Optimizing Two-Storage Inventory Management for Log-Gamma Decaying Goods with Quadratic Demand: A Genetic Algorithm Approach

This paper presents a sophisticated model for the optimal management of inventories comprising deteriorating items stored in two distinct warehouses. The model encompasses a nuanced treatment of shortages, utilizing a genetic algorithm to implement partial backlogging, where demand is contingent upon both selling price and time. In instances where the ordered quantity exceeds the primary warehouse's capacity, any surplus stock is strategically allocated to a rented warehouse. To minimize storage costs, the genetic algorithm prioritizes the release of items from the rented warehouse. Consequently, the stock in the rented warehouse gradually depletes to zero over intervals due to demand and deterioration, while items in the owned warehouse decrease solely due to deterioration. After a predetermined timeframe, the inventory level in the owned warehouse reaches zero, initiating shortages. The model assumes that both the rate of backlogging and demand follow generalized exponential decreasing functions with respect to selling price (p) and time (t). Numerical examples are employed to illustrate the application of the genetic algorithm-based model, showcasing its efficacy under diverse scenarios. Additionally, sensitivity analysis is conducted to scrutinize the model's behavior under various parameter variations.