On the exploration of convexity about the expected total cost per unit time of replenishment run time problem with machine breakdown and failure in rework

Abstract Recently, Chiu et al. [Expert Systems with Applications 39 (2012) 1291-1297] study the optimal replenishment run time for a production system with stochastic machine breakdown and failure in rework. Basically, their model is rather interesting. However, their solution procedure based on Theorem 1 of Chiu et al. (2012) has shortcomings from the fundamentals of mathematics. The main purpose of this paper not only indicates its shortcomings but also presents the correct solution procedure for Chiu et al. (2012).