ruslan Krenzler

    (Leuphana University of Lüneburg)

  • Lin Xie

    (Leuphana University of Lüneburg)

  • Hans Daduna

    (Universität Hamburg)

  • Karsten Kruse

    (Hamburg University of Technology)

Abstract

We consider a semi-open queueing network (SOQN), where one resource from a resource pool is needed to serve a customer. If on arrival of a customer some resource is available, the resource is forwarded to an inner network to complete the customer’s order. If no resource is available, the new customer waits in an external queue until one becomes available (“backordering”). When a resource exits the inner network, it is returned to the resource pool. We develop a new solution approach. In a first step we modify the system such that new arrivals are lost if the resource pool is empty (“lost customers”). We adjust the arrival rate of the modified system such that the throughputs in all nodes of the inner network are pairwise identical to those in the original network. Using queueing theoretical methods, in a second step we reduce this inner network to a two-station system including the resource pool. For this two-station systems, we invert the first step and obtain a standard SOQN which can be solved analytically. We apply our results to storage and delivering systems with robotic mobile fulfilment systems (RMFSs). Instead of sending pickers to the storage area to search for the ordered items and pick them, robots carry shelves with ordered items from the storage area to picking stations. We model the RMFS as an SOQN to determine the minimal number of robots.

Suggested Citation

  • Sonja Otten & Ruslan Krenzler & Lin Xie & Hans Daduna & Karsten Kruse, 2022. "Analysis of semi-open queueing networks using lost customers approximation with an application to robotic mobile fulfilment systems," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(2), pages 603-648, June.
  • Handle: RePEc:spr:orspec:v:44:y:2022:i:2:d:10.1007_s00291-021-00662-9
    DOI: 10.1007/s00291-021-00662-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00291-021-00662-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s00291-021-00662-9?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Merschformann, M. & Lamballais, T. & de Koster, M.B.M. & Suhl, L., 2019. "Decision rules for robotic mobile fulfillment systems," Operations Research Perspectives, Elsevier, vol. 6(C).
    2. Zou, Bipan & Xu, Xianhao & Gong, Yeming (Yale) & De Koster, René, 2018. "Evaluating battery charging and swapping strategies in a robotic mobile fulfillment system," European Journal of Operational Research, Elsevier, vol. 267(2), pages 733-753.
    3. Bijvank, Marco & Vis, Iris F.A., 2011. "Lost-sales inventory theory: A review," European Journal of Operational Research, Elsevier, vol. 215(1), pages 1-13, November.
    4. Debjit Roy, 2016. "Semi-open queuing networks: a review of stochastic models, solution methods and new research areas," International Journal of Production Research, Taylor & Francis Journals, vol. 54(6), pages 1735-1752, March.
    5. Shanthikumar, J. George & Yao, David D., 1986. "The preservation of likelihood ratio ordering under convolution," Stochastic Processes and their Applications, Elsevier, vol. 23(2), pages 259-267, December.
    6. Ronald Buitenhek & Geert‐Jan van Houtum & Henk Zijm, 2000. "AMVA‐based solution procedures for open queueing networks with population constraints," Annals of Operations Research, Springer, vol. 93(1), pages 15-40, January.
    7. Ivo Adan & Jan Van der Wal, 1989. "Monotonicity of the Throughput of a Closed Queueing Network in the Number of Jobs," Operations Research, INFORMS, vol. 37(6), pages 953-957, December.
    8. 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.
    9. B. Avi-Itzhak & D. P. Heyman, 1973. "Approximate Queuing Models for Multiprogramming Computer Systems," Operations Research, INFORMS, vol. 21(6), pages 1212-1230, December.
    10. Jing Jia & Sunderesh S. Heragu, 2009. "Solving Semi-Open Queuing Networks," Operations Research, INFORMS, vol. 57(2), pages 391-401, April.
    11. Lamballais, T. & Roy, D. & De Koster, M.B.M., 2017. "Estimating performance in a Robotic Mobile Fulfillment System," European Journal of Operational Research, Elsevier, vol. 256(3), pages 976-990.
    12. Xie, Lin & Thieme, Nils & Krenzler, Ruslan & Li, Hanyi, 2021. "Introducing split orders and optimizing operational policies in robotic mobile fulfillment systems," European Journal of Operational Research, Elsevier, vol. 288(1), pages 80-97.
    13. Zhe Yuan & Yeming Gong, 2017. "Bot-In-Time Delivery for Robotic Mobile Fulfillment Systems," Post-Print hal-02311982, HAL.
    14. 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).
    15. Bipan Zou & Xianhao Xu & Yeming Gong & René de Koster, 2018. "Evaluating battery charging and swapping strategies in a robotic mobile fulfillment system," Post-Print hal-02312110, HAL.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kaibo Liang & Li Zhou & Jianglong Yang & Huwei Liu & Yakun Li & Fengmei Jing & Man Shan & Jin Yang, 2023. "Research on a Dynamic Task Update Assignment Strategy Based on a “Parts to Picker” Picking System," Mathematics, MDPI, vol. 11(7), pages 1-29, March.

