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A note on “A LP-based heuristic for a time-constrained routing problem”

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  • Muter, İbrahim
  • İlker Birbil, Ş.
  • Bülbül, Kerem
  • Şahin, Güvenç

Abstract

In their paper, Avella et al. (2006) investigate a time-constrained routing problem. The core of the proposed solution approach is a large-scale linear program that grows both row- and column-wise when new variables are introduced. Thus, a column-and-row generation algorithm is proposed to solve this linear program optimally, and an optimality condition is presented to terminate the column-and-row generation algorithm. We demonstrate by using Lagrangian duality that this optimality condition is incorrect and may lead to a suboptimal solution at termination.

Suggested Citation

  • Muter, İbrahim & İlker Birbil, Ş. & Bülbül, Kerem & Şahin, Güvenç, 2012. "A note on “A LP-based heuristic for a time-constrained routing problem”," European Journal of Operational Research, Elsevier, vol. 221(2), pages 306-307.
    • Handle: RePEc:eee:ejores:v:221:y:2012:i:2:p:306-307
    DOI: 10.1016/j.ejor.2012.03.048
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    References listed on IDEAS

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    1. Avella, Pasquale & D'Auria, Bernardo & Salerno, Saverio, 2006. "A LP-based heuristic for a time-constrained routing problem," European Journal of Operational Research, Elsevier, vol. 173(1), pages 120-124, August.
    2. Zak, Eugene J., 2002. "Modeling multistage cutting stock problems," European Journal of Operational Research, Elsevier, vol. 141(2), pages 313-327, September.
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    Cited by:

    1. Muter, İbrahim & Birbil, Ş. İlker & Bülbül, Kerem, 2018. "Benders decomposition and column-and-row generation for solving large-scale linear programs with column-dependent-rows," European Journal of Operational Research, Elsevier, vol. 264(1), pages 29-45.
    2. Yi Tao & Ek Peng Chew & Loo Hay Lee & Yuran Shi, 2017. "A column generation approach for the route planning problem in fourth party logistics," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(2), pages 165-181, February.
    3. Muter, İbrahim & Sezer, Zeynep, 2018. "Algorithms for the one-dimensional two-stage cutting stock problem," European Journal of Operational Research, Elsevier, vol. 271(1), pages 20-32.
    4. Dollevoet, Twan & van Essen, J. Theresia & Glorie, Kristiaan M., 2018. "Solution methods for the tray optimization problem," European Journal of Operational Research, Elsevier, vol. 271(3), pages 1070-1084.
    5. Agustín Montero & Juan José Miranda-Bront & Isabel Méndez-Díaz, 2017. "An ILP-based local search procedure for the VRP with pickups and deliveries," Annals of Operations Research, Springer, vol. 259(1), pages 327-350, December.
    6. Dollevoet, T.A.B. & van Essen, J.T. & Glorie, K.M., 2017. "Solution methods for the tray optimization problem," Econometric Institute Research Papers EI2017-16, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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