Optimal retail shelf space allocation with dynamic programming using bounds

TLDR: It is found from experimental studies that NDP using bound was much more efficient to solve large problems as compared to original dynamic programming (ODP) without using bound.

Abstract: Efficient shelf space allocation increases profitability of a retail store and thus provides competitive advantage to the retailer. Several shelf space allocation models exist in literature. However, these models are generally solved using heuristic approaches due to NP-hard nature and there is a need to develop exact methods. In this paper, we present a non-linear shelf-space allocation model (NLSSAM) and optimally solve it with a new dynamic programming (NDP) using bounds which fathoms unpromising states. It is found from experimental studies that NDP using bound was much more efficient to solve large problems as compared to original dynamic programming (ODP) without using bound. ODP could not solve all problem instances of problem sizes (number of products, n = 30 and 40) within specified CPU time limit of 400 seconds while NDP could solved problem instances of size (n = 200) with average CPU time of 7.89 seconds.