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A data-driven distributionally robust newsvendor model with a Wasserstein ambiguity set

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  • Sangyoon Lee
  • Hyunwoo Kim
  • Ilkyeong Moon

Abstract

In this paper, we derive a closed-form solution and an explicit characterization of the worst-case distribution for the data-driven distributionally robust newsvendor model with an ambiguity set based on the Wasserstein distance of order p∈[1,∞). We also consider the risk-averse decision with the Conditional Value-at-Risk (CVaR) objective. For the risk-averse model, we derive a closed-form solution for the p = 1 case, and propose a tractable formulation to obtain an optimal order quantity for the p > 1 case. We conduct numerical experiments to compare out-of-sample performance and convergence results of the proposed solutions against the solutions with other distributionally robust models. We also analyze the risk-averse solutions compared to the risk-neutral solutions.

Suggested Citation

  • Sangyoon Lee & Hyunwoo Kim & Ilkyeong Moon, 2021. "A data-driven distributionally robust newsvendor model with a Wasserstein ambiguity set," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 72(8), pages 1879-1897, August.
    • Handle: RePEc:taf:tjorxx:v:72:y:2021:i:8:p:1879-1897
    DOI: 10.1080/01605682.2020.1746203
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    Cited by:

    1. Skalyga, Mikhail & Amelin, Mikael & Wu, Qiuwei & Söder, Lennart, 2023. "Distributionally robust day-ahead combined heat and power plants scheduling with Wasserstein Metric," Energy, Elsevier, vol. 269(C).
    2. David Winkelmann & Charlotte Kohler, 2024. "Subscription-Based Inventory Planning for E-Grocery Retailing," Papers 2404.04097, arXiv.org.
    3. Boylan, John E. & Babai, M. Zied, 2022. "Estimating the cumulative distribution function of lead-time demand using bootstrapping with and without replacement," International Journal of Production Economics, Elsevier, vol. 252(C).
    4. David Winkelmann & Matthias Ulrich & Michael Romer & Roland Langrock & Hermann Jahnke, 2022. "Dynamic Stochastic Inventory Management in E-Grocery Retailing," Papers 2205.06572, arXiv.org, revised Apr 2024.
    5. Kim, Yun Geon & Chung, Byung Do, 2024. "Data-driven Wasserstein distributionally robust dual-sourcing inventory model under uncertain demand," Omega, Elsevier, vol. 127(C).

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