Allocating the proper amount of shelf space to stock keeping units [SKUs] is an increasingly relevant and difficult topic for managers. Shelf space is a scarce resource and it has to be distributed across a larger and larger number of items. It is in particular important because the amount of space allocated to a specific item has a substantial impact on the sales level of that item. This relation between shelf space and sales has been widely documented in the literature. However, besides the amount of space, the exact location of the SKU on the shelf is also an important moderator of sales. At the same time, the effectiveness of marketing instruments of an SKU may also depend on the shelf layout. In practice, retailers recognize that these dependencies exist. However, they often revert to rules of thumb to actually arrange their shelf layout.
We propose a new model to optimize shelf arrangements in which we use a complete set of shelf descriptors. The goal of the paper is twofold. First of all, we aim to gain insight into the dependencies of SKU sales and SKU marketing effectiveness on the shelf layout. Second, we use these insights to improve the shelf layout in a practical setting. The basis of our model is a standard sales equation that explains sales from item-specific marketing-effect parameters and intercepts. In a Hierarchical Bayes fashion, we augment this model with a second equation that relates the effect parameters to shelf and SKU descriptors. We estimate the parameters of the two-level model using Bayesian methodology, in particular Gibbs sampling. Next, we optimize the total profit over the shelf arrangement. Using the posterior draws from our Gibbs sampling algorithm, we can generate the probability distribution of sales and profit in the optimization period for any feasible shelf arrangement. To find the optimal shelf arrangement, we use simulated annealing. This heuristic approach has proven to be able to effectively search an enormous solution space.
Our resu
