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Robust inventory problem with budgeted cumulative demand uncertainty

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Abstract

In this paper, a robust inventory problem with uncertain cumulative demands is considered. Interval-budgeted uncertainty sets are used to model possible cumulative demand scenarios. It is shown that under discrete budgeted uncertainty the robust min–max problem can be solved in polynomial time. On the other hand, for continuous budgeted uncertainty, the problem is weakly NP-hard. It can be solved in pseudopolynomial time and admits an FPTAS for nonoverlapping cumulative demand intervals.

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Acknowledgements

The authors wish to express their thanks to the anonymous referees for careful readings of the paper and for several helpful comments and suggestions that improved the presentation.

Funding

Romain Guillaume was partially supported by the project caasc ANR-18-CE10-0012 of the French National Agency for Research. Adam Kasperski and Paweł Zieliński were supported by the National Science Centre, Poland, Grant 2017/25/B/ST6/00486.

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Authors and Affiliations

  1. Université de Toulouse-IRIT, Toulouse, France

    Romain Guillaume

  2. Wrocław University of Science and Technology, Wrocław, Poland

    Adam Kasperski & Paweł Zieliński

Authors
  1. Romain Guillaume
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  2. Adam Kasperski
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  3. Paweł Zieliński
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Correspondence to Adam Kasperski.

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Guillaume, R., Kasperski, A. & Zieliński, P. Robust inventory problem with budgeted cumulative demand uncertainty. Optim Lett 16, 2543–2556 (2022). https://doi.org/10.1007/s11590-022-01875-9

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