Inventory model for damageable items with stock-dependent demand and shortages

Items made of glass, ceramics, etc. get damaged during the storage due to accumulated stress of stocked items. Inventory models of these items are developed here with finite rate of replenishment and inventory level-dependent demand. Both linear and non-linear damage and demand functions are considered, shortages are allowed and fully backlogged. Optimum order quantities are determined using the profit maximization principle in integral form. The models are illustrated with numerical examples and a sensitivity analysis is presented.