Nonlinear transportation problems

Abstract

Chapter 2 was devoted to the linear transportation problem. There we considered a directed arc-valuated graph (capacity restrictions!) with two vertices Q, S marked and one (return) arc (S, Q) marked of unbounded capacity. On the return arc of this graph we searched for a flow of a given value which was compatible with the capacities and minimized the transportation costs, with the costs k _ij resulting for the transportation of one product unit along the arc (i, j). The function to be minimized was

$$ Z = \sum\limits_{(i,j)} {{k_{ij}}{x_{ij}}} $$

with x _ij being the flow quantity compatible with the capacities on the arc (i, j).