Exact Methods for Gravity Trip-Distribution Models

Abstract

Gravity-type trip-distribution models are widely used to predict trip matrices. One of the reasons for the popularity of the gravity-type models is that simple and fast methods for computation of the trip matrices exist. These solution methods will not, however, solve the original trip-distribution problem, but an approximate problem in which the discrete and combinatorial nature of the problem is not taken into account. In this paper the solution methods for the ‘exact gravity trip-distribution model’, which is an integer programming problem, will be presented. It will be shown that with a certain amount of extra computational effort it is possible to derive the trip matrix that is the exact solution to the model and not just an asymptotic estimate of it. This also eliminates the infeasibility that will most probably occur as a result of rounding the solution to the continuous model. The solution methods presented herein are based on separable programming techniques. A one-step method is presented as well as the iterative shrinking-interval and moving-interval methods. Results that show the difference between the trip matrices produced by means of the exact method and the continuous approximation are also presented.