Societally optimal expansion of bicycle networks

In this paper, we consider the problem of expanding bicycle networks over time. The expansion of the network at a given point in time is based on the societal cost-benefit performance, which entails system-wide effects from previous expansions. The problem is challenging due to non-linearities of travel time benefits and the dimension of the problem, which is a consequence of the combinatorial complexity of the networks and the planning horizon. It rules out the use of conventional bottom-up cost-benefit analysis as evaluating even a small set of possible solutions becomes computationally infeasible. To circumvent this problem, we introduce a novel reverse geographical mapping approach where the monetary benefits are assigned back onto the network. This allows a more detailed geographical planning breakdown at the level of network links and makes it possible to apply a more stringent optimization approach with respect to the timing and prioritization of network expansions. Based on a linear approximation of travel time savings, we propose several variants of mathematical integer programs to solve the problem. This allows us to consider the case of growing a cycle superhighway network in the Copenhagen region over a time horizon of 50 years. We show that our approximations of travel time savings are largely similar to those obtained through actual traffic assignment. Furthermore, the optimization approach renders a development plan, which yields a net present value that is ten times larger than that of the actual infrastructure upgrades implemented since 2019. In a long-term scenario, it is shown that our solution returns an accumulated benefit-cost ratio of 2.7 over the period, which is a significant improvement over previous findings. This underlines the importance of optimal prioritization schemes of where and when to invest in bicycle network expansions.

Automated summary

This paper addresses the problem of expanding bicycle networks over time. The expansion is based on societal cost-benefit performance, considering the system-wide effects from previous expansions. Due to non-linear travel time benefits and the complexity of networks and planning, conventional cost-benefit analysis is not feasible. To overcome this, a reverse geographical mapping approach is introduced, enabling a more detailed geographical planning breakdown and a stringent optimization approach. Mathematical integer programs are proposed to solve the problem. The results show significant improvements in net present value and benefit-cost ratio compared to previous findings, underscoring the importance of optimal prioritization in bicycle network expansions.