Shelf space management when demand depends on the inventory level

Two factors that their influence on the demand has been investigated in many papers are (i) the shelf space allocated to a product and to its complement or supplement products and (ii) the instantaneous inventory level seen by customers. Here we analyze the joint shelf space allocation and inventory decisions for multiple items with demand that depends on both factors. The traditional approach to solve inventory models with a state-dependent demand rate uses a time domain approach. However, this approach often does not lead to closed-form expressions for the profit rate with both dependencies. We analyze the problem in the inventory domain via level crossing theory. This approach leads to closed-form expressions for a large set of demand rate functions exhibiting both dependencies. These closed-form expressions substantially simplify the search for optimal solutions; thus we use them to solve the joint inventory control and shelf space allocation problem. We consider examples with two products to investigate the significance of capturing both demand dependencies. We show that in some settings it is important to capture both dependencies. We consider two heuristics, each one of them ignores one of the two dependencies. Using these heuristics it seems that ignoring the dependency on the shelf space might be less harmful than ignoring the dependency on the inventory level, which, based on computational results, can lead to profit losses of more than 6%. We demonstrate that retailers should use their operational control, e.g., reorder point, to promote higher demand products.