Mathematical Modeling of Sustainable Inventory for Deteriorating Items with Two-Warehouse Considering Non-Linear Holding Costs Using Analytical Optimization Method

Effective and sustainable inventory modeling is essential for organizations, with the shelf life of goods being a key consideration. Goods are subject to deterioration over time due to factors such as damage, waste, decay, and drying, which reduce their value. Holding costs, another critical aspect of sustainable inventory management, are influenced by a range of variables. Typically, holding costs are time-dependent, with a linear time-dependent model assuming a constant rate of change in carrying costs over time. However, such a model rarely reflects real-world market systems. Conversely, an exponentially time-dependent holding cost is also impractical, as it suggests an unrealistic rate of change. A more realistic approach is the parabolic time-dependent holding cost model, which provides a more feasible solution. In this study, we develop a two-warehouse model for inventory management. One warehouse has finite capacity and is owned, while the other has unlimited capacity and is rented. The model assumes a constant deterioration rate for both warehouses, with demand following a linear time-dependent function. Shortages are allowed, with full backordering assumed to enhance realism. The primary objective is to maximize total average profit. To illustrate the model's applicability, a numerical example is provided, along with a sensitivity analysis to evaluate the impact of key system parameters. Graphical representations of the results are generated using MATLAB software (version 2021b).