An Empirical Analysis of Intra-Firm Product Substitutability in Fashion Retailing

This study offers an empirical investigation of inventory and sales dynamics in a large-scale retail network setting. We infer the impact of product shortages on sales in neighboring outlets using unique data from a large fast fashion retailing chain. Since the product shortages do not occur at the same time, we conduct a novel Difference-in-Differences (DiD) methodology to align the stock-out periods across the stores in the network. In addition, we stratify data based on the periods in which stock-out is observed and apply pairwise DiD analyses to validate the robustness of our results. Our analysis reveals that sales for a particular item at a focal store increases when that same item experiences stock-outs in neighboring stores, especially so for neighboring stores that are physically closer to the focal store. These findings suggest that there is substitutability across stores, and that this substitutability is the strongest in the period when the stock-out is observed for the first time, and decreases in the time since the stock-out and dissipates with physical distance. In order to assess the value of considering the impact of stock-outs on inventory allocation, we develop an optimization model and calibrate it by using parameters estimated via DiD analysis. The simulation analysis confirms that revenues markedly improve on average by 2.2% when neighboring stock-out information is taken into account for sales forecasting when optimizing inventory allocations. Finally, we conduct sensitivity analysis to evaluate how this effect changes with problem parameters such as product price, and inventory.