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Efficient triads related to transportation problem with common pivotal time

Author

Listed:
  • Sanchita Sharma

    (Indira Gandhi Delhi Technical University for Women)

  • Rita Malhotra

    (University of Delhi)

  • Shalini Arora

    (Indira Gandhi Delhi Technical University for Women)

Abstract

The present paper discusses a transportation problem with three objectives corresponding to the concept of common pivotal time. There may be a situation when different conflicting objectives have same pivotal time but routes consuming that pivotal time for those objectives are different. This may create a trade-off situation between the objectives over that pivotal time and thus create a desire for the associated efficient solutions. This paper explores such a situation by considering three linear conflicting objectives associated with the transportation problem. An algorithm has been proposed to obtain the desired triads of three objectives corresponding to all common pivotal followed by a theoretical justification. To exhibit the algorithm, a numerical illustration has been given at the end.

Suggested Citation

  • Sanchita Sharma & Rita Malhotra & Shalini Arora, 2019. "Efficient triads related to transportation problem with common pivotal time," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(5), pages 1353-1360, October.
    • Handle: RePEc:spr:ijsaem:v:10:y:2019:i:5:d:10.1007_s13198-019-00889-4
    DOI: 10.1007/s13198-019-00889-4
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    References listed on IDEAS

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    1. Y. P. Aneja & K. P. K. Nair, 1979. "Bicriteria Transportation Problem," Management Science, INFORMS, vol. 25(1), pages 73-78, January.
    2. V. Srinivasan & G. L. Thompson, 1977. "Determining Cost vs. Time Pareto-Optimal Frontiers in Multi-Modal Transportation Problems," Transportation Science, INFORMS, vol. 11(1), pages 1-19, February.
    3. Arthur M. Geoffrion, 1967. "Solving Bicriterion Mathematical Programs," Operations Research, INFORMS, vol. 15(1), pages 39-54, February.
    4. Prakash, Satya & Kumar, Pranav & Prasad, B.V.N.S. & Gupta, Anuj, 2008. "Pareto optimal solutions of a cost-time trade-off bulk transportation problem," European Journal of Operational Research, Elsevier, vol. 188(1), pages 85-100, July.
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