Network pricing optimization in multi-user and multimodal context with elastic demand

Network Pricing Optimization (NPO) is formulated first as a Network Design Problem where the design variables are tolls, the objective function is the Social Surplus and the equilibrium constraint is any current multi-user multimodal stochastic traffic assignment model with elastic demand up to trip generation and asymmetric arc cost function Jacobian. NPO is then formulated also as an Efficient Allocation Problem, where an optimal flow pattern, the System Optimum, is sought and tolls are consistently determined. Necessary and sufficient conditions for the solutions to both problems are stated, showing the validity of the marginal pricing principle in the context considered.