Multi-period Network Design Problem Under Demand Uncertainties

Transport infrastructure investment is essential to the strategic decision-making of urban planning and economic development. Most of the transport network project has three similar characteristics:high-cost, partial or complete irreversibility, and various uncertainties in the phase of planning. Currently, the majority of the study on trans-portation investment decisions is based on on a single point estimate of the future state. This decision does not take into account the uncertainty about the future, therefore, there is no possibility to take any modification to improve the system performance if the fu-ture state does not meet the expectation. Then the society will suffer huge economic loss. Therefore, the transportation network design problem under demand uncertainties is considered in this study.The stochastic demand brings about uncertainties in all parameters of the trans-portation network. When the network is under uncertainties, the standard UE condition will not be suitable since the link costs are also stochastic. Further, when deterministic link travel flows satisfy the UE conditions, while the expected link travel cost does not necessarily satisfy the UE conditions. Particularly, in the case of elastic demand, the stochastic travel cost will, in turn, affect the OD travel demand, therefore, influence the whole transportation network. In this case, the standard definition of UE condition is invalid. However, the UE condition under uncertainty of the elastic demand case is pro-posed in recent literature. Unfortunately, the explicit algorithm has not been proposed for that there is no explicit function reflecting the relationship between stochastic OD demand and travel cost. In this paper, we propose an algorithm for solving the UE con-ditions of the case of elastic and stochastic demand, based on some modification of the classic MSA algorithm. The numerical performance is tested on a classic network.Based on this, the multi-stage network design problem under uncertainty is con-sidered, mainly considering the road pricing design issues. Two kinds of uncertainties are involved:short term and long term stochasticities of the OD travel demand, that is, the day-to-day fluctuation of OD travel demand within each period and the growing parameter across periods. In order to characterize the stochastic growing parameter, the stochastic scenario-tree modeling method is proposed, which is one extension of conventional scenario-tree method. Further, it is taken into account the reliability be-tween periods, reflecting the impact of land use to some extent, which is more realistic. Based on the above analysis, we formulate the multi-stage network design problem under uncertainty as a bi-level stochastic mathematical programming with equilibrium constraints. The existence theorem of solution and solution algorithm framework based on genetic method is proposed. Finally, the numerical experiment of a classic network is given.