Multi-period transportation network design under demand uncertainty

The ability to make optimal transportation network investments decision is central to the strategic management of transportation systems. The presence of uncertainty in transportation systems presents new challenges in making optimal network investment decisions. In this paper, we develop a multi time period network design problem considering both demand uncertainty and demand elasticity. Such an approach affords the planner the flexibility to delay, change, or even abandon the future network investment. We measure the flexibility of investing over multiple time periods as compared to a single-stage network design decision. Initially, we provide a taxonomy and define many dimensions of transportation network flexibility. This is followed with the development of a flexible network design formulation (FNDP), in which the investment is staged over multiple time periods. The demand is assumed to be separable and the demand elasticity is captured using a negative exponential distribution. We develop the FNDP formulation as bilevel stochastic mathematical programming with complementarity constraints (STOCH-MPEC) in which the bi-level formulation is converted to a single level using non-linear complementarity constraints conditions for user equilibrium (UE) problem. The formulation is implemented on two test networks and the results show the benefits of FNDP over single-stage NDP—measured in terms of increase in present expected system consumer surplus (PESCS)—are in the range of 10–30%. The results clearly demonstrate that under demand uncertainty there are potential benefits of introducing flexibility in investment decisions. Finally, we conduct a sensitivity analysis of FNDP with different budget values and it is observed that certain paradoxical sharp corners are observed at certain budget values.