Vehicle substitution in heterogeneous round-trip carsharing systems

Carsharing has become a viable alternative mode of transportation which not only contributes to a better environment and less traffic congestion, but is often also cheaper for its users. It is a challenging task for carsharing system operators to design an efficient system which meets user demand while at the same time limiting operational expenses. This problem becomes even more difficult if the provider offers a fleet of heterogeneous vehicles to users as this introduces the opportunity to substitute vehicle types. Substitution occurs when the requested vehicle type is not available and the user is instead assigned to a different, typically larger, vehicle. This paper investigates the main drivers of vehicle substitution in a round-trip carsharing system and how it affects profit. To account for uncertainty of demand, a two-stage stochastic programming model is proposed in which variables associated with user requests are considered random. A sample average approximation approach is used to find solutions within acceptable computation time. A computational study shows that the proposed method is able to closely approximate the true expected profit. Sensitivity analysis of different problem parameters demonstrates how the number of vehicles in use and the users' spatial flexibility increase the number of substitutions. A detailed analysis of solutions shows how vehicle substitution always positively impacts the expected profit.