How big should my store be? On the interplay between shelf-space, demand learning and assortment decisions

A fundamental decision every merchant has to make is on is how large his stores should be. This is particularly true in light of the drastic changes retail concepts have seen in the last decade. There has been a noticeable tendency, particularly for food and convenience retailers, to open more and smaller stores. Also, there has been a well-documented recent shift in paradigm in apparel retailing with the so called fast-fashion business model. Short lead times have resulted in flexibility that allows retailers to adjust the assortment of products offered on sale at their stores quickly enough to adapt to popular fashion trends. Based on revised estimates of the merchandise's popularity, they then weed out unpopular items and re-stock demonstrably popular ones on a week-by-week basis. However, despite the obvious similarity of reliance on better demand learning, fashion-fashion retailers like Zara have opted to do exactly the opposite as groceries and opened sizable stores in premium locations. This paradox has not been explained in the literature so far. In this paper, we aim to calculate the profit of a retailer in such a complicated environment with demand learning and frequent assortment decisions in particular in dependence of the most valuable resource of a retailer: shelf-space. To be able to achieve this, we extend the recent approaches in the management literature to handle the sequential resource allocation problems that arises in this context with a concurrent need for learning. We investigate the use of multi-armed bandits to model the assortment decisions under demand learning, whereby this aspect is captured by a Bayesian Gamma-Poisson model. Our model enables us to characterize the marginal value of shelf-space and to calculate the optimal store size under learning and assortment decisions. An extensive numerical study confirms that the store size choices observed in real life can be explained by the varying length of selling seasons different retailers face.