The Taylor series approximations neglecting the third and higher order terms in the expansion of
are frequently used by many researchers to get closed‐form solutions to simplify the solution procedure to locate the optimal solution. However, they may cause significant penalty costs sometimes. Under some assumptions, Huang and Liao (2008) show that the total relevant cost per year is convex. With the convexity, they develop the solution procedures to locate the optimal cycle times to avoid the shortcoming of the significant penalty cost that the Taylor series approximations may cause. The main purpose of this paper not only removes those assumptions about the convexities of the total relevant costs per year described in Huang and Liao (2008) but also presents some simplified solution procedures free of using the convexity to improve Huang and Liao (2008)
