A practical approach to the shelf-space allocation and replenishment problem with heterogeneously sized shelves

This paper addresses the shelf-space and replenishment problem where a retailer must decide how much shelf space to assign to items and how frequently to replenish retail shelves. Since space is limited, these two decisions are interdependent. Existing optimization models approximate shelf sizes by reducing the shelf to a one-dimensional space. However, in practice shelf sizes and their shelf segments vary in width, height and depth. Without considering the actual shelf dimensions, results from optimization models cannot be transferred to actual shelves. To account for these constraints, we propose the first shelf-space model capable of modeling three-dimensional shelf characteristics. Our model determines optimal shelf quantities, an item’s optimal shelf segment, as well as optimal replenishment frequencies. To do this we include a space-elastic function that impacts the customer demand for an item depending on its allocated shelf space. We also consider different shelf segments in different positions.