The correct solution procedure on the replenishment run time problem with machine breakdown and failure in rework for supply chain management

Recently, Lin and Chiu [Lin, H. D., & Chiu, Y. S. P. (2012). Note on “Replenishment run time problem with machine breakdown and failure in rework. Expert Systems with Applications, <http://dx.doi.or10.1016/j.eswa.2012.05.001g/>] show that the long-run average production-inventory costs per unit time is a convex function. The main purpose not only reveals that their cost function is not a convex function but also presents the correct solution procedure to locate the optimal solution for Lin and Chiu (2012).