Bus Rapid Transit (BRT) systems can provide a fast and reliable service to passengers at lower costs compared to tram, metro and train systems. Therefore, they can be of great value to attract more passengers to use public transport, which is vital in reaching the Paris Agreement Targets. However, the main advantage of BRT systems, namely their flexible implementation, also leads to the risk that the system is only implemented partially to save costs. This paper focuses therefore on the Edge Investment Problem: Which edges (segments) of a bus line should be upgraded to full-level BRT? Motivated by the construction of a new BRT line around Copenhagen, we consider a setting in which multiple parties are responsible for different segments of the line. Each party has a limited budget and can adjust its investments according to the benefits provided to its passengers. We suggest two ways to determine the number of newly attracted passengers, prove that the corresponding problems are NP-hard and identify special cases that can be solved in polynomial time. In addition, problem relaxations are presented that yield dual bounds. Moreover, we perform an extensive numerical comparison in which we evaluate the extent to which these two ways of modeling demand impact the computational performance and the choice of edges to be upgraded.

When determining the paths of the passengers in public transport, the travel time is usually the main criterion. However, also the ticket price a passenger has to pay is a relevant factor for choosing the path. The ticket price is also relevant for simulating the minimum income a public transport company can expect. However, finding the correct price depends on the fare system used (e.g., distance tariff, zone tariff with different particularities, application of a short-distance tariff, etc.) and may be rather complicated even if the path is already fixed. An algorithm which finds a cheapest path in a very general case has been provided in [R. Euler and R. Borndörfer, 2019], but its running time is exponential. In this paper, we model and analyze different fare systems, identify important properties they may have and provide polynomial algorithms for computing a cheapest path.