This study studies the effects of machine breakdown, backlog and rework on the replenishment lot size. In real-life manufacturing systems, random defective rate and breakdown of equipment are inevitable. When backlogging is permitted during a production run, a random machine failure may take place either in backlog filling stage or in inventory piling time; this study focuses on the former situation and considers all defective items produced are repairable through a rework process. The objective of this study is to determine the optimal run time that minimizes the long-run average production-inventory costs. The result can be directly applied to the practical production planning and control field to assist practitioner in production management cost reduction.