With the increasing popularity of LBS services, spatial assignment has become an important problem nowadays. Nevertheless most existing works use Euclidean distance as the measurement of spatial proximity. In this paper, we investigate a variant of spatial assignment problem with road networks as the underlying space. Given a set of passengers and a set of vehicles, where each vehicle waits for the arrival of all passengers assigned to it, and then carries them to the same destination, our goal is to find an assignment from passengers to vehicles such that all passengers can arrive at earliest together. Such a passenger assignment problem has various applications in real life. However, finding the optimal assignment efficiently is challenging due to high computational cost in the fastest path search and combinatorial nature of capacity constrained assignment. In this paper, we first propose two exact solutions to find the optimal results, and then an approximate solution to achieve higher efficiency by trading off a little accuracy. Finally, performances of all proposed algorithms are evaluated on a real dataset.