Approximate solution of the control problem of supplies with many intervals and concave cost functions

The problem of searching for a cost-minimum plan of supplies of uniform products to one consumer is considered. The set of admissible intervals of the supply volume and concave cost functions of supplies within each interval are preassigned for each supplier. The totally polynomial $\varepsilon$-approximate algorithm for the given problem and the pseudopolynomial exact algorithm for its partial case are suggested.