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Online multiple one way non-preemptive time series search with interrelated prices

Author

Listed:
  • Jinghan Zhao

    (Xi’an Jiaotong University)

  • Yongxi Cheng

    (Xi’an Jiaotong University
    The State Key Lab for Manufacturing Systems Engineering)

  • Jan Eube

    (University of Bonn)

  • Haodong Liu

    (Xi’an Jiaotong University)

Abstract

This paper studies the online multiple time series search problem with interrelated prices (MTSS-ip). This perspective narrows the distance between the problem and the reality of market prices with limited variation. In MTSS-ip, the products arrive periodically, and the decision maker has a limited storage size without knowing future prices. The prices of two adjacent periods are interrelated. This study proposes an online zero-inventory algorithm (ZIA) and proves an upper bound of $$K+1-\frac{K}{\theta _2}$$ K + 1 - K θ 2 on the competitive ratio of ZIA. In addition, a lower bound on the competitive ratio of problem MTSS-ip for any deterministic online algorithm is established. For the case with a large storage size K, a lower bound of $$\frac{K}{48\log _{\theta _2} K}$$ K 48 log θ 2 K on the competitive ratio for MTSS-ip is proved.

Suggested Citation

  • Jinghan Zhao & Yongxi Cheng & Jan Eube & Haodong Liu, 2025. "Online multiple one way non-preemptive time series search with interrelated prices," Journal of Combinatorial Optimization, Springer, vol. 49(1), pages 1-21, January.
    • Handle: RePEc:spr:jcomop:v:49:y:2025:i:1:d:10.1007_s10878-024-01247-2
    DOI: 10.1007/s10878-024-01247-2
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    References listed on IDEAS

    as
    1. Hiroshi Fujiwara & Kazuo Iwama & Yoshiyuki Sekiguchi, 2011. "Average-case competitive analyses for one-way trading," Journal of Combinatorial Optimization, Springer, vol. 21(1), pages 83-107, January.
    2. Günter Schmidt, 2017. "Competitive analysis of bi-directional non-preemptive conversion," Journal of Combinatorial Optimization, Springer, vol. 34(4), pages 1096-1113, November.
    3. Wenming Zhang & Ye Zhang & Yongxi Cheng & Shankui Zheng, 2022. "An online trading problem with an increasing number of available products," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 518-531, August.
    4. Wenming Zhang & Yinfeng Xu & Feifeng Zheng & Yucheng Dong, 2012. "Optimal algorithms for online time series search and one-way trading with interrelated prices," Journal of Combinatorial Optimization, Springer, vol. 23(2), pages 159-166, February.
    5. Pascal Schroeder & Imed Kacem, 2022. "Optimal solutions for online conversion problems with interrelated prices," Operational Research, Springer, vol. 22(1), pages 423-448, March.
    Full references (including those not matched with items on IDEAS)

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