Mathematical Programming Formulation of Combined Transportation and Land Use Model

A mathematical programming model of combined trip distribution, equilibrium network assignment, and residential location choice is presented. The model is developed on the basis of Wardrop’s user equilibrium principle and the random utility theory. A traveler’s route choice behavior is assumed to follow the user-optimized principle, whereas the residential location choice behavior is captured by the random utility theory. The simultaneous choice of travel routes and residential location is based on the assumption that each individual tries to minimize his or her travel cost and maximize his or her living utility. On the basis of this assumption the choice of travel routes is determined by using a user equilibrium assignment model and the choice of residential location is quantified by using a multinomial logit model. After defining the system equations of the combined model, the model is reformulated as a mathematical programming problem so that the characteristics of the combined model can be explored clearly and the model can be solved efficiently. After the properties of the model are analyzed the process of using the gradient search technique with a maximum-likelihood criterion to calibrate the model and by using the Evans algorithm to solve the optimization problem is presented. Furthermore, the model application procedure is also clearly defined.