Mathematical modeling for solving manufacturing run time problem with defective rate and random machine breakdown

This paper employs mathematical modeling for solving manufacturing run time problem with random defective rate and stochastic machine breakdown. In real life manufacturing systems, generation of nonconforming items and unexpected breakdown of production equipment are inevitable. For the purpose of addressing these practical issues, this paper studies a system that may produce defective items randomly and it is also subject to a random equipment failure. A no resumption inventory control policy is adopted when breakdown occurs. Under such a policy, the interrupted lot is aborted and malfunction machine is immediately under repair. A new lot will be started only when all on-hand inventory are depleted. Modeling and numerical analyses are used to establish the solution procedure for such a problem. As a result, the optimal manufacturing run time that minimizes the long-run average production–inventory cost is derived. A numerical example is provided to show how the solution procedure works as well as the usages of research results.