In the management of a robotic workcell composed of a group of machine tools incorporatign a robot controlled by a supervisory computer for in-process material handling, the efficient system utilization is very important, since a fixed large initial investment is involved. In the course of dealing with the problem, the robot operations scheduling appears to be essential in terms of the system utilization improvement. In this thesis, we consider an operations scheduling problem for the robot in a two-machine flow-shop robotic workcell system. The problem is investigated in the next three procedures. Firstly, we analyze the property of an optimum operations schedule for the robot in the measure of the minimum makespan so as to achieve the early completion of all the jobs assigned at the robotic workcell. Secondly, we transform the problem into a traveling salesman problem so that known solution techniques can be easily employed. Finally, we discuss that under a special condition, the problem can be transformed into a problem requiring only O($n^2$) simple steps to get an optimal solution.