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A primal–dual simplex algorithm for bi-objective network flow problems

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Abstract

In this paper we develop a primal–dual simplex algorithm for the bi-objective linear minimum cost network flow problem. This algorithm improves the general primal–dual simplex algorithm for multi-objective linear programs by Ehrgott et al. (J Optim Theory Appl 134:483–497, 2007). We illustrate the algorithm with an example and provide numerical results.

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Authors and Affiliations

  1. Escola Superior de Tecnologia e Gestão, Instituto Politécnico de Leiria, Morro do Lena, Alto Vieiro, 2411-901, Leiria, Portugal

    Augusto Eusébio

  2. CEG-IST, Center for Management Studies, Instituto Superior Técnico, Technical University of Lisbon, TagusPark, Av. Cavaco Silva, 2780-990, Porto Salvo, Portugal

    Augusto Eusébio & José Rui Figueira

  3. LAMSADE, Université Paris-Dauphine, Place du Maréchal De Lattre de Tassigny, 75775, Paris Cedex 16, France

    José Rui Figueira

  4. Department of Engineering Science, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand

    Matthias Ehrgott

  5. LINA, Université de Nantes, 2, Rue de la Houssinieère, 44322, Nantes Cedex 03, France

    Matthias Ehrgott

Authors
  1. Augusto Eusébio
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  2. José Rui Figueira
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  3. Matthias Ehrgott
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Correspondence to Augusto Eusébio.

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Eusébio, A., Figueira, J.R. & Ehrgott, M. A primal–dual simplex algorithm for bi-objective network flow problems. 4OR-Q J Oper Res 7, 255–273 (2009). https://doi.org/10.1007/s10288-008-0087-3

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  • DOI: https://doi.org/10.1007/s10288-008-0087-3

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