The area coverage of machines on the production line to address the scheduling and routing problem of autonomous guided vehicles (AGV) is an innovative way to improve productivity in manufacturing enterprises. This paper proposed a new model for the optimal area coverage of machines in the production line by applying a single AGV to minimize both the transfer costs and the number of breakpoints of AGV. One of the unique advantages of the area coverage employed in the present study is that it minimizes transfer costs and breakpoints, and makes it possible to provide service for several machines simultaneously since the underlying assumption was finding a path to ensure that every point in a given workspace is covered at least once. Since rail AGV is used in this study, AGV can only pass horizontal and vertical distances in the production line. The reversal of the AGV path in vertical and horizontal distances implies failure and breakpoint in the present paper. The simulation results confirm the feasibility of the proposed method.