Max–min sum minimization transportation problem

Max–min sum minimization transportation problem

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Article ID: iaor2007454
Country: Netherlands
Volume: 143
Issue: 1
Start Page Number: 265
End Page Number: 275
Publication Date: Mar 2006
Journal: Annals of Operations Research
Authors: ,
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 {tij} sorted decreasingly and Tg 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.

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