A linearization approach in solving a non-linear shelf space allocation problem with vertical categorisation of sales potential levels

Abstract

Retail is a profit-driven, highly competitive industry. Customers expect retailers to provide appropriate assortment sets and excellent product visibility. The aim of this study was to develop and examine two models for optimising category-level shelf space management that maximise a retailer’s profit. The authors developed two shelf space allocation problem models. The first model combines three sets of constraints: shelf, product, and product group constraints, while the second model enlarges the first with the multi-shelves constraints. The study showed that this approach gives an optimal solution in a very short time (approximately 3 seconds on average and less than a second in 93 of the 134 instances for the first, and in 84 of the 146 instances in the second problem) for large-scale instances, which in most of the test cases is even less than a second. First, non-linear formulations of both problems were presented. Next, the authors proposed to use and adjust linearization techniques which allow transforming both problems into linear ones, thus obtaining the optimal solutions. Finally, both problems were solved using the CPLEX solver, the computational results were provided.