Remarks on the optimization method of a manufacturing system with stochastic breakdown and rework process in supply chain management

Chiu et al. (2010) [8] present the proof of convexity of the long-run average cost function E[TCU(t1)] for a manufacturing system with stochastic breakdown and rework process. This note not only demonstrates that E[TCU(t1)] is not convex but also adopts the rigorous methods of mathematics to develop the complete solution procedure to find the optimal solution for removing shortcomings of the above paper mentioned.