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Algorithms for the minimax transportation problem

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  • R. K. Ahuja

Abstract

In this paper, we consider a variant of the classical transportation problem as well as of the bottleneck transportation problem, which we call the minimax transportation problem. The problem considered is to determine a feasible flow xij from a set of origins I to a set of destinations J for which max(i,j)εIxJ{cijxij} is minimum. In this paper, we develop a parametric algorithm and a primal‐dual algorithm to solve this problem. The parametric algorithm solves a transportation problem with parametric upper bounds and the primal‐dual algorithm solves a sequence of related maximum flow problems. The primal‐dual algorithm is shown to be polynomially bounded. Numerical investigations with both the algorithms are described in detail. The primal‐dual algorithm is found to be computationally superior to the parametric algorithm and it can solve problems up to 1000 origins, 1000 destinations and 10,000 arcs in less than 1 minute on a DEC 10 computer system. The optimum solution of the minimax transportation problem may be noninteger. We also suggest a polynomial algorithm to convert this solution into an integer optimum solution.

Suggested Citation

  • R. K. Ahuja, 1986. "Algorithms for the minimax transportation problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 33(4), pages 725-739, November.
    • Handle: RePEc:wly:navlog:v:33:y:1986:i:4:p:725-739
    DOI: 10.1002/nav.3800330415
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    Cited by:

    1. Shalabh Singh & Sonia Singh, 2022. "Shipment in a multi-choice environment: a case study of shipping carriers in US," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 30(4), pages 1195-1219, December.
    2. Takahito Kuno & Kouji Mori & Hiroshi Konno, 1989. "A mofified gub algorithm for solving linear minimax problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(3), pages 311-320, June.
    3. Prabhjot Kaur & Anuj Sharma & Vanita Verma & Kalpana Dahiya, 2022. "An alternate approach to solve two-level hierarchical time minimization transportation problem," 4OR, Springer, vol. 20(1), pages 23-61, March.
    4. Ravindra K. Ahuja & James B. Orlin, 1991. "Distance‐directed augmenting path algorithms for maximum flow and parametric maximum flow problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(3), pages 413-430, June.

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