Production Systems with Backordering, Rework and Machine Failure Taking Place in Stock Piling Time

This paper studies the optimal inventory replenishment policy for an economic production quantity (EN) model with backordering, rework and machine breakdown taking place in stock piling time. A prior paper [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 examined the lot-sizing problem on an imperfect quality EPQ model. Due to another reliability factor - random machine breakdown seems to be inevitable in most real world manufacturing environments, and to deal with it the production planners must practically compute the mean time between failures (MTBF) and establish a robust production plan accordingly in terms of the optimal replenishment lot size that minimizes total production-inventory costs for such an unreliable system. This study extends Chiu's work and incorporates a machine breakdown taking place in the stock piling stage into his model. The effects of random machine failure on optimal run time and on the long-run average costs are examined in this paper. Mathematical modeling and cost analysis are employed. The renewal reward theorem is utilized to cope with variable cycle length. Convexity of the long-run average cost function is proved and an optimal lot-size that minimizes the expected overall costs for such an imperfect system is derived. Numerical example is given to demonstrate its practical usage. Managers in the field can adopt this run time decision to establish their own robust production plan accordingly.