An Improved Mathematical Approach for Ameliorated Inventory Models

This paper solves the open problem mentioned by Lin that was published in 2026 of Algorithms to prove the uniqueness property for the solution procedure proposed by Lin. The developed mathematical verification fulfills the research gap left by Lin. Moreover, for the local maximum point near the starting point (denoted as 3×10−7) of the amelioration inventory model, this study presents an alternative explanation to help researchers execute their numerical methods with confidence such that, without the analytical procedure developed by Lin, only a rough numerical method can help researchers locate two local maximum points.