Assortment planning for multiple chain stores

In retail, assortment planning refers to selecting a subset of products to offer that maximizes profit. Assortments can be planned for a single store or a retailer with multiple chain stores where demand varies between stores. In this paper, we assume that a retailer with a multitude of stores wants to specify her offered assortment. To suit all local preferences, regionalization and store-level assortment optimization are widely used in practice and lead to competitive advantages. When selecting regionalized assortments, a trade-off between expensive, customized assortments in every store and inexpensive, identical assortments in all stores that neglect demand variation is preferable. We formulate a stylized model for the regionalized assortment planning problem (APP) with capacity constraints and given demand. In our approach, a common assortment that is supplemented by regionalized products is selected. While products in the common assortment are offered in all stores, products in the local assortments are customized and vary from store to store. The model is both applicable for optimizing a total assortment as well as a particular category of an assortment. Concerning the computational complexity, we show that the APP is strongly NP-hard. We formulate the APP as an integer program and provide algorithms and methods for obtaining approximate solutions and solving large-scale instances. Moreover, we extend our model to include substitution effects. Lastly, we perform computational experiments to analyze the benefits of regionalized assortment planning depending on the variation in customer demands between stores.