Acta Mathematica Vietnamica

In this paper, we extend the parametrization technique of Tuy et al. into a class of concave production-transportation problems with $m$ $(\geq 3)$ sources, $n$ terminals and three nonlinear variables. We develop a depth-first-search algorithm for finding a globally optimal solution of this rank three concave minimization problem and show that the algorithm is pseudo-polynonomial in the problem input length but polynomial in $m$ and $n$.

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