We study an inventory placement optimization problem where demand is sensitive to service response time, under the online retailing setting. The main challenge is to achieve the optimal trade‐off between revenue benefits from shorter delivery time and the increase in inventory cost associated with placing inventory closer to market demand. To predict the effects of modified demand under service response time variations, we introduce a demand prediction and elasticity model to quantify the sensitivity in demand for particular product categories. Of course, shortening response time by positioning products close to market demand may increase inventory costs. Hence, the team developed a novel data‐driven two‐stage stochastic programming approach complementing the demand prediction and elasticity model, which optimally trades safety stock with service response time and hence revenue increase. We then illustrate the impact of our approach through data provided by an e‐commerce retailer in North America. Our approach offers supply chain managers a general‐purpose decision support tool that optimizes the inventory network to generate recommended stocking levels for stores, distribution centers, and warehouses on a daily basis.