Inventory management for depreciating items with stochastic demand

We develop an inventory management model for depreciating items whose depreciation process is assumed to be of a linear or exponential trend with white noise volatility, while the demand is also considered to be stochastic. The model is formulated under the assumption that replenishments only occur at discrete time points over a fixed planning horizon. Through this model, we obtain the optimal replenishment policy, including the time schedule and the quantity per order. Finally, when the decline of the purchasing cost is considered, we derive an extension to the model.