Public transport (PT) fare policy remains subject to innovations, not least evident in the Mobility as a Service discussion. Mode integration and related fare strategies can be used to increase the attractiveness of PT by compensating for potential delays. This study proposes “premium fares” as a novel pricing tool that can evaluate and improve the travel time reliability on a multimodal transportation network. The premium fare is higher than the standard fare but allows passengers to use an alternative service free of charge if waiting for the delayed public transport service is anticipated to be longer than a certain qualification threshold. Properties that guarantee monotonicity of the premium fare with respect to distance traveled are developed. The operator aims to find the premium fare price and qualification threshold that can maximize its profit, based on the probability distributions of delay and passengers’ value of time (VOT). We model this optimization problem for a railway line given a limited capacity of alternative mode services, e.g., the number of taxis. A two-stage approach using nonlinear and dynamic programming is developed to obtain the optimal decision variables and associated capacity allocation plan. Our results show that the introduction of the premium fare can benefit both operators and travelers with increased profits and improved travel time reliability. The interplay between fares and the qualification threshold is illustrated using various delay and VOT distributions. To attract enough customers the premium fare has to be set below a specific level dependent on the VOT distribution. Meanwhile, the operator adjusts the qualification threshold to control the cost paid to the alternative service provider.
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