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The bottleneck transportation problem

Author

Listed:
  • R. S. Garfinkel
  • M. R. Rao

Abstract

The bottleneck transportation problem can be stated as follows: A set of supplies and a set of demands are specified such that the total supply is equal to the total demand. There is a transportation time associated between each supply point and each demand point. It is required to find a feasible distribution (of the supplies) which minimizes the maximum transportaton time associated between a supply point and a demand point such that the distribution between the two points is positive. In addition, one may wish to find from among all optimal solutions to the bottleneck transportation problem, a solution which minimizes the total distribution that requires the maximum time Two algorithms are given for solving the above problems. One of them is a primal approach in the sense that improving fcasible solutions are obtained at each iteration. The other is a “threshold” algorithm which is found to be far superior computationally.

Suggested Citation

  • R. S. Garfinkel & M. R. Rao, 1971. "The bottleneck transportation problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 18(4), pages 465-472, December.
    • Handle: RePEc:wly:navlog:v:18:y:1971:i:4:p:465-472
    DOI: 10.1002/nav.3800180404
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    Citations

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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. Sonia & Munish Puri, 2004. "Two level hierarchical time minimizing transportation problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(2), pages 301-330, December.
    3. Prabuddha De & Jay B. Ghosh & Charles E. Wells, 1992. "On the solution of a stochastic bottleneck assignment problem and its variations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(3), pages 389-397, April.
    4. I. Stancu-Minasian & R. Caballero & E. Cerdá & M. Muñoz, 1999. "The stochastic bottleneck linear programming problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(1), pages 123-143, June.
    5. Singh, Gurwinder & Singh, Amarinder, 2023. "Extension of Particle Swarm Optimization algorithm for solving two-level time minimization transportation problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 727-742.
    6. 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.
    7. K. Mathur & M. Puri & S. Bansal, 1995. "On ranking of feasible solutions of a bottleneck linear programming problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 3(2), pages 265-283, December.
    8. Fanrong Xie & Zuoan Li, 2022. "An iterative solution technique for capacitated two-stage time minimization transportation problem," 4OR, Springer, vol. 20(4), pages 637-684, December.
    9. Abraham P. Punnen & Ruonan Zhang, 2011. "Quadratic bottleneck problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(2), pages 153-164, March.

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