Production Systems with Rework and Machine Failure Taking Place in Backorder Filling Time

This paper investigates the optimal refilling policy for an economic production quantity (EPQ) model with rework and breakdown taking place in backorder replenishing time. A recent published article [Chiu, Y.P., 2003. Determining the optimal lot size for the finite production model with random defective rate, the rework process, and backlogging. Engineering Optimization 35, 427-437] has studied the lot-sizing problem on an imperfect quality EPQ model. However, another reliability factor random machine breakdown is inevitable in most real-life production systems. To deal with stochastic machine failures, production planners must practically calculate the mean time between failures (MTBF) and establish the robust plan accordingly, in terms of the optimal production run time that minimizes total production-inventory costs for such an unreliable system. This study extends Chiu’s work and assumes that a machine failure takes place in the backorder replenishing stage. Mathematical modeling and cost analysis are employed. The renewal reward theorem is used to cope with variable cycle length. Convexity of the long-run average cost function is proved and an optimal manufacturing lot-size that minimizes the expected overall costs for such an imperfect system is derived. Numerical example is provided to demonstrate its practical usages. Key-Words: Optimization, Lot size, Breakdown, Backorder, Production run time, Rework, Inventory