Online Dial-A-Ride Problem with Unequal-Length Time-Windows

In the online dial-a-ride problem (ODARP) with time windows, objects are to be transported between points in a metric space. Transportation requests are released over time, specifying the objects to be transported and the corresponding source and destination. One serve travels in the metric space at constant unit speed, picking up the objects at their sources and drops them at their destinations. Each request also specifies a deadline. If a request is not be served by its deadline, it will be called off. The goal is to plan the motion of server in an online way so that the maximum number of requests is met by their deadlines. Usually it is assumed that the time windows are equal length. That is, each request has the same length of maximum waiting time. We study the problem in a more general case in which the lengths of maximum time that requests can wait are different. We perform competitive analysis of two online strategies for the problem in two special metric spaces, the uniform metric space and the K-constrained metric space, respectively. The competitive ratios of the strategies are obtained.