Equitable Network Design

The Network Design Problem (NDP) refers to the optimization problem faced by a planner whose aim is to improve a transport network, drawing on limited resources. Though the NDP may lead to, for example, a set of tolls that maximise social welfare, often no consideration is made of the distribution of resulting benefits and costs across the population of travellers. We consider a network under probit stochastic user equilibrium (SUE) with elastic demand, disaggregated into multiple user classes with different values of time and link-specific tolls. We propose the Theil measure for quantifying equity, which can be incorporated either into the objective function or the constraints within the NDP. A sensitivity analysis of the SUE flows provides the basis for computing the Jacobian of the social welfare function and of the Theil measure. This allows gradient-based optimisation algorithms to be used in solving the NDP. Numerical examples are reported.