Continuous Equilibrium Network Design Model under Demand and Capacity Uncertainty

Transport network planning and construction face many uncertain factors. In order to reduce investment risk this study proposes a robust continuous equilibrium network design model under demand and capacity uncertainty. Transport demand and link capacity are taken as random variables with know probability distributions. The link generalized cost function considering degradable capacity is set up first. Then a bi-level programming model is formulated to determine the capacity improvement. In the lower level program we propose a stochastic user equilibrium model under each demand realization. Instead of finding the optimal solutions for a given future demand scenario, the goal of the road manger in the upper level program is to minimize the weighted sum of expected value and variance of the system all over the demand realizations. A numerical example on small network is presented to illustrate the benefit of this model. Result shows that the importance of accounting for uncertain demand and degradable capacity in continuous network design problem simultaneously.