Printed circuit board (PCB) assembly is popular in today's electronic manufacturing industry while component placement is critical in PCB assembly since it determines the efficiency and productivity of a PCB assembly line. This paper first discusses a cycle time determination problem in a PCB assembly line. Then the problem is formulated into a pure integer programming model with the objective of minimizing the cycle time of the PCB assembly line. Furthermore, the mathematical model is solved by the branch-and-bound (B&B) algorithm in order to get the optimal solution. Finally, a numerical example is presented to illustrate the mathematical model and the B&B algorithm.