Replenishment run time problem with machine breakdown and failure in rework

This paper studies the optimal replenishment run time for a production system with stochastic machine breakdown and failure in rework. In most real world manufacturing processes, generation of defective items and random breakdown of equipment are inevitable. This research addresses such reliability issues by examining a production system with a Poisson breakdown rate and an imperfect reworking process. When machine breaks down, no-resumption policy is adopted. Under such a policy, the present production run is aborted and will be restarted only when all on-hand inventories are depleted. Mathematical modeling is used. Derivations of production- inventory cost functions and proofs of theorems and proposition are presented, with the objective of determination of the optimal replenishment run time and lot size that minimize the expected costs per unit time. An illustrating example is provided to show its practical usage.