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Max-min sum minimization transportation problem

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  • Sonia Puri
  • M. Puri

Abstract

A non-convex optimization problem involving minimization of the sum of max and min concave functions over a transportation polytope is studied in this paper. Based upon solving at most (g+1)(> p) cost minimizing transportation problems with m sources and n destinations, a polynomial time algorithm is proposed which minimizes the concave objective function where, p is the number of pairwise disjoint entries in the m× n time matrix {t ij } sorted decreasingly and T g is the minimum value of the max concave function. An exact global minimizer is obtained in a finite number of iterations. A numerical illustration and computational experience on the proposed algorithm is also included. Copyright Springer Science + Business Media, Inc. 2006

Suggested Citation

  • Sonia Puri & M. Puri, 2006. "Max-min sum minimization transportation problem," Annals of Operations Research, Springer, vol. 143(1), pages 265-275, March.
    • Handle: RePEc:spr:annopr:v:143:y:2006:i:1:p:265-275:10.1007/s10479-006-7387-9
    DOI: 10.1007/s10479-006-7387-9
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    References listed on IDEAS

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    1. Éva Tardos, 1986. "A Strongly Polynomial Algorithm to Solve Combinatorial Linear Programs," Operations Research, INFORMS, vol. 34(2), pages 250-256, April.
    2. Sherali, Hanif D., 1982. "Equivalent weights for lexicographic multi-objective programs: Characterizations and computations," European Journal of Operational Research, Elsevier, vol. 11(4), pages 367-379, December.
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