On the Structural Analysis of Inventory-dependent Demand Problems

We will consider a set of problems that address the interface between marketing and operations. Research on retail inventory management has traditionally been based on the assumption that underlying demand does not vary with inventory levels. A growing body of marketing research supports the contention that the validity of this assumption has substantial implications for optimal inventory policies. Indeed, such research provides solid empirical evidence to show that a store's sales depend on the amount of stock displayed on its shelves.In the proposed study, we will investigate how inventory should be managed when inventory affects sales. We will assume inventory levels are monitored and determined periodically. In the basic setting, our concern is with inventory management when demand is uncertain, but is influenced by the displayed stock quantity. Our goal is to answer the open problem of a general demand function by which demand varies with the stocking quantity and a general cost structure. To gain insights into this problem and obtain structural results, we first assume that replenishment orders are delivered instantly after ordering. We then relax this restriction by allowing non-zero delivery leadtimes. We also consider the pricing effect, in addition to the inventory effect, on demand. Building upon the prior experience gained in related inventory-pricing control problems, we aim to establish structural results for general problems.Reports indicate that a lack of attention to the inventory effects on demand is one of the main reasons that store managers often overwrite the automated order advices generated by standard software packages developed by enterprise resource planning (ERP) vendors. The outcome of this research will be a set of inventory models and solution techniques that will serve as useful decision support in the field of supply chain management in general and inventory management in particular.