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Polynomial Time Algorithms to Minimize Total Travel Time in a Two-Depot Automated Storage/Retrieval System

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  • Amir Hossein Gharehgozli

    (Rotterdam School of Management, Erasmus University, 3062 PA Rotterdam, Netherlands)

  • Yugang Yu

    (School of Management, University of Science and Technology of China, Hefei 230026, China)

  • Xiandong Zhang

    (Department of Management Science, School of Management, Fudan University, Shanghai 200433, China)

  • RenĂ© de Koster

    (Rotterdam School of Management, Erasmus University, 3062 PA Rotterdam, Netherlands)

Abstract

We sequence storage and retrieval jobs to minimize total travel time of a storage/retrieval ( S / R ) machine in a two-depot automated storage/retrieval system. These systems include storage systems with aisle-captive S/R machines and storage blocks with bridge cranes. The S/R machine must move retrieval unit loads from their current locations in the system to one of the two depots. In addition, it must move storage unit loads from given depots to given locations in the system. We model the problem as an asymmetric traveling salesman problem, which is in general đ’©đ’«-hard. We develop an algorithm to solve the problem in polynomial time, using the property that the system has two depots and the S/R machine always returns to one of the depots to pick up or deliver a load. Furthermore, we develop additional polynomial time algorithms for the following four special cases: (1) retrieval loads have to be delivered to given depots; (2) the system has one input depot and one output depot; (3) the system has a single depot; and (4) there are arbitrary S/R machine starting and ending locations. The computational results show the effectiveness of the proposed algorithms. Compared to first-come-first-served and nearest neighbor algorithms, commonly used in practice, the total travel time reduces on average by more than 30% and 15%, respectively.

Suggested Citation

  • Amir Hossein Gharehgozli & Yugang Yu & Xiandong Zhang & RenĂ© de Koster, 2017. "Polynomial Time Algorithms to Minimize Total Travel Time in a Two-Depot Automated Storage/Retrieval System," Transportation Science, INFORMS, vol. 51(1), pages 19-33, February.
    • Handle: RePEc:inm:ortrsc:v:51:y:2017:i:1:p:19-33
    DOI: 10.1287/trsc.2014.0562
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    Cited by:

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    4. Chen, Ran & Yang, Jingjing & Yu, Yugang & Guo, Xiaolong, 2023. "Retrieval request scheduling in a shuttle-based storage and retrieval system with two lifts," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 174(C).
    5. Yang, Jingjing & de Koster, René B.M. & Guo, Xiaolong & Yu, Yugang, 2023. "Scheduling shuttles in deep-lane shuttle-based storage systems," European Journal of Operational Research, Elsevier, vol. 308(2), pages 696-708.
    6. Gharehgozli, Amir & Yu, Yugang & de Koster, René & Du, Shaofu, 2019. "Sequencing storage and retrieval requests in a container block with multiple open locations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 125(C), pages 261-284.
    7. Amir Gharehgozli & Debjit Roy & Suruchika Saini & Jan-Kees Ommeren, 2023. "Loading and unloading trains at the landside of container terminals," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 25(3), pages 549-575, September.
    8. Agra, Agostinho & Oliveira, Maryse, 2018. "MIP approaches for the integrated berth allocation and quay crane assignment and scheduling problem," European Journal of Operational Research, Elsevier, vol. 264(1), pages 138-148.
    9. Galle, Virgile & Barnhart, Cynthia & Jaillet, Patrick, 2018. "Yard Crane Scheduling for container storage, retrieval, and relocation," European Journal of Operational Research, Elsevier, vol. 271(1), pages 288-316.
    10. 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).
    11. Derhami, Shahab & Smith, Jeffrey S. & Gue, Kevin R., 2020. "A simulation-based optimization approach to design optimal layouts for block stacking warehouses," International Journal of Production Economics, Elsevier, vol. 223(C).
    12. Gharehgozli, Amir & Xu, Chao & Zhang, Wenda, 2021. "High multiplicity asymmetric traveling salesman problem with feedback vertex set and its application to storage/retrieval system," European Journal of Operational Research, Elsevier, vol. 289(2), pages 495-507.
    13. Bipan Zou & René De Koster & Xianhao Xu, 2018. "Operating Policies in Robotic Compact Storage and Retrieval Systems," Transportation Science, INFORMS, vol. 52(4), pages 788-811, August.
    14. Xiaoyi Man & Feifeng Zheng & Feng Chu & Ming Liu & Yinfeng Xu, 2021. "Bi-objective optimization for a two-depot automated storage/retrieval system," Annals of Operations Research, Springer, vol. 296(1), pages 243-262, January.
    15. Amir Gharehgozli & Nima Zaerpour & Rene Koster, 2020. "Container terminal layout design: transition and future," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 22(4), pages 610-639, December.

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