In this paper, we formulate the material transportation problem as a multi-agent pickup and delivery with time synchronization (MAPD-TS) problem, which is an extension of the well-known multi-agent pickup and delivery (MAPD) problem. In MAPD-TS, we consider the synchronization of the movement of transportation agents with that of external agents, such as trucks arriving and departing from time to time in a warehouse and elevators that transfer materials to and from different floors in a construction site. We then propose methods via which agents autonomously select the tasks for improving overall efficiency by reducing unnecessary waiting times. MAPD is an abstract formation of material transportation tasks, and a number of methods have been proposed only for efficiency and collision-free movement in closed systems. However, as warehouses and construction sites are not isolated closed systems, transportation agents must sometimes synchronize with external agents to achieve real efficiency, and our MAPD-TS is the abstract form of this situation. In our proposed methods for MAPD-TS, agents approximately estimate their arrival time at the carry-in/out port connected with external agents and autonomously select the task to perform next for improved synchronization. Thereafter, we evaluate the performance of our methods by comparing them with the baseline algorithms. We demonstrate that our proposed algorithms reduce the waiting times of both agents and external agents and thus could improve overall efficiency.