On the Combined Distribution-Assignment of Traffic

It has been remarked that in the practice of transportation planning the distribution and assignment computations are treated sequentially as independent problems, although ideally they should be solved simultaneously. A case has been made by many practitioners for repeating the distribution and assignment computations in order to obtain more consistent results. The purpose of this paper is to shed some light on the eventual results of sequentially solving the distribution and assignment problem. Our conclusion, based on rigorous arguments, is that such practice does not lead to valid results. Also, we develop an approach to solving the distribution and assignment problem simultaneously and relate it to other methods that were proposed for this problem. A numerical example illustrates the conclusions drawn.