An optimal production scheduling problem for an assembly process with buffers at the input and output sides of a machine is dealt with. The problem has two kinds of constraints. One constraint is that the buffers' capacity is limited. The other constraint is that the cycle time of the worker is constant without waiting time. An optimal production ordering is determined, subject to these constraints, in such a way that the rate of use of parts to produce each product should be as constant as possible. A procedure to apply the genetic algorithm to this problem is shown. The operations of reproduction, crossover and mutation are presented. It is observed from numerical results that the genetic algorithm gives a better suboptimal solution than the greedy method.