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An online trading problem with an increasing number of available products

Author

Listed:
  • Wenming Zhang

    (Northwest University)

  • Ye Zhang

    (Northwest University)

  • Yongxi Cheng

    (Xi’an Jiaotong University)

  • Shankui Zheng

    (Beijing Interstellar Glory Space Technology Co., Ltd.)

Abstract

In this paper, we study a multiple time series search problem in which at the first n periods, one product is produced in each period and becomes sellable. The total length of the trading horizon N ( $$N>n$$ N > n ), i.e., the total number of trading periods (which includes the first n periods when the products are produced), is unknown beforehand. All the n products are homogeneous. At each period, a price is observed and the player must decide immediately the number of available products to sell at this period, without the knowledge of future prices and when the trading horizon ends. The objective is to maximize the total revenue from selling the n products. We present an online algorithm ON for this problem and prove its competitive ratio. A lower bound on the competitive ratio for this online problem is also proved. Numerical results for the theoretical competitive ratio of algorithm ON and the lower bound are also reported.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:1:d:10.1007_s10878-021-00841-y
    DOI: 10.1007/s10878-021-00841-y
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    References listed on IDEAS

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    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. Karina Copil & Martin Wörbelauer & Herbert Meyr & Horst Tempelmeier, 2017. "Simultaneous lotsizing and scheduling problems: a classification and review of models," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(1), pages 1-64, January.
    3. Günter Schmidt, 2017. "Competitive analysis of bi-directional non-preemptive conversion," Journal of Combinatorial Optimization, Springer, vol. 34(4), pages 1096-1113, November.
    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.
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