Economic lot sizing for an imperfect production system subject to random breakdowns

This article considers an economic manufacturing quantity model for an imperfect production process that is subject to random machine breakdowns. The product is manufactured intermittently in batches to meet a constant demand. During a production run, the system is assumed to deteriorate over time. As a result, a fixed proportion of items produced are defective. The system is also subject to random breakdowns. A no-resumption inventory control policy is adopted. Under this policy, the production run is aborted when a breakdown occurs. Production will be resumed only when all on-hand inventories are depleted. Corrective maintenance is carried out immediately after a breakdown. The time-to-shift and the time-to-breakdown are two random variables following different exponential distributions. The objective is to find an optimal production lot size that minimizes the expected (long-run) total cost per unit time. Several models are investigated and a numerical approach is developed to obtain an optimal production lot size.