Gravity models with multiple objectives-- Theory and applications

The gravity model has been widely used to predict trip matrices in transportation planning, both as a descriptive and an optimizing model. In this paper we present multiobjective programming formulations of the gravity model. The models use the concept of entropy, both as a measure of interactivity in the system, and as a distance measure, for measuring the distance from a reference or target point suggested by the planner. We also present gravity model formulations which do not require consistent estimates for the demand and supply in the different sites. These relaxed multiobjective gravity models include objectives for the demands and supplies, where the distance from some a priori given values is measured in entropy terms. The use of the models is illustrated on 1975 census data from the county of Östergötland, Sweden.