Inventory models with inventory-level-dependent demand: A comprehensive review and unifying theory

Marketing researchers and practitioners have long recognized the demand of many retail items is proportional to the amount of inventory displayed. Recently, two distinct types of inventory control models reflecting this relationship have appeared in the literature, models in which the demand rate of an item is a function of the initial inventory level and those in which it is dependent on the instantaneous inventory level. We present a comprehensive overview of this literature and demonstrate the equivalence of the two types of models through the use of a simple, periodic-review model. An alternative approach to sensitivity analysis for inventory models with inventory-level-dependent demand is also presented.