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Solving Constrained Transportation Problems

Author

Listed:
  • D. Klingman

    (University of Texas, Austin, Texas)

  • R. Russell

    (University of Tulsa, Tulsa, Oklahoma)

Abstract

This paper presents a specialized method for solving transportation problems with several additional linear constraints. The method is basically the primal simplex method, specialized to exploit fully the topological structure embedded in the problem. It couples the poly-ω technique of C harnes and C ooper with the row-column sum method to yield an “inverse compactification” that minimizes the basis information to be stored between successive iterations, and in addition minimizes the arithmetic calculations required in pivoting. In particular, the solution procedure only requires the storage of a spanning tree and a ( q + 1) × q matrix (where q is the number of additional constraints) for each basis. The steps of updating costs and finding representations reduce to a sequence of simpler operations that utilize fully the triangularity of the spanning tree. Procedures for obtaining basic primal “feasible” starts are also presented.

Suggested Citation

  • D. Klingman & R. Russell, 1975. "Solving Constrained Transportation Problems," Operations Research, INFORMS, vol. 23(1), pages 91-106, February.
    • Handle: RePEc:inm:oropre:v:23:y:1975:i:1:p:91-106
    DOI: 10.1287/opre.23.1.91
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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. Raúl Pérez-Fernández & Bernard De Baets, 2017. "Recursive Monotonicity of the Scorix: Borda Meets Condorcet," Group Decision and Negotiation, Springer, vol. 26(4), pages 793-813, July.
    3. 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.
    4. 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.
    5. Pankaj Gupta & Mukesh Mehlawat, 2007. "An algorithm for a fuzzy transportation problem to select a new type of coal for a steel manufacturing unit," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 114-137, July.
    6. 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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