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Dynamic lot-sizing in sequential online retail auctions

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  • Chen, Xi
  • Ghate, Archis
  • Tripathi, Arvind

Abstract

Retailers often conduct non-overlapping sequential online auctions as a revenue generation and inventory clearing tool. We build a stochastic dynamic programming model for the seller's lot-size decision problem in these auctions. The model incorporates a random number of participating bidders in each auction, allows for any bid distribution, and is not restricted to any specific price-determination mechanism. Using stochastic monotonicity/stochastic concavity and supermodularity arguments, we present a complete structural characterization of optimal lot-sizing policies under a second order condition on the single-auction expected revenue function. We show that a monotone staircase with unit jumps policy is optimal and provide a simple inequality to determine the locations of these staircase jumps. Our analytical examples demonstrate that the second order condition is met in common online auction mechanisms. We also present numerical experiments and sensitivity analyses using real online auction data.

Suggested Citation

  • Chen, Xi & Ghate, Archis & Tripathi, Arvind, 2011. "Dynamic lot-sizing in sequential online retail auctions," European Journal of Operational Research, Elsevier, vol. 215(1), pages 257-267, November.
    • Handle: RePEc:eee:ejores:v:215:y:2011:i:1:p:257-267
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    References listed on IDEAS

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    Cited by:

    1. Wang, Hong, 2017. "Analysis and design for multi-unit online auctions," European Journal of Operational Research, Elsevier, vol. 258(3), pages 1191-1203.
    2. Ghate, Archis, 2015. "Circumventing the Slater conundrum in countably infinite linear programs," European Journal of Operational Research, Elsevier, vol. 246(3), pages 708-720.
    3. Ghate, Archis, 2015. "Optimal minimum bids and inventory scrapping in sequential, single-unit, Vickrey auctions with demand learning," European Journal of Operational Research, Elsevier, vol. 245(2), pages 555-570.
    4. Bakker, Hannah & Dunke, Fabian & Nickel, Stefan, 2020. "A structuring review on multi-stage optimization under uncertainty: Aligning concepts from theory and practice," Omega, Elsevier, vol. 96(C).
    5. Kartikeya Puranam & Michael Katehakis, 2014. "On optimal bidding and inventory control in sequential procurement auctions: the multi period case," Annals of Operations Research, Springer, vol. 217(1), pages 447-462, June.
    6. Lorentziadis, Panos L., 2016. "Optimal bidding in auctions from a game theory perspective," European Journal of Operational Research, Elsevier, vol. 248(2), pages 347-371.
    7. Katehakis, Michael N. & Puranam, Kartikeya S., 2012. "On bidding for a fixed number of items in a sequence of auctions," European Journal of Operational Research, Elsevier, vol. 222(1), pages 76-84.
    8. Jiang, Zhong-Zhong & Fang, Shu-Cherng & Fan, Zhi-Ping & Wang, Dingwei, 2013. "Selecting optimal selling format of a product in B2C online auctions with boundedly rational customers," European Journal of Operational Research, Elsevier, vol. 226(1), pages 139-153.
    9. Xu, Haoxuan & Gong, Yeming (Yale) & Chu, Chengbin & Zhang, Jinlong, 2017. "Dynamic lot-sizing models for retailers with online channels," International Journal of Production Economics, Elsevier, vol. 183(PA), pages 171-184.
    10. Yixin Lu & Alok Gupta & Wolfgang Ketter & Eric van Heck, 2019. "Dynamic Decision Making in Sequential Business-to-Business Auctions: A Structural Econometric Approach," Management Science, INFORMS, vol. 65(8), pages 3853-3876, August.
    11. Guo, Peijun & Li, Yonggang, 2014. "Approaches to multistage one-shot decision making," European Journal of Operational Research, Elsevier, vol. 236(2), pages 612-623.

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