Dilemma of rented warehouse and shelf for inventory systems with displayed stock level dependent demand

Impact of display stock has been extensively discussed in literature in terms of stock dependent demand rate. In some recent papers a three-component inventory level dependent demand (as displayed stock level (DSL)) has been proposed. It has been assumed that demand is independent of instantaneous inventory level if inventory is above a certain level in a shelf. As the demand is independent of instantaneous inventory level, a retailer is always in dilemma whether inventory additional to that level will be kept in the shelf or to rent a new storage. In this paper we focus on this by developing three mathematical models. We show that the problem in choosing rented storage or shelf to keep additional inventory can always be eliminated (a) without the knowledge of optimal stocking points or (b) with the knowledge of any one optimal stocking point. Also, if there is enough opportunity to have an extra storage and a mild limit on inventory holding cost in the shelf is satisfied, then there is no need to display inventory in the shelf above the certain level. The results are illustrated by numerical examples and sensitivity analysis is carried out.