Mathematical Approach for Ameliorated Inventory Models

Hwang developed inventory models with amelioration items and applied the graphical method to locate the optimal solution. In this study, we derive an analytical method to find two local maximum points and one local minimum point. Our maximum profit is greatly superior to that of Hwang, because his maximum profit is about 0.246% of ours. The local maximum point near the starting point (denoted as 3×10−7) is almost impossible to discoverby the numerical method, illustrating the effectiveness of our analytical method.