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A Branch-and-Bound Method for the Fixed Charge Transportation Problem

Author

Listed:
  • Udatta S. Palekar

    (Department of Mechanical and Industrial Engineering, University of Illinois at Urbana Champaign, 1206 West Green Street, Urbana, Illinois 61801)

  • Mark H. Karwan

    (Department of Industrial Engineering, State University of New York at Buffalo, Buffalo, New York 14260)

  • Stanley Zionts

    (School of Management, State University of New York at Buffalo, Buffalo, New York 14260)

Abstract

In this paper we develop a new conditional penalty for the fixed charge transportation problem. This penalty is stronger than both the Driebeek penalties and the Lagrangean penalties of Cabot and Erenguc. Computational testing shows that the use of these penalties leads to significant reductions in enumeration and solution times for difficult problems in the size range tested. We also study the effect of problem parameters on the difficulty of the problem. The ratio of fixed charges to variable costs, the shape of the problem, arc density in the underlying network and fixed charge arc density are shown to have a significant effect on problem difficulty for problems involving up to 40 origins and 40 destinations.

Suggested Citation

  • Udatta S. Palekar & Mark H. Karwan & Stanley Zionts, 1990. "A Branch-and-Bound Method for the Fixed Charge Transportation Problem," Management Science, INFORMS, vol. 36(9), pages 1092-1105, September.
    • Handle: RePEc:inm:ormnsc:v:36:y:1990:i:9:p:1092-1105
    DOI: 10.1287/mnsc.36.9.1092
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    Citations

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    Cited by:

    1. 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.
    2. Sun, Minghe, 2002. "The transportation problem with exclusionary side constraints and two branch-and-bound algorithms," European Journal of Operational Research, Elsevier, vol. 140(3), pages 629-647, August.
    3. Lev, Benjamin & Kowalski, Krzysztof, 2011. "Modeling fixed-charge problems with polynomials," Omega, Elsevier, vol. 39(6), pages 725-728, December.
    4. Jesús Sáez Aguado, 2009. "Fixed Charge Transportation Problems: a new heuristic approach based on Lagrangean relaxation and the solving of core problems," Annals of Operations Research, Springer, vol. 172(1), pages 45-69, November.
    5. Dukwon Kim & Xinyan Pan & Panos Pardalos, 2006. "An Enhanced Dynamic Slope Scaling Procedure with Tabu Scheme for Fixed Charge Network Flow Problems," Computational Economics, Springer;Society for Computational Economics, vol. 27(2), pages 273-293, May.
    6. Guinet, Alain, 2001. "Multi-site planning: A transshipment problem," International Journal of Production Economics, Elsevier, vol. 74(1-3), pages 21-32, December.
    7. Sun, Minghe & Aronson, Jay E. & McKeown, Patrick G. & Drinka, Dennis, 1998. "A tabu search heuristic procedure for the fixed charge transportation problem," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 441-456, April.
    8. Gurwinder Singh & Amarinder Singh, 2021. "Solving fixed-charge transportation problem using a modified particle swarm optimization algorithm," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 12(6), pages 1073-1086, December.
    9. Yogesh Agarwal & Yash Aneja, 2012. "Fixed-Charge Transportation Problem: Facets of the Projection Polyhedron," Operations Research, INFORMS, vol. 60(3), pages 638-654, June.
    10. Francesca Maggioni & Michal Kaut & Luca Bertazzi, 2009. "Stochastic optimization models for a single-sink transportation problem," Computational Management Science, Springer, vol. 6(2), pages 251-267, May.
    11. Klose, Andreas & Drexl, Andreas, 2001. "Combinatorial optimisation problems of the assignment type and a partitioning approach," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 545, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    12. A. N. Balaji & J. Mukund Nilakantan & Izabela Nielsen & N. Jawahar & S. G. Ponnambalam, 2019. "Solving fixed charge transportation problem with truck load constraint using metaheuristics," Annals of Operations Research, Springer, vol. 273(1), pages 207-236, February.
    13. 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.
    14. Adlakha, Veena & Kowalski, Krzysztof, 2003. "A simple heuristic for solving small fixed-charge transportation problems," Omega, Elsevier, vol. 31(3), pages 205-211, June.
    15. Jeffery L. Kennington & Charles D. Nicholson, 2010. "The Uncapacitated Time-Space Fixed-Charge Network Flow Problem: An Empirical Investigation of Procedures for Arc Capacity Assignment," INFORMS Journal on Computing, INFORMS, vol. 22(2), pages 326-337, May.
    16. Gavin J. Bell & Bruce W. Lamar & Chris A. Wallace, 1999. "Capacity improvement, penalties, and the fixed charge transportation problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(4), pages 341-355, June.
    17. 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.
    18. ORTEGA, Francisco & WOLSEY, Laurence, 2000. "A branch-and-cut algorithm for the single commodity uncapacitated fixed charge network flow problem," LIDAM Discussion Papers CORE 2000049, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    19. Dimitri J. Papageorgiou & Alejandro Toriello & George L. Nemhauser & Martin W. P. Savelsbergh, 2012. "Fixed-Charge Transportation with Product Blending," Transportation Science, INFORMS, vol. 46(2), pages 281-295, May.
    20. H. Neil Geismar & Gilbert Laporte & Lei Lei & Chelliah Sriskandarajah, 2008. "The Integrated Production and Transportation Scheduling Problem for a Product with a Short Lifespan," INFORMS Journal on Computing, INFORMS, vol. 20(1), pages 21-33, February.
    21. Adlakha, Veena & Kowalski, Krzysztof, 1999. "On the fixed-charge transportation problem," Omega, Elsevier, vol. 27(3), pages 381-388, June.
    22. 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.
    23. 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.
    24. Jawahar, N. & Balaji, A.N., 2009. "A genetic algorithm for the two-stage supply chain distribution problem associated with a fixed charge," European Journal of Operational Research, Elsevier, vol. 194(2), pages 496-537, April.
    25. 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.

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