The combined distribution andstochastic assignment problem

The combined distribution and assignment problem is the problem of the simultaneousdetermination of the distribution of trips between origins and destinations in a transportationnetwork and the assignment of trips to routes in each origin - destination pair. In the modelmost widely used, the distribution is assumed to follow a gravity model with a negativeexponential deterrence function and the assignment is made according to the deterministicuser equilibrium principle. In this paper, we describe an extension of this model in whichthe 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 modelsassuming deterministic or stochastic route choice. In particular, we describe how they can bederived using the efficiency principle from discrete choice theory; the combined distributionand stochastic assignment model is obtained as the continuous approximation of the discreteproblem of finding the most probable flow pattern under the assumption of efficient tripmaking behaviour. We outline an algorithm for the solution of the model which is based onroute (column) generation, disaggregate simplicial decomposition, and partial linearization.

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