    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. Zhuang, Yanling & Zhou, Yun & Yuan, Yufei & Hu, Xiangpei & Hassini, Elkafi, 2022. "Order picking optimization with rack-moving mobile robots and multiple workstations," European Journal of Operational Research, Elsevier, vol. 300(2), pages 527-544.
    2. Lamballais, T. & Merschformann, M. & Roy, D. & de Koster, M.B.M. & Azadeh, K. & Suhl, L., 2022. "Dynamic policies for resource reallocation in a robotic mobile fulfillment system with time-varying demand," European Journal of Operational Research, Elsevier, vol. 300(3), pages 937-952.
    3. Jiang, Min & Leung, K.H. & Lyu, Zhongyuan & Huang, George Q., 2020. "Picking-replenishment synchronization for robotic forward-reserve warehouses," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 144(C).
    4. Justkowiak, Jan-Erik & Pesch, Erwin, 2023. "Stronger mixed-integer programming-formulations for order- and rack-sequencing in robotic mobile fulfillment systems," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1063-1078.
    5. Jiang, Min & Huang, George Q., 2022. "Intralogistics synchronization in robotic forward-reserve warehouses for e-commerce last-mile delivery," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 158(C).
    6. Zhuang, Yanling & Zhou, Yun & Hassini, Elkafi & Yuan, Yufei & Hu, Xiangpei, 2022. "Rack retrieval and repositioning optimization problem in robotic mobile fulfillment systems," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 167(C).
    7. 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).
    8. Roy, Debjit & Nigam, Shobhit & de Koster, René & Adan, Ivo & Resing, Jacques, 2019. "Robot-storage zone assignment strategies in mobile fulfillment systems," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 122(C), pages 119-142.
    9. Zhuang, Yanling & Zhou, Yun & Hassini, Elkafi & Yuan, Yufei & Hu, Xiangpei, 2024. "Improving order picking efficiency through storage assignment optimization in robotic mobile fulfillment systems," European Journal of Operational Research, Elsevier, vol. 316(2), pages 718-732.
    10. Xie, Lin & Thieme, Nils & Krenzler, Ruslan & Li, Hanyi, 2021. "Introducing split orders and optimizing operational policies in robotic mobile fulfillment systems," European Journal of Operational Research, Elsevier, vol. 288(1), pages 80-97.
    11. Jianming Cai & Xiaokang Li & Yue Liang & Shan Ouyang, 2021. "Collaborative Optimization of Storage Location Assignment and Path Planning in Robotic Mobile Fulfillment Systems," Sustainability, MDPI, vol. 13(10), pages 1-26, May.
    12. Ding, Tianrong & Zhang, Yuankai & Wang, Zheng & Hu, Xiangpei, 2024. "Velocity-based rack storage location assignment for the unidirectional robotic mobile fulfillment system," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 186(C).
    13. Kaveh Azadeh & René De Koster & Debjit Roy, 2019. "Robotized and Automated Warehouse Systems: Review and Recent Developments," Transportation Science, INFORMS, vol. 53(4), pages 917-945, July.
    14. Chen, Wanying & Gong, Yeming & Chen, Qi & Wang, Hongwei, 2024. "Does battery management matter? Performance evaluation and operating policies in a self-climbing robotic warehouse," European Journal of Operational Research, Elsevier, vol. 312(1), pages 164-181.
    15. Russell Allgor & Tolga Cezik & Daniel Chen, 2023. "Algorithm for Robotic Picking in Amazon Fulfillment Centers Enables Humans and Robots to Work Together Effectively," Interfaces, INFORMS, vol. 53(4), pages 266-282, July.
    16. Kumar, Suryakant & Sheu, Jiuh-Biing & Kundu, Tanmoy, 2023. "Planning a parts-to-picker order picking system with consideration of the impact of perceived workload," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 173(C).
    17. Fragapane, Giuseppe & de Koster, René & Sgarbossa, Fabio & Strandhagen, Jan Ola, 2021. "Planning and control of autonomous mobile robots for intralogistics: Literature review and research agenda," European Journal of Operational Research, Elsevier, vol. 294(2), pages 405-426.
    18. Justkowiak, Jan-Erik & Pesch, Erwin, 2023. "A column generation driven heuristic for order-scheduling and rack-sequencing in robotic mobile fulfillment systems," Omega, Elsevier, vol. 120(C).
    19. Carmen, Raïsa & Van Nieuwenhuyse, Inneke & Van Houdt, Benny, 2018. "Inpatient boarding in emergency departments: Impact on patient delays and system capacity," European Journal of Operational Research, Elsevier, vol. 271(3), pages 953-967.
    20. Tappia, Elena & Roy, Debjit & Melacini, Marco & De Koster, René, 2019. "Integrated storage-order picking systems: Technology, performance models, and design insights," European Journal of Operational Research, Elsevier, vol. 274(3), pages 947-965.

    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:spr:orspec:v:44:y:2022:i:2:d:10.1007_s00291-021-00662-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.