Optimal replenishment policy for manufacturing systems with failure in rework, backlogging and random breakdown

This article studies the optimal replenishment policy for an economic manufacturing quantity (EMQ) model with failure in rework, backlogging and random breakdown. A recent article [P.A. Hayek and M.K. Salameh, Prod. Plann. Control 2001;12:584--590] investigated the optimal lot size problem on an imperfect quality EMQ model. However, in most real-life manufacturing systems random breakdown is another inevitable reliability factor. To cope with the stochastic machine failures, the production planners need to calculate the mean time between failures and establish a robust plan accordingly, so that the overall production-inventory costs for such an unreliable system can be minimized. This study incorporates random machine breakdown and failure in rework factors into the imperfect EMQ model examined by the aforementioned paper. Mathematical modelling and cost analysis are employed and the renewal reward theorem is used to deal with variable cycle length. Convexity of the long-run average cost function is proved and optimal replenishment policy for such an imperfect EMQ model is derived. Numerical example demonstrates its practical usages.