Optimal Markdown Pricing and Inventory Allocation for Retail Chains with Inventory Dependent Demand

We analyze how inventory dependence of demand affects the optimal pricing and distribution of inventory across multiple retail locations. Our problem formulation corresponds to the typical markdown management decisions in a retail chain. The solution methodology determines the optimal combinations of three important operational levers—pricing, inventory allocation, and store consolidation. Inventory dependence causes the optimal price trajectory to decrease over time as the current on-hand inventory decreases. The optimal inventory allocation shifts more inventory to the larger stores as the inventory effect becomes stronger. Solution methodologies are also developed for the case of optimal constant prices, which leads to the same optimal inventory allocations. If all stores have the same seasonal variations and the inventory is allocated optimally, then all stores have identical price trajectories. Optimal consolidation of the inventory to a subset of the stores is also determined. Consolidation of inventory to a subset of stores can be beneficial even when there are no fixed costs of stocking a store. Using some typical parameter values for retail items, our calculations show that significant benefits can result from taking the inventory effect into account in pricing, inventory allocation, and store consolidation decisions. The online appendix is available at https://doi.org/10.1287/msom.2016.0609 .