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An Exact Algorithm for the Fixed Charge Transportation Problem Based on Matching Source and Sink Patterns

Author

Listed:
  • Aristide Mingozzi

    (Department of Mathematics, University of Bologna, 40126 Bologna, Italy)

  • Roberto Roberti

    (VU University Amsterdam, 1081 HV Amsterdam, Netherlands)

Abstract

This paper describes an exact algorithm for the fixed charge transportation problem based on a new integer programming formulation that involves two sets of variables representing flow patterns from sources to sinks and from sinks to sources. The formulation states to select a pattern for each source and each sink and to match the corresponding flows. The linear relaxation of this new formulation is enforced by adding a pseudo-polynomial number of equations that are shown to contain, as special cases, different valid inequalities recently proposed for the problem. The resulting lower bound dominates the lower bounds proposed in the literature. Such a lower bound is embedded into an exact branch-and-cut-and-price algorithm. Computational results on benchmark instances show that the proposed algorithm is several times faster than the state-of-the-art exact methods and could solve all open instances. New harder instances with up to 120 sources and 120 sinks were solved to optimality.

Suggested Citation

  • Aristide Mingozzi & Roberto Roberti, 2018. "An Exact Algorithm for the Fixed Charge Transportation Problem Based on Matching Source and Sink Patterns," Transportation Science, INFORMS, vol. 52(2), pages 229-238, March.
    • Handle: RePEc:inm:ortrsc:v:52:y:2018:i:2:p:229-238
    DOI: 10.1287/trsc.2017.0742
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    References listed on IDEAS

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    1. John Fisk & Patrick McKeown, 1979. "The pure fixed charge transportation problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 26(4), pages 631-641, December.
    2. Warren M. Hirsch & George B. Dantzig, 1968. "The fixed charge problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 15(3), pages 413-424, September.
    3. 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).
    4. Rardin, Ronald L. & Wolsey, Laurence A., 1993. "Valid inequalities and projecting the multicommodity extended formulation for uncapacitated fixed charge network flow problems," European Journal of Operational Research, Elsevier, vol. 71(1), pages 95-109, November.
    5. Roberto Roberti & Enrico Bartolini & Aristide Mingozzi, 2015. "The Fixed Charge Transportation Problem: An Exact Algorithm Based on a New Integer Programming Formulation," Management Science, INFORMS, vol. 61(6), pages 1275-1291, June.
    6. Zonghao Gu & George L. Nemhauser & Martin W. P. Savelsbergh, 1999. "Lifted Cover Inequalities for 0-1 Integer Programs: Complexity," INFORMS Journal on Computing, INFORMS, vol. 11(1), pages 117-123, February.
    7. Yogesh Agarwal & Yash Aneja, 2012. "Fixed-Charge Transportation Problem: Facets of the Projection Polyhedron," Operations Research, INFORMS, vol. 60(3), pages 638-654, June.
    8. Adlakha, Veena & Kowalski, Krzysztof, 2003. "A simple heuristic for solving small fixed-charge transportation problems," Omega, Elsevier, vol. 31(3), pages 205-211, June.
    9. Hultberg, Tim H. & Cardoso, Domingos M., 1997. "The teacher assignment problem: A special case of the fixed charge transportation problem," European Journal of Operational Research, Elsevier, vol. 101(3), pages 463-473, September.
    10. Warren E. Walker, 1976. "A Heuristic Adjacent Extreme Point Algorithm for the Fixed Charge Problem," Management Science, INFORMS, vol. 22(5), pages 587-596, January.
    11. Erika Buson & Roberto Roberti & Paolo Toth, 2014. "A Reduced-Cost Iterated Local Search Heuristic for the Fixed-Charge Transportation Problem," Operations Research, INFORMS, vol. 62(5), pages 1095-1106, October.
    12. Zonghao Gu & George L. Nemhauser & Martin W. P. Savelsbergh, 1998. "Lifted Cover Inequalities for 0-1 Integer Programs: Computation," INFORMS Journal on Computing, INFORMS, vol. 10(4), pages 427-437, November.
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