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On a Linear-Programming, Combinatorial Approach to the Traveling-Salesman Problem

Author

Listed:
  • G. B. Dantzig

    (The Rand Corporation, Santa Monica, California)

  • D. R. Fulkerson

    (The Rand Corporation, Santa Monica, California)

  • S. M. Johnson

    (The Rand Corporation, Santa Monica, California)

Abstract

This paper elaborates a method of attack on traveling-salesman problems, proposed by the authors in an earlier paper, in which linear programming is used to reduce the combinatorial magnitude of such problems. To illustrate the method, a step-by-step solution of Barachet's ten-city example is presented.

Suggested Citation

  • G. B. Dantzig & D. R. Fulkerson & S. M. Johnson, 1959. "On a Linear-Programming, Combinatorial Approach to the Traveling-Salesman Problem," Operations Research, INFORMS, vol. 7(1), pages 58-66, February.
    • Handle: RePEc:inm:oropre:v:7:y:1959:i:1:p:58-66
    DOI: 10.1287/opre.7.1.58
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    Cited by:

    1. Akbari, Sina & Escobedo, Adolfo R., 2023. "Beyond kemeny rank aggregation: A parameterizable-penalty framework for robust ranking aggregation with ties," Omega, Elsevier, vol. 119(C).
    2. Aardal, K. & van Hoesel, C.P.M., 1995. "Polyhedral techniques in combinatorial optimization," Research Memorandum 014, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    3. Šůcha, Přemysl & Agnetis, Alessandro & Šidlovský, Marko & Briand, Cyril, 2021. "Nash equilibrium solutions in multi-agent project scheduling with milestones," European Journal of Operational Research, Elsevier, vol. 294(1), pages 29-41.
    4. Malandraki, Chryssi & Dial, Robert B., 1996. "A restricted dynamic programming heuristic algorithm for the time dependent traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 90(1), pages 45-55, April.
    5. Lee, Chia-Yen & Johnson, Andrew L. & Moreno-Centeno, Erick & Kuosmanen, Timo, 2013. "A more efficient algorithm for Convex Nonparametric Least Squares," European Journal of Operational Research, Elsevier, vol. 227(2), pages 391-400.
    6. Keshvari, Abolfazl, 2017. "A penalized method for multivariate concave least squares with application to productivity analysis," European Journal of Operational Research, Elsevier, vol. 257(3), pages 1016-1029.

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