Inventory models with the demand rate dependent on stock and shortage levels

This paper investigates an inventory system in which the demand rate during stockout periods differs from that during the in-stock period by a given amount. The previous analysis conducted in this area formulated the model as a cost-minimization model. This type of formulation will intentionally try to decrease demand, by increasing the stockout period, in order to decrease costs. This paper appropriately considers the model as a profit-maximization model and develops a closed-form solution. The model is then further generalized to incorporate the effect of stock-level-dependent demand rates and considers initial-stock-dependent demand as well as instantaneous-stock-dependent demand rates.