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Demand for different modes of transportation clearly interacts. If public transit is delayed or out of service, customers might use mobility on demand (MoD), including taxi and carsharing for their trip, or discard the trip altogether, including a first and last mile that might otherwise be covered by MoD. For operators of taxi and carsharing services, as well as dispatching agencies, understanding increasing demand, and changing demand patterns due to outages and delays is important, as a more precise demand prediction allows for them to more profitably operate. For public authorities, it is paramount to understand this interaction when regulating transportation services. We investigate the interaction between public transit delays and demand for carsharing and taxi, as measured by the fraction of demand variance that can be explained by delays and the changing OD-patterns. A descriptive analysis of the public transit data set yields that delays and MoD demand both highly depend on the weekday and time of day, as well as the location within the city, and that delays in the city and in consecutive time intervals are correlated. Thus, demand variations must by corrected for these external influences. We find that demand for taxi and carsharing increases if the delay of public transit increases and this effect is stronger for taxi. Delays can explain at least 4.1% (carsharing) and 18.8% (taxi) of the demand variance, which is a good result when considering that other influencing factors, such as time of day or weather exert stronger influences. Further, planned public transit outages significantly change OD-patterns of taxi and carsharing.

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Competition between one-way car-sharing operators is currently increasing. Fleet relocation as a means to compensate demand imbalances constitutes a major cost factor in a business with low profit margins. Existing decision support models have so far ignored the aspect of a competitor when the fleet is rebalanced for better availability. We present mixed-integer linear programming formulations for a pickup and delivery orienteering problem under different business models with multiple (competing) operators. Structural solution properties, including existence of equilibria and bounds on losses as a result of competition, of the competitive pickup and delivery problem under the restrictions of unit-demand stations, homogeneous payoffs, and indifferent customers based on results for congestion games are derived. Two algorithms to find a Nash equilibrium for real-life instances are proposed. One can find equilibria in the most general case; the other can only be applied if the game can be represented as a congestion game, that is, under the restrictions of homogeneous payoffs, unit-demand stations, and indifferent customers. In a numerical study, we compare different business models for car-sharing operations, including a merger between operators and outsourcing relocation operations to a common service provider (coopetition). Gross profit improvements achieved by explicitly incorporating competitor decisions are substantial, and the presence of competition decreases gross profits for all operators (compared with a merger). Using a Munich, Germany, case study, we quantify the gross profit gains resulting from considering competition as approximately 35% (over assuming absence of competition) and 12% (over assuming that the competitor is omnipresence) and the losses because of the presence of competition to be approximately 10%.

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