In the retail industry both breadth and depth of an assortment are critical strategic decisions to satisfy the heterogeneous consumer needs in the long run and to foster store loyalty. While the breath of an assortment specifies the number of different product categories (or product lines) in a store, the assortment depth defines the different SKUs (versions) of a product within a specific product category. Typical examples for different versions of a product within a product category are parallel offerings of, for example, national brands and private labels, or conventional and organic products. In both examples, the two product versions are very similar as they only differ in a few product features, which implies that when one version is out of stock or otherwise not available, some consumers may buy the other version instead.
Determining optimal inventory levels of multiple products within a product category considering stockout-based substitution is still a huge challenge not only in practice but also academic research has shown that this problem is not easy to tackle, not even for a simple two-product problem. In this paper, we develop an approach to solve the multi-product assortment and inventory planning problem with stockout-based substitution, specifically for vertically differentiated products. Demand and substitution rates are derived from a utility-based choice model. Compared to previous research, our approach considers substitution rates endogenously, derived from consumer choice model. Additionally, we consider multiple substitution attempts in case of stockout of a product where previous research was mainly focusing on a single substitution attempt. We show the benefits of an integrated assortment and inventory planning compared to a sequential approach where first the assortment is optimized and subsequently, optimal inventory levels are determined.