Abstract
We discuss the polynomial solvability of the minimum concave cost network flow problem (MCCNFP) with fixed numbers of sources and nonlinear arc costs and present some approximation algorithms for this variant of MCCNFP. In the single source uncapacitated case the MCCNFP is shown to be polynomially equivalent to a concave production transportation problem. A new strongly polynomial-time algorithm is presented for the latter problem, together with a new efficient approximation approach based on monotonic optimization.
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