An integrated assortment and shelf-space optimization model with demand substitution and space-elasticity effects

Retailers must define their assortments and assign shelf space to the items included in these assortments. These two planning problems are mutually dependent if space is scarce. We formulate a model that maximizes a retailer's profit by selecting the optimal assortment and assigning limited shelf space to items. This model is the first decision model to integrate assortment and shelf-space planning by considering stochastic and space-elastic demand, out-of-assortment and out-of-stock substitution effects. To solve the model, we develop a specialized heuristic that efficiently yields near-optimal results, even for large-scale problems. We show that our approach outperforms alternative approaches, e.g. a sequential planning approach that first picks assortments and then assigns shelf space by up to 18%, and a greedy algorithm by up to 16% in terms of profit. We test our model on two real data sets for perishable and non-perishable items and show how it can support retailers in increasing their profits by up to 25%. We then use the model to generalize these results and find that space elasticity and substitution effects have a significant impact on profits, assortment size as well as facing decisions, and that both effects reinforce each other. Using our model, we finally derive rules-of-thumb for planners in practice.