Finite production rate model with backlogging, service level constraint, rework, and random breakdown

Sa？etak In most real-life production systems, both random machine breakdown and the production of nonconforming items are inevitable, and adopting a backlogging policy with a predetermined minimum acceptable service level can sometimes be an effective strategy to help the management reduce operating cost or smoothen the production schedule. With the aim of addressing the aforementioned practical situations in production, this study explores the optimal production runtime for the finite production rate (FPR) model with allowable backlogging and service level constraint, rework of defective products, and random machine breakdown. Mathematical modelling is employed along with optimization techniques to derive the optimal production runtime that minimizes the long-run average system costs for the proposed FPR model. The joint effects of the allowable backlogging with a planned service level, rework, and random machine breakdown on optimal runtime decision have been carefully investigated through a numerical example and sensitivity analysis. As a result, important insights regarding various system parameters are revealed in order to enable the management to better understand, plan, and control such a practical production system