Time-dependent transport network design under cost-recovery

Transport infrastructure projects typically take place over a long time span. They will take a few years to plan and construct, and will last decades into the future. Moreover, revenue collection (from tolls) and investments in infrastructure improvement accrue over time. It is, therefore, crucial to determine the optimal project initiation time, phasing, scaling, toll collection strategies, and financial arrangements over the planning horizon. This paper considers the time dimension in the continuous network design problem and focuses on analyzing the aspect of cost-recovery. We develop a flexible framework under two principles of cost-recovery as a single-level optimization program, solve it through the generalized reduced gradient algorithm, and illustrate through numerical examples three considerations: namely, (i) time-dependent demands and gradual network improvements, (ii) comparison between the two cost-recovery principles, and (iii) spatial equity issues from the perspective of consumer surplus. Moreover, this study proves that Mohring and Harwitz's self-financing result for a single facility in a static framework can be extended to the time-dependent network design problem under the same set of assumptions.