At the beginning of a sales season, retailers often face two key questions: which products should be sold, and how much inventory should be stocked for each product? This decision is challenging, especially when customers may choose substitutable products when their preferred items are sold out. For example, if a customer wants to buy a specific blue shirt but finds that it's out of stock, they might opt for a different color or a similar style. This substitution behavior means that retailers have difficulty accurately predicting demand for each product in advance, without knowing the inventory levels. At the same time, inventory levels must be determined based on customer demand, creating a two-way relationship between demand and inventory.

In addition to inventory concerns, selecting the right product assortment is also a challenge. If too few products are available, customers may not find what they are looking for and leave without making a purchase. On the other hand, if too many products are offered, low-margin products might distract customers and reduce the sales of high-margin items.

To address these challenges, we developed a new method using mathematical models to help retailers optimize inventory decisions. Specifically, under a widely used choice model in both practice and research, we demonstrated that our method can generate efficient inventory solutions, even when product variety and demand are both large. This is especially valuable for online retailers who deal with a wide range of products and large volumes of demand.

*The article was contributed by Prof. Jingwei Zhang at School of Data Science