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Relaxation Methods for Minimum Cost Ordinary and Generalized Network Flow Problems

Author

Listed:
  • Dimitri P. Bertsekas

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

  • Paul Tseng

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

Abstract

We propose a new class of algorithms for linear cost network flow problems with and without gains. These algorithms are based on iterative improvement of a dual cost and operate in a manner that is reminiscent of coordinate ascent and Gauss-Seidel relaxation methods. We compare our coded implementations of these methods with mature state-of-the-art primal simplex and primal-dual codes, and find them to be several times faster on standard benchmark problems, and faster by an order of magnitude on large, randomly generated problems. Our experiments indicate that the speedup factor increases with problem dimension.

Suggested Citation

  • Dimitri P. Bertsekas & Paul Tseng, 1988. "Relaxation Methods for Minimum Cost Ordinary and Generalized Network Flow Problems," Operations Research, INFORMS, vol. 36(1), pages 93-114, February.
    • Handle: RePEc:inm:oropre:v:36:y:1988:i:1:p:93-114
    DOI: 10.1287/opre.36.1.93
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    Citations

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    Cited by:

    1. Kraft, Edwin R., 2002. "Scheduling railway freight delivery appointments using a bid price approach," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(2), pages 145-165, February.
    2. Elsie Sterbin Gottlieb, 2002. "Solving generalized transportation problems via pure transportation problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(7), pages 666-685, October.
    3. Sharma, R. R. K. & Sharma, K. D., 2000. "A new dual based procedure for the transportation problem," European Journal of Operational Research, Elsevier, vol. 122(3), pages 611-624, May.
    4. Meyr, Herbert, 2002. "Simultaneous lotsizing and scheduling on parallel machines," European Journal of Operational Research, Elsevier, vol. 139(2), pages 277-292, June.
    5. Sebastian Lozano & Belarmino Adenso-Diaz, 2018. "Network DEA-based biobjective optimization of product flows in a supply chain," Annals of Operations Research, Springer, vol. 264(1), pages 307-323, May.
    6. P. Beraldi & F. Guerriero & R. Musmanno, 1997. "Efficient Parallel Algorithms for the Minimum Cost Flow Problem," Journal of Optimization Theory and Applications, Springer, vol. 95(3), pages 501-530, December.
    7. Balaji Gopalakrishnan & Seunghyun Kong & Earl Barnes & Ellis Johnson & Joel Sokol, 2011. "A least-squares minimum-cost network flow algorithm," Annals of Operations Research, Springer, vol. 186(1), pages 119-140, June.
    8. Antonio Frangioni & Antonio Manca, 2006. "A Computational Study of Cost Reoptimization for Min-Cost Flow Problems," INFORMS Journal on Computing, INFORMS, vol. 18(1), pages 61-70, February.
    9. B Karimi & S M T Fatemi Ghomi & J M Wilson, 2006. "A tabu search heuristic for solving the CLSP with backlogging and set-up carry-over," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(2), pages 140-147, February.
    10. Meyr, Herbert & Mann, Matthias, 2013. "A decomposition approach for the General Lotsizing and Scheduling Problem for Parallel production Lines," European Journal of Operational Research, Elsevier, vol. 229(3), pages 718-731.
    11. Carvalho, Desiree M. & Nascimento, Mariá C.V., 2022. "Hybrid matheuristics to solve the integrated lot sizing and scheduling problem on parallel machines with sequence-dependent and non-triangular setup," European Journal of Operational Research, Elsevier, vol. 296(1), pages 158-173.
    12. Jeffrey L. Huisingh & Harold M. Yamauchi & Randy Zimmerman, 2001. "Saving Federal Travel Dollars," Interfaces, INFORMS, vol. 31(5), pages 13-23, October.

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