This paper deals with the sequencing problem in the operation of the manufacturing systems with the constraint of buffer capacity. Some of studies for this theme have been progressed for several years. And then most of them consiedred only one objective, such as maximum lateness, machine utilization, makespan, mean flowtime and so on. This study deal with two objectives of the delivery for customers and the idle time of machines for producers. For the decision of sequence, the utility function is used. The developed heuristic algorithm presents a good solution. Through a numerical example, the procedures of the job sequencing is explained.