Car-Sharing: Online Scheduling k Cars Between Two Locations

Songhua Li, Leqian Zheng, Victor C. S. Lee

Abstract: This paper studies a special setting of the online order-dispatching problem in the car-sharing system (CSS). Once an order is released online by a user at its booking time, it specifies the departure time and two locations (in which one is the departure location while the other is the destination). The CSS operator needs to determine whether to accept or reject an online order at its booking time. Once accepting an order, the operator should assign a car among k cars to serve the order right at its departure time, gaining a constant revenue paid by the user. However, a movement without taking an order (i.e., empty movement) incurs a constant cost for the operator. The goal is to schedule the k cars to serve a set of online released orders that maximizes the overall profits (i.e., the overall revenue minus the overall cost generated by accepted orders). With regard to the cost of empty movement and the time gap between an order’s booking time and departure time, we consider different settings. We show the lower bounds on the competitive ratio for different settings respectively, and propose two online algorithms GD and BD, with their competitive ratios matching and approaching the lower bounds in corresponding settings respectively.