We consider the operational scheduling or dispatching problem of assigning servicemen to service requests that arrive in real time. The objective is to optimize responsiveness, i.e., to minimize waiting in excess of a promised response time. We study how responsiveness is influenced by modeling decisions and solution methods that arise when solving the dynamic problem by repeatedly solving real-time problems. Most results are derived using a set-partitioning based solution approach, which is shown to perform best among considered alternatives. Our research is based on a large-scale real-life application regarding roadside service assistance.