Partially-linear transportation problems, obtained by means of absolute value functions

Nonlinear transportation problems may be successfully used to model problems in economics, due to the nonlinear relationship between quantities and the real cost for their transportation. In this paper we consider transportation problems with two-piece linear functions on arcs (which may be nonconvex), where the nonlinearity is represented by absolute value functions. A necessary and sufficient condition for local optimality is given and an algorithm for solving these problems is suggested.