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DOI: 10.4230/LIPIcs.ESA.2021.79

Restricted Adaptivity in Stochastic Scheduling

Authors: Guillaume Sagnol and Daniel Schmidt genannt Waldschmidt

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract

We consider the stochastic scheduling problem of minimizing the expected makespan on m parallel identical machines. While the (adaptive) list scheduling policy achieves an approximation ratio of 2, any (non-adaptive) fixed assignment policy has performance guarantee Ω((log m)/(log log m)). Although the performance of the latter class of policies are worse, there are applications in which non-adaptive policies are desired. In this work, we introduce the two classes of δ-delay and τ-shift policies whose degree of adaptivity can be controlled by a parameter. We present a policy - belonging to both classes - which is an 𝒪(log log m)-approximation for reasonably bounded parameters. In other words, an exponential improvement on the performance of any fixed assignment policy can be achieved when allowing a small degree of adaptivity. Moreover, we provide a matching lower bound for any δ-delay and τ-shift policy when both parameters, respectively, are in the order of the expected makespan of an optimal non-anticipatory policy.

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Guillaume Sagnol and Daniel Schmidt genannt Waldschmidt. Restricted Adaptivity in Stochastic Scheduling. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 79:1-79:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{sagnol_et_al:LIPIcs.ESA.2021.79,
  author =	{Sagnol, Guillaume and Schmidt genannt Waldschmidt, Daniel},
  title =	{{Restricted Adaptivity in Stochastic Scheduling}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{79:1--79:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.79},
  URN =		{urn:nbn:de:0030-drops-146603},
  doi =		{10.4230/LIPIcs.ESA.2021.79},
  annote =	{Keywords: stochastic scheduling, makespan minimzation, approximation algorithm, fixed assignment policy, non-anticipatory policy}
}

Document

DOI: 10.4230/OASIcs.SCOR.2012.1

A Case Study on Optimizing Toll Enforcements on Motorways

Authors: Ralf Borndörfer, Guillaume Sagnol, and Elmar Swarat

Published in: OASIcs, Volume 22, 3rd Student Conference on Operational Research (2012)

Abstract

In this paper we present the problem of computing optimal tours of toll inspectors on German motorways. This problem is a special type of vehicle routing problem and builds up an integrated model, consisting of a tour planning and a duty rostering part. The tours should guarantee a network-wide control whose intensity is proportional to given spatial and time dependent traffic distributions. We model this using a space-time network and formulate the associated optimization problem by an integer program (IP). Since sequential approaches fail, we integrated the assignment of crews to the tours in our model. In this process all duties of a crew member must fit in a feasible roster. It is modeled as a Multi-Commodity Flow Problem in a directed acyclic graph, where specific paths correspond to feasible rosters for one month. We present computational results in a case-study on a German subnetwork which documents the practicability of our approach.

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Ralf Borndörfer, Guillaume Sagnol, and Elmar Swarat. A Case Study on Optimizing Toll Enforcements on Motorways. In 3rd Student Conference on Operational Research. Open Access Series in Informatics (OASIcs), Volume 22, pp. 1-10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{borndorfer_et_al:OASIcs.SCOR.2012.1,
  author =	{Bornd\"{o}rfer, Ralf and Sagnol, Guillaume and Swarat, Elmar},
  title =	{{A Case Study on Optimizing Toll Enforcements on Motorways}},
  booktitle =	{3rd Student Conference on Operational Research},
  pages =	{1--10},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-39-2},
  ISSN =	{2190-6807},
  year =	{2012},
  volume =	{22},
  editor =	{Ravizza, Stefan and Holborn, Penny},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.SCOR.2012.1},
  URN =		{urn:nbn:de:0030-drops-35418},
  doi =		{10.4230/OASIcs.SCOR.2012.1},
  annote =	{Keywords: Vehicle Routing Problem, Duty Rostering, Integer Programming, Operations Research}
}

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Documents authored by Sagnol, Guillaume

Restricted Adaptivity in Stochastic Scheduling

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A Case Study on Optimizing Toll Enforcements on Motorways

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