Inventory model with inventory-level dependent demand rate, variable holding cost and shortages

Inventory models in which the demand rate depends on the inventory level are based on the common real-life observation that greater product availability tends to stimulate more sales. Previous models incorporating stock-level dependent demand rate assume that the holding cost is constant for the entire inventory cycle. In this model we will discuss an inventory-level dependent demand rate, variable holding cost and shortages. The holding cost per unit of the item per unit time is assumed to be linear function of the quantity in storage. Procedures are developed for determining the optimal order quantity and the optimal cycle time.