Determining production run time with random defective rate and stochastic breakdown

This study derives the optimal run time for a production system with random defective rate and Poisson breakdown. In a real-life manufacturing system, generation of defective items and machine failures are inevitable. With the purpose of addressing these practical issues, this study examines a production system that has random defective items produced, and it also is subject to an equipment failure that may take place randomly. An abort/ resume inventory control policy is adopted when breakdown occurs. Under such a policy, the malfunction machine is under repair immediately and the interrupted lot will be resumed right after restoration of the machine. Mathematical modeling and analyses, along with a recursive searching algorithm are used and proposed in this paper for deriving the optimal replenishment run time that minimizes the long-run average cost for such a practical production system. An example is provided to demonstrate how the proposed solution procedure works as well as its application.