Remarks on the optimization process of a manufacturing system with stochastic breakdown and rework

This paper reexamines the optimization process of a manufacturing system with stochastic breakdown and rework proposed by Chiu S.W. Chiu, An optimization problem of manufacturing systems with stochastic machine breakdown and rework process, Applied Stochastic Models in Business and Industry 24 (2008) 203–219]. The proof of convexity of the long-run average cost function for the aforementioned manufacturing system is provided in this note. It can be used to replace the conditional convexity given in Theorem 1 of Chiu (2008) 1]. Therefore, when determining the optimal solution for such a real-life system, computational efforts in verifying the conditional convexity can now be omitted, due to the improved quality of the optimization process.