The process scheduling, is one of the most important tasks of the operating system. One of the most common scheduling algorithms used by the most operating systems is the round robin method in which, the ready processes waiting in ready queue, seize the processor for a short period of time known as the quantum (or time slice) circularly. In this paper, a non-linear programming mathematical model is developed to determine the optimum value of the time quantum, in order to minimize the average waiting time of the processes.