Linear approximations in a dynamic programming approach for the uncapacitated single-source minimum concave cost network flow problem in acyclic networks
Re. Burkard et al., Linear approximations in a dynamic programming approach for the uncapacitated single-source minimum concave cost network flow problem in acyclic networks, J GLOB OPT, 19(2), 2001, pp. 121-139
We consider minimum concave cost flow problems in acyclic, uncapacitated ne
tworks with a single source. For these problems a dynamic programming schem
e is developed. It is shown that the concave cost functions on the arcs can
be approximated by linear functions. Thus the considered problem can be so
lved by a series of linear programs. This approximation method, whose conve
rgence is shown, works particularly well, if the nodes of the network have
small degrees. Computational results on several classes of networks are rep
orted.