Multiclass network toll design problem with social and spatial equity constraints

In congestion pricing, apart from the conventional social equity issue between poor and rich drivers who pay the same toll charge, there exists a spatial equity issue in the sense that the changes of the generalized travel costs of drivers travelling between different origin-destination (O-D) pairs may be significantly different when tolls are charged at some selected links, The former has been debated extensively, whereas the later is blatantly ignored in the literature. In this paper, we propose bilevel programming models for the network toll design problem by explicitly incorporating the social and spatial equity constraints in terms of the maximum relative increase of the generalized equilibrium O-D travel costs between all O-D pairs for various classes of drivers with different values of time. A penalty function approach, using a simulated annealing method, is applied for solving the equity-constrained toll design problem and demonstrated with a simple network example.