Standard cell design style has been widely applied for the design automation of VLSI circuits because of the easy implementation of the layout design. Since the aim of most of standard cell design systems is to minimize the utilization of chip area, the number of feedthrough cells in a standard cell layout will be further minimized to reduce the layout size. In this paper, first, we model a row assignment problem to minimize the number of feedthrough cells in a standard cell placement. Furthermore, an integer linear programming (ILP) optimal approach is proposed to minimize the number of feedthrough cells for the row assignment in a standard cell placement. Finally, two standard cell benchmarks, Primary1 and Primary2, have been tested on the proposed ILP approach for the assignment of different number of rows, and the experimental results show that the ILP approach is efficient for the assignment of cell rows.