in fact, if the total
annual cost function of the inventory model is convex, it is easier to find the optimal solution by using the convexity property.
Therefore, it is worth to study the convexity of the total annual cost function of the inventory model to locate the optimal
solution. Consequently, the exploration of the convexity of the total annual cost function is still one of the main research
topics of the inventory models. In fact, the algebraic approach discussed in [13] cannot be used to explore the convexities of
Model (I) and (II). However, Lemmas 1 and 2 in this paper give the explorations of the convexities o