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Solving Singly Constrained Transshipment Problems

Author

Listed:
  • F. Glover

    (University of Colorado, Boulder, Colorado)

  • D. Karney

    (The Williams Companies, Tulsa, Oklahoma)

  • D. Klingman

    (The University of Texas at Austin, Austin, Texas)

  • R. Russell

    (University of Tulsa, Tulsa, Oklahoma)

Abstract

This paper develops a primal simplex procedure to solve transshipment problems with an arbitrary additional constraint. The procedure incorporates efficient methods for pricing-out the basis, determining certain key vector representations, and implementing the change of basis. These methods exploit the near triangularity of the basis in a manner that takes advantage of computational schemes and list structures used to solve the pure transshipment problem. We have implemented these results in a computer code, I / O PNETS-I . Computational results (necessarily limited) confirm that this code is significantly faster than APEX-III on some large problems. We have also developed a fast method for determining near optimal integer solutions. Computational results show that the near optimum integer solution value is usually within 0.5% of the value of the optimum continuous solution value.

Suggested Citation

  • F. Glover & D. Karney & D. Klingman & R. Russell, 1978. "Solving Singly Constrained Transshipment Problems," Transportation Science, INFORMS, vol. 12(4), pages 277-297, November.
    • Handle: RePEc:inm:ortrsc:v:12:y:1978:i:4:p:277-297
    DOI: 10.1287/trsc.12.4.277
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    Cited by:

    1. 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.
    2. Minghe Sun, 2005. "Warm-Start Routines for Solving Augmented Weighted Tchebycheff Network Programs in Multiple-Objective Network Programming," INFORMS Journal on Computing, INFORMS, vol. 17(4), pages 422-437, November.
    3. Minghe Sun, 2003. "Procedures for Finding Nondominated Solutions for Multiple Objective Network Programming Problems," Transportation Science, INFORMS, vol. 37(2), pages 139-152, May.
    4. Holzhauser, Michael & Krumke, Sven O. & Thielen, Clemens, 2017. "A network simplex method for the budget-constrained minimum cost flow problem," European Journal of Operational Research, Elsevier, vol. 259(3), pages 864-872.
    5. ÇalIskan, Cenk, 2011. "A specialized network simplex algorithm for the constrained maximum flow problem," European Journal of Operational Research, Elsevier, vol. 210(2), pages 137-147, April.

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