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APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2021.23
Approximating Two-Stage Stochastic Supplier Problems

Authors: Brian Brubach, Nathaniel Grammel, David G. Harris, Aravind Srinivasan, Leonidas Tsepenekas, and Anil Vullikanti

Published in: LIPIcs, Volume 207, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)

Abstract
The main focus of this paper is radius-based (supplier) clustering in the two-stage stochastic setting with recourse, where the inherent stochasticity of the model comes in the form of a budget constraint. We also explore a number of variants where additional constraints are imposed on the first-stage decisions, specifically matroid and multi-knapsack constraints. Our eventual goal is to provide results for supplier problems in the most general distributional setting, where there is only black-box access to the underlying distribution. To that end, we follow a two-step approach. First, we develop algorithms for a restricted version of each problem, in which all possible scenarios are explicitly provided; second, we employ a novel scenario-discarding variant of the standard Sample Average Approximation (SAA) method, in which we crucially exploit properties of the restricted-case algorithms. We finally note that the scenario-discarding modification to the SAA method is necessary in order to optimize over the radius.
Cite as

Brian Brubach, Nathaniel Grammel, David G. Harris, Aravind Srinivasan, Leonidas Tsepenekas, and Anil Vullikanti. Approximating Two-Stage Stochastic Supplier Problems. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 207, pp. 23:1-23:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{brubach_et_al:LIPIcs.APPROX/RANDOM.2021.23,
  author =	{Brubach, Brian and Grammel, Nathaniel and Harris, David G. and Srinivasan, Aravind and Tsepenekas, Leonidas and Vullikanti, Anil},
  title =	{{Approximating Two-Stage Stochastic Supplier Problems}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)},
  pages =	{23:1--23:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-207-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{207},
  editor =	{Wootters, Mary and Sanit\`{a}, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2021.23},
  URN =		{urn:nbn:de:0030-drops-147163},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2021.23},
  annote =	{Keywords: Approximation Algorithms, Stochastic Optimization, Two-Stage Recourse Model, Clustering Problems, Knapsack Supplier}
}
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