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A branching method for the fixed charge transportation problem

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  • Adlakha, Veena
  • Kowalski, Krzysztof
  • Lev, Benjamin

Abstract

This paper presents a branching method for the solution of the fixed charge transportation problem. Starting with a linear formulation of the problem, we develop the method which converges to the optimal solution. The method is based on the computation of a lower bound and an upper bound embedded within a branching process. We present a detailed numerical example to illustrate the proposed method.

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  • Adlakha, Veena & Kowalski, Krzysztof & Lev, Benjamin, 2010. "A branching method for the fixed charge transportation problem," Omega, Elsevier, vol. 38(5), pages 393-397, October.
    • Handle: RePEc:eee:jomega:v:38:y:2010:i:5:p:393-397
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    2. Kowalski, Krzysztof & Lev, Benjamin, 2008. "On step fixed-charge transportation problem," Omega, Elsevier, vol. 36(5), pages 913-917, October.
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    7. Adlakha, Veena & Kowalski, Krzysztof, 2003. "A simple heuristic for solving small fixed-charge transportation problems," Omega, Elsevier, vol. 31(3), pages 205-211, June.
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    12. Li, Jing-Quan & Borenstein, Denis & Mirchandani, Pitu B., 2008. "Truck scheduling for solid waste collection in the City of Porto Alegre, Brazil," Omega, Elsevier, vol. 36(6), pages 1133-1149, December.
    13. ORTEGA , Francisco & WOLSEY, Laurence A., 2003. "A branch-and-cut algorithm for the single-commodity, uncapacitated, fixed-charge network flow problem," LIDAM Reprints CORE 1611, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    15. YazgI Tütüncü, G. & Carreto, Carlos A.C. & Baker, Barrie M., 2009. "A visual interactive approach to classical and mixed vehicle routing problems with backhauls," Omega, Elsevier, vol. 37(1), pages 138-154, February.
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    Cited by:

    1. Bertazzi, Luca & Maggioni, Francesca, 2018. "A stochastic multi-stage fixed charge transportation problem: Worst-case analysis of the rolling horizon approach," European Journal of Operational Research, Elsevier, vol. 267(2), pages 555-569.
    2. Khurana, Archana & Adlakha, Veena & Lev, Benjamin, 2018. "Multi-index constrained transportation problem with bounds on availabilities, requirements and commodities," Operations Research Perspectives, Elsevier, vol. 5(C), pages 319-333.
    3. Adlakha, Veena & Kowalski, Krzysztof & Wang, Simi & Lev, Benjamin & Shen, Wenjing, 2014. "On approximation of the fixed charge transportation problem," Omega, Elsevier, vol. 43(C), pages 64-70.
    4. Lev, Benjamin & Kowalski, Krzysztof, 2011. "Modeling fixed-charge problems with polynomials," Omega, Elsevier, vol. 39(6), pages 725-728, December.
    5. J R Montoya-Torres & A Aponte & P Rosas, 2011. "Applying GRASP to solve the multi-item three-echelon uncapacitated facility location problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(2), pages 397-406, February.
    6. Kowalski, Krzysztof & Lev, Benjamin & Shen, Wenjing & Tu, Yan, 2014. "A fast and simple branching algorithm for solving small scale fixed-charge transportation problem," Operations Research Perspectives, Elsevier, vol. 1(1), pages 1-5.
    7. Huang, Shan-Huen & Lin, Pei-Chun, 2015. "Vehicle routing–scheduling for municipal waste collection system under the “Keep Trash off the Ground” policy," Omega, Elsevier, vol. 55(C), pages 24-37.
    8. V. Adlakha & K. Kowalski, 2015. "Fractional Polynomial Bounds for the Fixed Charge Problem," Journal of Optimization Theory and Applications, Springer, vol. 164(3), pages 1026-1038, March.
    9. Gaudioso, Manlio & Monaco, Maria Flavia & Sammarra, Marcello, 2021. "A Lagrangian heuristics for the truck scheduling problem in multi-door, multi-product Cross-Docking with constant processing time," Omega, Elsevier, vol. 101(C).
    10. Turabieh, Hamza & Abdullah, Salwani, 2011. "An integrated hybrid approach to the examination timetabling problem," Omega, Elsevier, vol. 39(6), pages 598-607, December.

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