Max-min sum minimization transportation problem

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.