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.