Retail inventory policy under demand uncertainty and inventory-level-dependent demand

The purpose of this paper is to determine the inventory replenishment policies when demand rate is a function of the inventory space allocated to the products on retail shelves. Existing results on inventory policies with inventory-level-dependent demand (ILDD) assume deterministic functional forms of the demand rate. In this paper, the authors model the inventory decisions when demand is a function of shelf-space allocation and random uncertainty. The authors provide managerial insights of this paper's results.

The demand rate is assumed to be a function of shelf-space allocation based on two settings in the literature. First, the authors model the demand rate as a function of initial shelf-space allocation. In the next setting, the authors assume that the demand rate is a function of instantaneous inventory level on shelves. In both the settings, the authors also model random demand uncertainty in addition to the shelf-space dependency of demand rate. The objective is to maximize the expected profit and determine the inventory parameters.

In addition to the demand uncertainty, the authors consider linear, power and exponential functional forms of demand rate. Inventory policy that maximizes expected profit is determined when demand rate is a function of initial allocation and displayed inventory level. The results are implementable for practitioners for optimizing the shelf-space allocation and related inventory policy.

Most of the extant results on inventory policy with shelf-space-dependent demand do not model the demand uncertainty. The authors model a variety of functional forms of demand rate with ILDD in addition to the demand uncertainty. The results are a building block for more applications in inventory management for real-life applications.