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Allocation of Transportation Units to Alternative Trips—A Column Generation Scheme with Out-of-Kilter Subproblems

Author

Listed:
  • M. R. Rao

    (United States Steel Corporation, Monroeville, Pennsylvania)

  • S. Zionts

    (United States Steel Corporation, Monroeville, Pennsylvania)

Abstract

The problem of allocating transportation units to alternative trips can be solved by linear programming. However, the linear programming formulation has three shortcomings: (1) the optimal solution obtained does not have an integer number of trips; (2) the optimal solution may have sets of disconnected cycles; and (3) problems of considerable size will be intractable because of the vast number of variables and constraints. In some applications, it has been found that shortcomings 1 and 2 are not serious, but the third one—the size of the problem—presents considerable difficulty. This paper describes an approach—a column generation scheme with out-of-kilter subproblems—that reduces the size of the problem considerably. An algorithm for the method is given, and it is proved that the algorithm solves the problem in a finite number of steps. Computational experience thus far with this method has been limited, but encouraging.

Suggested Citation

  • M. R. Rao & S. Zionts, 1968. "Allocation of Transportation Units to Alternative Trips—A Column Generation Scheme with Out-of-Kilter Subproblems," Operations Research, INFORMS, vol. 16(1), pages 52-63, February.
    • Handle: RePEc:inm:oropre:v:16:y:1968:i:1:p:52-63
    DOI: 10.1287/opre.16.1.52
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    Cited by:

    1. Gilbert Laporte, 2009. "Fifty Years of Vehicle Routing," Transportation Science, INFORMS, vol. 43(4), pages 408-416, November.
    2. Lin, Dung-Ying & Chang, Yu-Ting, 2018. "Ship routing and freight assignment problem for liner shipping: Application to the Northern Sea Route planning problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 110(C), pages 47-70.
    3. Lin, Dung-Ying & Tsai, Yu-Yun, 2014. "The ship routing and freight assignment problem for daily frequency operation of maritime liner shipping," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 67(C), pages 52-70.

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