Welfare optimal bicycle network expansions with induced demand

In this paper, we determine a welfare-optimal investment strategy for bicycle networks while considering the joint impact of travel time savings and induced demand throughout the investment horizon. The paper extends an expansion strategy with fixed demand recently published in Paulsen and Rich (2023). Accommodating induced demand requires that we can express how expansions of the network affect demand through changes in travel time, and also how demand contributes to the net present value function due to accumulated health and travel time savings. It is shown how the net present value function can be approximated through approximations of demand and consumer surplus functions enabling optimisation on a large scale. This process is formulated as a sequence of binary mathematical programs spanning the entire period. We test the approach by applying it to a large-scale network of Cycle Superhighways for Greater Copenhagen. It is demonstrated that the optimised infrastructure investment plan renders benefit–cost ratios exceeding 10 and that accounting for demand effects in the optimisation increases the societal net present value by more than 15% while also changing the geographical structure of the invested network. The paper emphasises the significance of approaching infrastructure investment strategies from a dynamic perspective instead of relying on static evaluations, which is the predominant practice in practical planning.