The combined distribution and stochastic assignment problem

The combined distribution and assignment problem is the problem of the simultaneous determination of the distribution of trips between origins and destinations in a transportation network and the assignment of trips to routes in each origin–destination pair. In the model most widely used, the distribution is assumed to follow a gravity model with a negative exponential deterrence function and the assignment is made according to the deterministic user equilibrium principle. In this paper, we describe an extension of this model in which the allocation of trips to routes is made according to the principle of stochastic user equilibrium. We discuss the behavioural foundations of trip assignment and combined models assuming deterministic or stochastic route choice. In particular, we describe how they can be derived using the efficiency principle from discrete choice theory; the combined distribution and stochastic assignment model is obtained as the continuous approximation of the discrete problem of finding the most probable flow pattern under the assumption of efficient trip making behaviour. We outline an algorithm for the solution of the model which is based on route (column) generation, disaggregate simplicial decomposition, and partial linearization.