Analytical Approach for Optimal Inventory Policies with Salvage Value and Partial Backlogging: Convexity Insights and Sensitivity Observations

Abstract- The paper shows optimization of an inventory model with the considered assumptions that the demand rate is quadratic time-dependent and the deterioration rate is exponential. Further we have included the assumptions of the salvage value and partial backlogging Taking ideas by the limitations of prior research where constant or linear demand models are taken, the given inventory model considers scenarios in which the customer demand changes non linearly (quadratically) and the item deterioration has an exponential rate pattern, commonly observed in the industries that deal with the decaying or technology driven items or products A total expense function is formulated and an optimal replenishment time interval is calculated to minimize overall inventory expenses. The convexity of the inventory expense function is analytically checked with the help of to make sure that the unique optimal solution of this optimized inventory model exists Also a sensitivity analysis is performed using to check the influence or impact of key inventory parameters on the optimal solutions, providing important results for decision-making. Further, the effects of the salvage value on the optimization are shown to reflect practical applicability in the modern inventory systems Numerical examples supported by graphical analysis and explanation, shows the significant applicability and efficiency of this given inventory model along with the dynamic market conditions