A fractionally owned autonomous vehicle fleet sizing problem with time slot demand substitution effects

We study an autonomous transport service for population where users buy future time slots in which they are guaranteed service. A bilevel fleet sizing-vehicle routing-time slot pricing model, sensitive to users’ activity scheduling decisions in the lower level is developed. Upper level model is solved using Bender's decomposition and the results are sent to lower level finding an equilibrium using the values of willingness to pay by population under different pricing mechanisms. The values of willingness to pay and the reservation of vehicles among users depends on the fleet size and routing/scheduling results obtained from the upper level model, where spatial temporal distribution of the demand for ride by users impacts the solution to fleet sizing problem. Numerical models are used to explain the methods, to test scalability of the proposed solution algorithms, and to illustrate the potential application of the proposed formulation in simultaneous assessment and modeling of population behavior and optimum fleet sizing model.