A hybrid finite production rate system featuring random breakdown and rework

To reduce the order response time or achieve optimal utilization, manufacturers often include an outsourcing alternative in their production plans. Further, undesirable machine breakdowns and nonconforming items produced during the in-house processes must also be effectively managed/corrected to adhere to the fabrication schedules and meet the desired quality level. This study addresses the aforementioned concerns by examining a hybrid finite production rate (FPR) system featuring: breakdown that follows the Poisson distribution, and rework/repair of all the nonconforming goods produced. A portion of the batch size is outsourced to an external supplier, who guarantees quality but at a higher unit cost than that incurred in-house. A mathematical model is explicitly built to represent the features of the proposed hybrid FPR system. We use the optimization approach and an algorithm to determine the optimal replenishing runtime that minimizes total costs; results are demonstrated through a numerical example and sensitivity analyses. Diverse crucial system information available to assist manufacturers in production planning includes the individual and joint influence of rework, outsourcing, and breakdown on: (a) variable rework cost; (b) the optimal runtime; (c) total system cost; (d) utilization; (e) detail of system's cost elements; and (f) other important system parameters.