In this paper we present mathematical programming models for the problem of estimating a trip matrix from network data. The models presented are based on the results of Nguyen (1977) who has shown that trip matrices that reproduces observed linkflows in a congested network can be obtained by solving an elastic demand traffic assignment problem with a specific linear demand function.
It can be shown that this elastic traffic assignment problem has a unique optimal solution with respect to the linkflows but that the resulting trip matrix not necessarily is unique.
The mathematical programming models presented will deal with the problem of deriving one of the optimal trip matrices from Nguyens elastic demand traffic assignment problem.
Models with different choice criteria will be discussed and solution methods based on decomposition techniques will be presented for the various models.
The presented models will all be examples of implicit optimization models, i.e. optimization models in which the constraints involve another optimization model.