Criterion to ensure uniqueness for minimum solution by algebraic method for inventory model

Chinshin Lau, Enju Chou, Julian Dementia

This paper aims to solve inventory models without depending on calculus. This is an important issue such that many practitioners who are not familiar with calculus, then, can realize inventory models. There are more than one hundred papers that had worked on this research issue, however, most of them have overlooked the positivity of the item in a square root, and then some researchers can claim that they created a simplified solution procedure for algebraic approach. Their derivations are partially corrected under the restriction that the positivity of the sign of the item inside the square root is preserved. However, for other cases, when the positivity of the sign of the item inside the square root is violated, then their results will contain questionable derivations. Ignore the sign of the term inside a square root is a serious matter in algebraic methods such that other practitioners should provide revisions to constitute a well-defined algebraic approach. In this paper, we provided a detailed analysis to construct criterion to guarantee the existence and uniqueness of the optimal solution by algebraic method. Our findings will provide a prior work for researchers to further study inventory models under algebraic method environment.