System-optimal stochastic transportation network design

In transportation engineering, the network design problem (NDP) aims at finding an optimal link improvement in a network for given demand. Although traffic demand is essentially uncertain, many previous studies assumed it to be deterministic. The demand stochasticity is incorporated and formulas are developed for system-optimal (SO) flow stochastic NDP. The SO assumption is justified by comparing results from SO deterministic NDP with those of user-equilibrium NDP. The difference in social cost between the two approaches is found to be less than 5%. Two two-stage stochastic programs with recourse formulations are proposed: one with penalty function and the other without. The main advantage of the first formulation is that a planner can exert better control on improvement by appropriately weighing reduction in the congestion versus improvement costs. The challenge, however, lies in selecting an appropriate penalty function. A nonlinear penalty function is found suitable for the test network studied. The second formulation does not require penalty function but results in a large number of scenarios. Nonanticipativity constraints are introduced in the second formulation to arrive at uniform improvement over all scenarios. Both formulations are solved on a test network. It is found that necessary improvements and the total costs with both models are more than those for average demand.