On the Online Min-Wait Relocation Problem

In a carsharing system, a fleet of cars is distributed at stations in an urban area, customers can take and return cars at any time and station. For operating such a system in a satisfactory way, the stations have to keep a good ratio between the total number of places and cars in each station, in order to refuse as few customer requests as possible. This leads to the problem of relocating cars between stations. We consider the Online Min-Wait Relocation Problem, aiming at satisfying all customer requests with a minimal total waiting time, and show the non-existence of competitive online algorithms against several adversaries. Furthermore, we consider the max/max ratio, and show that this ratio cannot be used to theoretically evaluate online algorithms for the Online Min-Wait Relocation Problem either.