Joint Shelf Design and Space Planning Problem With Placement Options

Kurzfassung/Abstract

This article introduces the first joint shelf design and space planning problem that considers two placement options for items—hanging and shelving—on flexible shelves. These types of shelves are used in sectors such as do-it-yourself and toy retail, and for household goods in grocery stores. However, they have received limited attention in the literature, which typically focuses on regular shelves with a single placement option: placing items on shelf panels. The problem requires three interdependent decisions: (1) the placement option for each item (shelving or hanging), (2) the shelf design (number and vertical positioning of shelf panels), and (3) the shelf space planning (assignment of facings as well as the vertical and horizontal positioning of items). We formalize this problem as a mixed-integer linear program (MILP) and develop a greedy multi-start matheuristic to efficiently solve practical instances. Computational experiments demonstrate that our algorithm outperforms both a commercial solver and a benchmark method for two-dimensional shelf space planning in terms of runtime and solution quality. A comprehensive analysis of synthetic instances and a real-world case study provides several managerial insights. First, hanging items enables more flexible use of shelf space, which is especially beneficial when item variety is high. However, when large vertical grabbing gaps must be considered, stacking items on shelf panels may be more advantageous. In turn, there is a risk of wasted space due to height or width mismatches. Second, the number and size of the segments on the shelf significantly influence layout profitability, highlighting the need to jointly optimize shelf design and space allocation. Third, it is common practice to arrange hanging items in horizontal rows, which can be facilitated by segmenting the shelf space. While this improves visual appeal, increasing the number of segments tends to reduce overall space utilization and profitability. Finally, a real-world case study involving 237 products across six categories from a European grocery retailer confirms the practical applicability of our approach. It demonstrates significant potential for improving space utilization and layout efficiency.