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Step fixed-charge solid transportation problem: a Lagrangian relaxation heuristic approach

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Abstract

A new large-scale optimization problem in the field of transportation engineering is introduced in this paper as step fixed-charge solid transportation problem, where products are sent from sources to destinations by some conveyances in existence of both unit and step fixed-charges. The problem has many real-world applications in transportation area. As a moderate-sized instance of this problem becomes intractable for general-purpose solvers, we propose a dual decomposition approach, which is based on a Lagrangian relaxation and capable of tackling larger instances. The Lagrangian approach is also equipped with a Lagrangian heuristic to produce upper bounds. Our extensive numerical experiments show that the approach produces high-quality solutions in very reasonable time when compared with general-purpose solvers such as CPLEX. The applicability of the step fixed-charge solid transportation problem is also shown by a real-life example of furniture production company.

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Acknowledgments

We would like to express our sincere thanks to the editors and anonymous referees of the journal for their helpful comments and suggestions which helped us to improve the quality of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran

    Masoud Sanei

  2. Department of Mathematics, Masjed-Soleiman Branch, Islamic Azad University, Masjed-Soleiman, Iran

    Ali Mahmoodirad

  3. Department of Industrial Engineering, Firouzabad Institute of Higher Education, Firouzabad, Fars, Iran

    Sadegh Niroomand

  4. Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran

    Ali Jamalian

  5. Université Lille Nord de France, 59000, Lille, France

    Shahin Gelareh

  6. Laboratoire Génie Informatique et Automatique, Université d’Artois, 62400, Béthune, France

    Shahin Gelareh

Authors
  1. Masoud Sanei
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  2. Ali Mahmoodirad
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  3. Sadegh Niroomand
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  4. Ali Jamalian
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  5. Shahin Gelareh
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Corresponding author

Correspondence to Sadegh Niroomand.

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Communicated by Andreas Fischer.

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Sanei, M., Mahmoodirad, A., Niroomand, S. et al. Step fixed-charge solid transportation problem: a Lagrangian relaxation heuristic approach. Comp. Appl. Math. 36, 1217–1237 (2017). https://doi.org/10.1007/s40314-015-0293-5

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  • DOI: https://doi.org/10.1007/s40314-015-0293-5

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