A replenishment policy for items with a price-dependent demand and a varying rate of deterioration

Substantial literature has been written over the years on the subject of deteriorating inventory, but little attention has been directed to the price-dependent demand of items that have a varying rate of deterioration. In this study an optimal replenishment policy is formulated for items with a linear price function of demand. A variable proportion of the items will deteriorate per time-unit while they are in storage and shortages of items are completely backordered. It is shown that the presented model is a generalization of the current models in the literature. An algorithm is developed to maximize net profit.